American Political Science Review, Forthcoming

WHAT YOU SEE IS NOT ALWAYS WHAT YOU GET: BARGAINING BEFORE AN AUDIENCE UNDER MULTIPARTY GOVERNMENT

LANNY W. MARTIN ∗

GEORG VANBERG ∗∗

Abstract. Party elites in coalition governments are acutely aware that the deals they strike will be critically evaluated by their supporters, and that they risk losing support if they are perceived as ineffective negotiators. This has a powerful influence on the bargains parties strike. Because most supporters are unaware of the complex aspects of bargains, and instead rely on simple heuristics to evaluate their most visible features, parties have incentives to meet supporter expectations primarily on easily observable outcomes. To do so, they make tradeoffs on less observable outcomes. This implies that the more visible features of a bargain typically do not accurately reflect the relative success of parties in coalition negotiations. We evaluate our argument using original data on the office rewards and policy risks of portfolio allocation in 16 parliamentary democracies. Our findings support our argument, and they have important implications for the nature of representation under multiparty government.

American Political Science Review, Forthcoming

* Professor, Department of Social and Political Sciences, Dondena Centre for Research on Social Dynamics and Public Policy, Bocconi University. [email protected].

** Professor, Department of Political Science, Duke University. [email protected].

We wish to thank Christoph Vanberg, as well as seminar participants at Aarhus University, Emory Univer- sity, Humboldt University, King’s College London, the University of Bologna, the University of Essex, the University of Kentucky, the University of Mannheim, the University of Milan, and the University of Zurich for helpful comments on previous versions of this article. 1

Introduction

Coalition government is a ubiquitous feature of politics in most parliamentary democracies.1 One of its central characteristics is that it requires bargaining and compromise among parties with distinct electoral platforms. Coalition partners must agree on a common policy, and must distribute important ministries and other perquisites of oﬃce. What is the nature of these bargains? How successful are parties in securing what they value, and what factors shape their ability to do so? These questions are important not only for academics and political analysts, but also for citizens as they make voting decisions, gauge the performance of their elected representatives, and evaluate the quality of governance.

We offer an answer to these questions by proposing a theory of coalition bargaining that focuses on two features of negotiations that have, to date, not been explicitly addressed. The first is that party elites worry about how the bargain they agree to will be perceived by their supporters. Making this aspect of bargaining more explicit matters because there are different types of supporters on which parties rely. Some follow politics closely, and are aware of the details of coalition negotiations. Others

(including the majority of voters) are politically less knowledgeable, and are only aware of the most salient and easily observable aspects of coalition bargains. The second feature we focus on is that parties bargain over a range of “goods,” including policy and oﬃces. Importantly, not all of these goods are equally “visible” to politically less knowledgeable supporters. As we show, the combination of these two features has signiﬁcant implications for the nature of the bargains parties strike.

Specifically, to secure the continued backing of politically less knowledgeable supporters, parties face incentives to negotiate outcomes that reflect supporter expectations on the most salient, easily observable dimensions of the bargain. At the same time, outcomes that reflect those expectations will typically not align with the underlying bargaining positions of the parties. As a result, party elites use side payments of less observable goods to reconcile the overall coalition bargain with relative bargaining power. Parties that are “undercompensated” (relative to their bargaining strength) with respect to the more visible aspects of the bargain will be remunerated by their “overcompensated” partners through concessions on more complex, less visible aspects of the bargain. Thus, a central implication of our

1 For reviews of the coalition literature, see, e.g., Laver and Schofield(1998) and Martin and Vanberg(2015). 2 argument is that the more easily observable features of a bargain typically do not accurately reflect the influence of the various parties on the overall outcome of negotiations. In other words, looks can be deceiving—a conclusion that has far-reaching consequences for the nature of representation under multiparty government.

Empirically, we provide initial support for our argument with a fresh examination of how parties distribute ministerial portfolios. A long-standing tension in coalition research concerns the contrast between a theoretically-grounded expectation about portfolio allocation and a well-known empirical regularity. Descriptively, coalition members tend to receive a share of cabinet ministries that is roughly proportional to the share of legislative seats they contribute to the coalition, a pattern referred to as

“Gamson’s Law” (Gamson 1961; Browne and Franklin 1973; Warwick and Druckman 2006; Falc´o-

Gimeno and Indridason 2013). In contrast, standard bargaining models lead to the expectation that the distribution of spoils during coalition negotiations should reﬂect the bargaining power of the parties, which typically does not correspond to their seat shares. Our argument reconciles this tension.

Speciﬁcally, we contend that coalition parties—anticipating voter expectations—have strong reason to favor a “Gamsonian” allocation of the easily observable numerical distribution of portfolios. They align this allocation with the bargaining power of the parties by making side payments with less visible goods. Our analysis of one less observable feature of portfolio allocation—namely, the “policy risk” inherent in the distribution of cabinet ministries—provides clear support for this expectation and, by implication, for our broader theoretical argument.

Coalition Bargaining and Supporter Evaluations

Multiparty government requires bargaining and compromise. This poses a challenge for parties. On the one hand, they must come to an agreement and cooperate with their partners on a common agenda.

To maintain support, on the other hand, they must convince supporters that they are not overly ac- commodating, and that they represent their interests eﬀectively (Martin and Vanberg 2011; Fortunato

2019). As a result, the types of bargains elites will agree to depend partly on their expectations of how those bargains will be evaluated by their supporters. 3

Existing accounts of coalition politics do not explicitly focus on this feature of bargaining (though the assumption that the preferences of party elites are induced by the underlying concerns of supporters

(see, e.g., Strøm 1990) does suggest an implicit connection). Our argument puts supporter evaluations at center stage. Doing so allows us to explore the implications of an important fact of life in modern democracies: Not all citizens are equally sophisticated or knowledgeable about politics (see, e.g.,

Fortunato, Stevenson and Vonnahme 2016). While some supporters, such as highly involved political activists or interest groups, are suﬃciently motivated and resource-endowed to follow politics closely, this is not true for all of them. In particular, a long tradition of research in political psychology suggests that many voters—a key source of party support—lack deep political knowledge. Rational ignorance and lack of interest mitigate against detailed assessments of complex political information (Downs

1957; Tullock 1967). Instead, many voters employ readily available information and informational shortcuts—“heuristics,” in the language of this literature—to evaluate the performance of policymakers

(see, e.g., Healy and Malhotra 2013; Fortunato and Stevenson 2019).2

Consider the implications for coalition bargaining. These ﬁndings suggest that in evaluating how well their party has represented their interests in coalition negotiations, less sophisticated supporters— including most voters—focus on results they can more easily assess using informational shortcuts.

Empirical work ﬁnds clear support for this idea. For example, Lin et al.(2017) demonstrate that voters employ a “proportionality heuristic”: Voters expect that, in coalition governments, parties will secure shares of cabinet ministries that correspond to their relative size.3 Duch and Stevenson(2013) show that voters rely on a “responsibility attribution heuristic” to draw inferences about policy inﬂuence based on the agenda power of particular cabinet members (such as the prime minister). Similarly,

Bowler, Gschwend and Indridason(N.d.) show that voters rely on party size as well as ideological centrality as heuristics to estimate the policy inﬂuence of coalition parties. These ﬁndings have an important implication: The approval of politically less knowledgeable supporters—primarily voters—is likely to depend on how well a party “measures up” against a yardstick supplied by the informational shortcuts they employ.

2 While heuristics are often “ecologically rational” (Goldstein and Gigerenzer 2012; Fortunato, Stevenson and Von- nahme 2016), they can also lead to systematic bias and mistaken inferences, incentivizing policymakers to focus on outcomes that voters’ heuristics tap into (Healy and Malhotra 2013, 299). 3 They also show that voters assess fairly accurately party seat shares and portfolio distributions. 4

Critically, not all the “goods” over which partners bargain are equally susceptible to informational shortcuts. Some are highly salient, information about them is readily available, and the relative success of parties in obtaining them can be evaluated by voters using simple heuristics. For example, voters can easily perceive whether the share of cabinet portfolios received by a party corresponds to its relative size (Lin et al. 2017). Most voters are also likely aware of whether the most prestigious cabinet ministries (such as the Prime Ministership) are awarded to the largest coalition party. Con- sistent with this expectation, Browne and Franklin(1973) ﬁnd that the largest party is most likely to secure the PM position. Similarly, for parties focusing on a small set of issues, even less sophisticated supporters may be aware of whether the party obtains the relevant ministry (e.g., whether a Green party secures the Environment ministry). Consistent with this expectation, B¨ack, Debus and Dumont

(2011) demonstrate that niche parties are typically successful in securing the ministry most salient for them. In contrast, other aspects of coalition bargains are more complex. For instance, evaluating policy compromises on technically challenging subjects, as well as assessing the relative success of parties in inﬂuencing these agreements, requires considerable time and eﬀort in gathering and processing detailed information. Consequently, bargaining outcomes on such issues are less susceptible to accurate assessments using informational shortcuts, and are therefore less likely to be “picked up” by the evaluations of politically less knowledgeable supporters.4

A simple model. To analyze these implications more formally, we consider a simple model.5 We assume that there are two coalition parties negotiating over the allocation of two types of goods.

The ﬁrst good is “simple” in that information about the relative distribution of the good is easy to obtain and evaluate against a heuristic. The second good is “complex,” indicating that the agreement reached by the parties about the relative distribution of the good is far more diﬃcult for outside actors to observe (in a way we make more precise below). A “coalition bargain” consists of an allocation of a share of the simple and complex goods to party A, with the remainder going to party B. We denote a

4 Bowler, Gschwend and Indridason(N.d.) show that voters rely on party size and ideological centrality as shortcuts to estimate policy influence. Importantly, as they note, their findings do not speak to the connection between voter expectations and the actual policy compromises coalitions reach. The critical point for our argument is that it is more difficult for supporters to evaluate complex policy against their heuristic, i.e., to determine whether the actual coalition bargain corresponds to supporter expectations. 5 We provide the intuition behind the model here; for technical results, see Appendix A in the Supplementary Infor- mation (SI). 5 bargain by Ω = {s, c}, where s ∈ (0, 1) is the share of the simple good going to party A and c ∈ (0, 1) is the share of the complex good going to party A.6

Second, we assume that each party has a target constituency whose support for the party is a function of the party’s ability to secure a favorable bargain Ω. These supporters are divided into two types. Some supporters are sophisticated, and form accurate evaluations of their party’s performance.

These supporters might be politically interested voters or, more likely, organized interests with policy expertise and particularly high stakes in the policy process. Backing for a party (electorally, monetarily, or through organizing eﬀorts) from these supporters increases as the party obtains a “better” deal.

That is, support for a party by sophisticated supporters is given by a “support function” that increases

(at a diminishing rate) as the party secures a greater share of the simple and complex goods.

The second—and more numerous—class of supporters do not evaluate party performance by assessing the overall coalition bargain. These supporters’ evaluations focus on salient information that is easily assessed using informational shortcuts. We incorporate this feature by assuming that unsophisticated supporters are unaware of the distribution of the complex good. Instead, they make evaluations only on the basis of the simple good. Moreover, we assume that the supporters’ heuristic establishes some “yardstick” of what their party ought to secure. They continue to support parties that do so, but support from this group drops signiﬁcantly if parties fail to meet these expectations. Supporters may shift their backing to other parties, or become less likely to turn out (or lend other forms of support). In other words, the behavior of unsophisticated supporters does not respond “smoothly” to what the party accomplishes. Instead, support depends critically on whether the coalition bargain meets—in the terminology used by Kahneman and Tversky(1979)—the reference point established by

7 the supporters’ heuristic for the simple good. We denote this reference point by pi.

6 These goods can be genuinely distributive, but can also refer to policy agreements, with the proviso that parties bargain over where in the Pareto set policy will be located. 7 Informally, this implies that the support function for unsophisticated supporters does not depend on the complex good. For the simple good, it has a steeper slope below the reference point implied by the heuristic than the support function for sophisticated supporters, as well as a more shallow slope above the reference point. Of course, simple and complex goods are merely analytically convenient ends of a spectrum—many of the goods that parties bargain over, whether cabinet portfolios, budgets, or policy agreements, can be more or less complex and diﬃcult to assess. What is critical for our argument is merely that there is a meaningful distinction in the readiness with which unsophisticated supporters can use their heuristics to assess coalition bargains for diﬀerent types of goods. 6

In the context of coalition governance, there are numerous heuristics supporters might rely upon.

For example, they may expect that the largest coalition party should receive the Prime Ministership.

Or supporters of niche parties may expect their party to secure the most salient ministry associated with the party’s core issue (B¨ack, Debus and Dumont 2011). The relative size of coalition partners may also be a natural and easily observed focal point (Schelling 1960) indicating what a party is “entitled to,” especially with respect to goods that can be assessed in relative terms. Of course, other heuristics are possible as well. The key point for our argument is simply that supporters employ “shortcuts” that deﬁne expectations over what a party should secure—and that the likelihood that they will support a party drops sharply if it fails to secure its “fair share.”8

We assume that parties are motivated by a desire to maximize support—which depends on the backing they receive from sophisticated and unsophisticated supporters (and the relative size of these groups). All else equal, support for a party increases as it is able to secure a greater share of simple and complex goods in coalition negotiations. However, given the fact that the vast number of supporters are unsophisticated, backing for a party is especially sensitive to whether the bargain provides a share of the simple good that satisﬁes its supporters’ reference-point expectations. Bargains that fail to do so lead to signiﬁcant losses among the group of less sophisticated supporters, while bargains that provide at least a “fair share” of the simple good retain their support.

We can explore the consequences for coalition bargaining in the familiar Edgeworth Box framework, displayed in Figure1. The x-axis indicates the allocation of the simple good between the two parties.

The y-axis shows the allocation of the complex good. Thus, at the origin, party A receives no allocation of either good, with party B fully controlling both, while party A’s share of the goods increases as we move right and/or up. Along the x-axis, pA marks the “fair share” reference point implied by the informational shortcut of less sophisticated supporters (e.g., if supporters employ a proportionality heuristic, then the parties’ relative sizes establish the reference expectations, and pA corresponds to party A’s seat share). (Since less sophisticated supporters are assumed not to be able to assess the complex good, pA is omitted from the y-axis.)

8 We focus here on heuristics that generate compatible expectations across parties. Relative size—which we focus on below—meets this condition. Exploring the implications of non-compatible heuristics is an obvious avenue for future work. 7

Figure 1. Coalition Bargaining Space 1 −→ A’s share of complex good

0 0 pA 1 A’s share of simple good −→

A’s iso-support curve B’s iso-support curve

Graphically, we can indicate the parties’ payoﬀs from the various allocations of the two goods by

“iso-support curves,” which depict combinations of the two goods that result in the same level of support for the party. These curves are shown by solid lines for party A, and dashed lines for party

B. Because parties are motivated to maximize support, they are indiﬀerent among bundles that lie on the same iso-support curve, and prefer bundles on “higher” iso-support curves to those on lower ones.

Sensibly, this means that Party A prefers allocations towards the northeast of the quadrant while party

B prefers allocations towards the southwest.

Consider the shape of the iso-support curves. Allocations that provide less than a party’s “fair share” of the simple good result in a signiﬁcant loss of support among less sophisticated supporters.

This implies that below the reference point pi, to maintain the same level of support (i.e., to stay on the same iso-support curve), reductions in the simple good need to be compensated by increases in the allocation of the complex good—i.e., the loss of support by less knowledgeable supporters must be balanced by increased support by those who are sophisticated. Given the relative sizes of the two groups, this requires a substantial increase in the allocation of the complex good. The same is not true above the reference point, where the backing of unsophisticated supporters is largely assured, and additional allocations of the simple good primarily aﬀect support only among the sophisticated. Put 8

Figure 2. Coalition Bargaining Space 1 1

u2 −→ −→

u1 x1 x1

bA bA A’s share of complex good A’s share of complex good

0 0 0 1 0 1 pA bA pA bA A’s share of simple good −→ A’s share of simple good −→

A’s iso-support curve A’s iso-support curve B’s iso-support curve B’s iso-support curve

Panel (a) Panel (b) diﬀerently, the parties’ iso-support curves have a “kink” at the reference point, and have a steeper slope below the “fair share” point than above it. For party A, this means that the curve has a steeper slope to the left of pA; for party B, it means that the curve drops oﬀ more sharply to the right of pA.

We are now in position to consider the implications for the nature of the agreed-upon coalition bargain. Without loss of generality, suppose that the relative bargaining strength of party A (under whatever bargaining protocol the parties employ) is given by bA. Given this, based on the parties’ bargaining positions, we would expect party A to secure a share bA of both goods. As indicated in Figure 2, Panel (a), this implies a coalition compromise at x1. Note that at x1, party A’s share of the simple good—based on its bargaining power—exceeds the expectations of its unsophisticated supporters (e.g., the party’s relative size under a proportionality heuristic), while party B’s allocation of the simple good falls below the expectations of its unsophisticated supporters. Put diﬀerently, there is some divergence between the bargaining strength of the parties, and the share of the spoils they are expected to secure under the heuristic employed by unsophisticated supporters.

Critically, the premise that parties are concerned to maximize support, which depends on how supporters perceive the bargain that is struck, implies that the allocation at x1 is inefficient: there are 9 bargains that both parties prefer to x1. Because x1 provides Party B with less of the simple good than its unsophisticated supporters expect (resulting in a significant loss of support), Party B is willing to offer substantial concessions to increase its share of this good. Trading away the complex good results in some losses among the sophisticated group, but these are more than compensated by retaining the support of the (larger) group of unsophisticated supporters. For Party A, such a trade is similarly attractive. As long as it retains a share of the simple good that meets supporter expectations, it can maintain the support of its unsophisticated group while increasing support among its sophisticated group by obtaining a larger share of the complex good. This is highlighted by the fact that moving from x1 towards the northwest will place both parties on higher iso-support curves. As illustrated in

Panel (b), such trades only become impossible when the iso-support curves are just tangent—which occurs at allocations, such as Y , that split the simple good exactly at pA. The bold part of the line at pA between u1 and u2 represents the contract curve of (eﬃcient) bargains that are preferred by both parties to x1.

Note that for all of these bargains, Party A (the party in the strong bargaining position) accepts a bargain that “undercompensates” it—relative to what the party could extract on the basis of its bargaining power—with respect to the simple good. In exchange, the party receives a greater amount of the complex good than it could expect on the basis of its bargaining strength. The reverse is true for Party B (which is in a weaker bargaining position). In short, if parties bargain eﬃciently, they will allocate the simple good in proportion to pA, and use the complex good as a side payment that reconciles the bargain with the parties’ bargaining power.

Implication 1. The distribution of simple goods in a coalition bargain will correspond closely to the distribution implied by the heuristic employed by unsophisticated supporters.

Implication 2. Parties that are undercompensated relative to their bargaining power in terms of simple goods will be overcompensated relative to their bargaining power in terms of complex goods.

In addition, the argument implies that as the degree of undercompensation with respect to the simple good increases for a party, the contract curve over the complex good shifts in that party’s favor.

◦ To see this, note that shifting bA to the right while holding pA ﬁxed causes x1 to slide up the 45 line. 10

This induces the contract curve for eﬃcient bargains (whose lower bound is marked by Party A’s iso- support curve through x1, and whose upper bound is marked by Party B’s iso-support curve through x1) to move up. Of course, in the absence of assumptions regarding a speciﬁc bargaining process, the theory yields no point prediction about precisely where on the contract curve a bargain will be struck. Nevertheless, a reasonable expectation is that for a wide range of bargaining protocols, as a party is more severely undercompensated with respect to simple good, it will secure an increasingly favorable allocation of the complex goods as the contract curve shifts in its favor. This would be true, for example, for any bargaining protocol that implies bargains that are proportional to a constant, e.g., protocols under which party A receives some proportion s ∈ (0, 1) of the surplus and party B receives proportion 1 − s.9

Expectation 1. As the extent of a party’s undercompensation relative to its bargaining power in terms of simple goods increases, the party is compensated with an increasing allocation of complex goods.

The intuition underlying these results is clear: Party elites anticipate that accepting less than the share of easily observable “spoils” that unsophisticated supporters expect them to secure threatens significant losses, as the party is likely to be perceived as an ineffective negotiator. The same is not true of less observable (complex) payoffs, which these supporters are much less likely to be aware of.

Consequently, party elites face incentives to exchange side payments of less observable goods to obtain a share of simple goods that meets supporter expectations. Importantly, this conclusion depends only on the nature of party preferences, and is independent of the speciﬁc bargaining protocol that determines the overall distribution of spoils. In other words, this result derives from the nature of parties’ preferences—induced by a concern for how supporters evaluate a coalition bargain—not the structure of the bargaining situation.

Of course, our simple model presents the logic in stark form—namely, a precise correspondence of simple goods to the distribution implied by the supporter heuristic. Embedding this logic in real- world bargaining will attenuate this precision. Goods may be “lumpy” in ways that prevent precise

9 To see this, denote the initial contract curve by [l1, u1] and the new contract curve by [l2, u2], with l2 > l1 and u2 > u1. Then the initial bargain is given by Y1 = l1 +s(u1 −l1) and the new bargain is given by Y2 = l2 +s(u2 −l2). Then Y2 > Y1 if s(u2 − u1) + (1 − s)(l2 − l1) > 0, which must be true. 11 division. Similarly, getting “close” to the allocation expected by unsophisticated supporters may be suﬃcient. Moreover, many aspects of coalition bargaining are not simple or complex, but fall along a continuum. Finally, supporters are not sophisticated or unsophisticated, but vary in political awareness.

Nevertheless, the underlying logic applies: Party elites have strong incentives to work towards bargains that approximate supporter expectations for goods that supporters can more easily assess, using those aspects that they are less likely to be aware of as side payments. As we discuss in the conclusion, this fact has signiﬁcant implications for the quality of representation—most importantly, for the ability of citizens to hold their parties accountable.

An Application to Portfolio Allocation

There are several possible ways to evaluate our argument empirically. One is to examine our underlying assumptions about supporter behavior: Do supporters (especially voters) employ heuristics that establish “yardsticks” by which party performance is judged, and does the use of such heuristics vary with political sophistication? Does party failure to meet the expectations implied by the heuristics result in a loss of support? Another way is to examine our assumptions about elite behavior: Is there evidence that party leaders involved in coalition negotiations are concerned about how supporters will perceive bargaining outcomes, and do these concerns shape what leaders are willing to agree to? Fi- nally, an empirical evaluation could investigate the implications of these behavioral assumptions for the actual bargains that are struck by party elites: Do these bargains reﬂect the tradeoﬀs across more and less observable goods that are predicted by the argument?

Given the limited scope of the current study, we focus on this last avenue of investigation here, leaving the first two for future work. We recognize, of course, that examining these behavioral implications provides only partial evidence. At the same time, it is important to stress that (as we show below) these implications discriminate between our argument and the most prominent alternative explanations of bargaining in the coalition literature, thus increasing confidence that the results we report offer initial support for the theory.

We focus on a salient aspect of coalition bargaining: the allocation of ministerial portfolios. Coalition research, almost since its inception, has confronted a tension between a well-known empirical regularity 12 and the predictions of most theoretical models of coalition bargaining. The regularity is referred to as “Gamson’s Law”—the robust ﬁnding, conﬁrming the intuition of Gamson(1961), that coalition members tend to receive a share of cabinet ministries that is roughly proportional to the share of legislative seats they contribute to the government (Browne and Franklin 1973; Warwick and Druckman

2006). From a theoretical perspective, Gamson’s Law poses a puzzle because the vast majority of bargaining models do not predict it. Instead, most models lead to the expectation that the distribution of spoils should correspond to the bargaining power of the parties, which often does not coincide with their seat shares (see, e.g., Morelli 1999; Montero and Vidal-Puga 2011).10

Our argument provides an avenue for reconciling this tension. The relative size of parties provides a readily available yardstick that supporters may use to assess their party’s performance for outcomes that are easily measured against it. The numerical distribution of cabinet portfolios is an obvious example. It is salient, widely reported, easily understood, and readily assessed using a “relative party size” heuristic. If less sophisticated supporters make use of this heuristic, and party elites are concerned about their perceptions, one would expect these elites to construct bargains that ensure that the numerical allocation of portfolios follows relative size closely.11

Of course, the Gamsonian regularity is also consistent with an alternative explanation: a simple commitment by party elites to proportionality; i.e., it is possible that party leaders do not worry about supporter perceptions, but simply act in accordance with a fairness norm that focuses on party size rather than bargaining power. Indeed, Verzichelli(2008, 239) argues that such a proportionality norm underlies coalition bargaining since it “means that each coalition party is rewarded in proportion to its contribution to the parliamentary strength of the government, which corresponds to many people’s

10 Bassi(2013) presents a model that predicts proportionality of portfolios to seats, providing a theoretical foundation for Gamson’s Law. However, this result requires a specific bargaining protocol, possibly limiting its applicability to “real world” bargaining, which, as Laver, de Marchi and Mutlu(2011) point out, is relatively unstructured and free-flowing. 11 Most supporters are unlikely to retain detailed information regarding the initial portfolio distribution, and to make active use of such information in later voting decisions. Rather, as the “online tally” model of supporter decision- making suggests (Lodge, Steenbergen and Brau 1995), exposure to such information affects the summary evaluations of a party. Such summary evaluations have been found to be long-lasting, even if the particular information underlying them is quickly forgotten (Lodge, McGraw and Stroh 1989). 13 ideas of fairness.” Another alternative explanation holds that party leaders might simply use proportionality as a focal solution in structuring the coalition bargain irrespective of voter perceptions (Bäck,

Meier and Persson 2009).

The key aspect that distinguishes our argument from these alternatives is that it implies that the distribution of goods is conditional on their observability. If the proportional allocation of spoils is a consequence of an intrinsic commitment to “fair” distribution in accordance with relative size or its focal qualities, then the observability of goods by less sophisticated supporters is irrelevant for their distribution. In contrast, under our argument, it is supporter perceptions that are critical. Easily observable goods are allocated proportionally because those party leaders whose bargaining power is below their seat share—wary of losing the backing of unsophisticated supporters by failing to secure a proportional share of an easily observable good—are trading away less observable goods to parties in a stronger bargaining position. This leads directly to an implication that discriminates between our argument and the alternative accounts. Speciﬁcally, our argument implies that—by accepting a

Gamsonian distribution of portfolios—parties whose bargaining power exceeds their seat share agree to be “undercompensated” (relative to their bargaining power) in terms of the easily observable share of portfolios, but are remunerated by side payments in the form of complex goods. Moreover, these side payments increase the more signiﬁcant the party’s undercompensation. Neither of the alternative accounts leads to this expectation.

There are numerous complex goods that can potentially serve as side payments. Most obviously, parties might demand policy concessions (which, especially for more complex issues, are less likely to be observable for less sophisticated supporters). One attractive and important “complex” good in this context concerns the policy implications that flow from the particular assignment of specific ministries to specific parties. Ministries, headed by a particular cabinet member, play a key role in translating abstract policy agreements into concrete proposals. Legislative initiatives are drafted under the direction of a minister, presented by that minister to the cabinet, and then introduced in parliament. While the precise degree of ministerial influence, and the conditions under which ministers can exercise discretion, continues to be a rich subject of academic debate (Laver and Shepsle 1996;

Martin and Vanberg 2011), there exists a general consensus that ministers can exercise policy inﬂuence 14 unless coalition partners expend resources to monitor and constrain ministerial discretion. This implies that a key consideration for party leaders in evaluating a portfolio allocation is the extent to which it grants power to ministers who pose a potential threat.

The extent of this “policy risk” inherent in a portfolio distribution depends on two features. First, given the issues under the jurisdiction of a given ministry, how significant are the policy differences between a coalition partner and the party controlling the portfolio? If the parties have few policy differences, ministerial discretion poses little danger. Second, how important are the issues under the jurisdiction of the ministry to the party and its constituents? If the issues relevant for a particular ministry are not salient for the party, then ministerial discretion is of less concern, even if there are policy differences between the parties. In short, the “policy risk payoffs” of a portfolio allocation for a coalition party depend on the extent to which it confers influence to partners with significantly different preferences on issues the party cares about.

Assessing policy risk is a challenging task for unsophisticated supporters. Doing so requires an understanding of the jurisdictions and responsibilities of ministries, as well as of the speciﬁc policy goals of the parties, and the extent to which these goals are in conﬂict. In other words, the policy risk aspect of the portfolio allocation is a complex good—and thus provides one way to deliver side payments to parties that are undercompensated with respect to the numerical allocation of portfolios.

Moreover, this side payment may be particularly attractive because it is “paid” directly alongside the Gamsonian distribution of portfolios, reducing concerns about enforcement of the compensation agreement. Thus, the theoretical implications outlined earlier lead to the following hypotheses:

Hypothesis 1. The numerical allocation of cabinet portfolios should be highly proportional to parties’ relative size.

Hypothesis 2. As a party is more severely undercompensated (relative to its bargaining power) in the number of portfolios it receives, it will be compensated with a more favorable policy risk payoﬀ from the portfolio allocation. 15

Analysis and Findings

To test these hypotheses, we examine original data on the allocation of 5,910 ministerial posts in

308 coalition bargaining situations in 16 European democracies. In SI Appendix B, we provide more detail on the set of governments included, and we also list the archival sources used to create the data on ministry assignments. Across the 308 governments, our sample consists of 910 observations on government parties (the units of analysis).

Hypothesis 1 predicts that parties will receive a share of ministries that corresponds closely to their seat contributions to the government. Numerous studies have examined this relationship, typically via a simple linear regression of the portfolio shares of parties on their relative seat shares. We conduct a similar analysis for our sample, with results shown in Table1. 12

Table 1. Eﬀect of Relative Legislative Size on Share of Ministerial Posts

Explanatory Variables Estimates

Seat Contribution 0.790 ∗∗∗ (0.011) Intercept 0.068 ∗∗∗ (0.004)

Displayed are OLS coeﬃcient estimates, with standard errors in parentheses. Depen- dent variable: Numerical share of cabinet ministries. N: 602 coalition parties (after 308 parties, one per bargaining situation, are randomly dropped from the analysis—see footnote 12). R2 = 0.89. Signiﬁcance levels : ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%.

The parameter estimates are close to those produced by previous studies (see, e.g., Warwick and

Druckman 2006, 648). The share of seats a party contributes to the government has a strong positive effect on the share of ministries it receives. Notably, the match is not perfectly proportional. The coefficient on Seat Contribution is statistically below unity and the intercept is statistically above zero, meaning that smaller parties receive more than their “fair share” of portfolios, a finding that is in line with previous results (Browne and Franklin 1973). This tendency can be seen in Figure3, which

12 Because the dependent variable is compositional, the error terms are correlated across parties. Following the approach of Carroll and Cox(2007), we randomly drop one party from each bargaining situation. We also estimate multilevel models on this subsample (shown in SI Appendix C) to account for the possibility that the mean level of proportionality, and the effect of seat share on portfolio share, may differ by bargaining situation. Likelihood ratio tests reveal no significant improvement over the model shown in Table1. 16 plots the fitted prediction from Table1 (with 95% confidence bounds) against a 45 ◦ line. Most small parties lie above the “perfect proportionality” line, while most large parties lie below it. Nonetheless, on average, for every 5% increase in a party’s seat share, its expected share of ministries increases by approximately 4%.

1 Perfect proportionality

Prediction .8 .6 .4 Portfolio Share .2 0 0 .2 .4 .6 .8 1 Seat Share

Figure 3. Eﬀect of Relative Legislative Size on Share of Ministerial Posts

Of course, as noted earlier, such proportionality is also consistent with some models of coalition bargaining (e.g., Bassi 2013), or a general commitment by party elites to proportionality as a “fair” or “focal” bargaining solution. The distinguishing feature of our argument is that the proportional allocation of portfolios is induced by party elites’ concerns for the perceptions of their supporters, leading us to the expectation (captured in Hypothesis 2) that elites will reconcile the proportional allocation of the number of portfolios with the underlying bargaining strength of the parties by using less observable aspects of the bargain as side payments.

As we discussed, there are numerous complex goods that can serve as side payments. We focus on a complex good that derives from the initial allocation of ministries. Since cabinet ministers are 17 responsible for supervising the formulation and implementation of policies in their domains, gaining control of a ministry can give a coalition party a significant advantage in shaping policy outcomes in its purview. By the same token, a party can incur significant costs from handing over control of a ministry to one of its partners, especially if the ministry deals with salient, divisive issues. Again, we refer to these costs as the “policy risk payoffs” of the allocation. To measure them, we must perform two tasks. First, we have to measure the positions of parties on a set of policy dimensions, and assess the importance they place on those dimensions. Second, we must associate the dimensions with specific ministerial posts.

To measure party positions and issue salience, we must ﬁrst deﬁne the nature of the policy space.

This is an inherently subjective task. As Benoit and Laver(2006, 69) point out, “there is no such thing as the ‘true’ underlying dimensionality of any policy space,” which means ultimately that, in terms of both the number and the substance of policy dimensions, “[the] type of space we want to measure depends upon the type of model we want to analyze.” In deﬁning the policy space for our purposes, we attempt to satisfy two criteria. First, we want the number of dimensions to be suﬃciently high as to adequately capture both the major areas in which ministers make decisions and the areas in which their parties compete. Second, in terms of substance, we want our dimensions to correspond roughly to the set of dimensions other researchers have highlighted as important in party competition, and to produce similar patterns of party contestation.

Based on these criteria, we deﬁne a policy space of six conceptually distinct dimensions: economic regulation and state services, traditional morality, environmental protection, internationalism and

European integration, social cohesion and national identity, and conﬂict and military power. Using the MARPOR quasi-sentence coding categories, and the scaling approach developed by Lowe et al.

(2011), we calculate issue saliency scores and policy positions for parties on these dimensions, described in SI Appendix D. We also present there a conﬁrmatory factor analysis to demonstrate that the chosen

MARPOR categories load on the predeﬁned policy dimensions in reasonable ways, and we investigate the face validity of our measures by plotting their averages for party families in postwar Western

Europe. While we do not expect our deﬁnition of the policy space to be the “last word” on the matter, 18 we are encouraged by these results, and believe that future eﬀorts in this area should entail similar construct and face validity checks.

Matching these policy dimensions to specific ministries obviously requires knowledge of ministerial competences. We have assessed these based on information from a variety of sources, including historical descriptions provided by the ministries, formal legislative documents detailing the policy competences of each department, and the types of government bills and directives introduced by ministers. Most of the time, multiple ministers share responsibility within a given policy area; furthermore, any individual minister typically deals with issues in several policy areas. Accordingly, in our coding scheme, ministries that have significant policymaking responsibility in different policy areas are assigned to multiple policy dimensions.13

To test Hypothesis 2, the key concept we need to capture with the dependent variable is the level of policy risk a government party is exposed to as a result of the agreed-upon distribution of ministries.

Is it the case, as we have argued, that a party that “gives away” a number of ministries it “deserves”

(based on its bargaining strength) to achieve numerical proportionality for all coalition parties does so in such a way as to lower its policy risk? That is, does an “undercompensated” party generally avoid ceding ministries to ideologically distant partners on dimensions the party cares a lot about? On the other side of the bargain, is an “overcompensated” party generally willing to tolerate greater policy risk to attain numerical proportionality? That is, in exchange for receiving a greater number of ministries than warranted by its bargaining strength, is such a party inclined to allow its undercompensated partner to control ministries on important dimensions on which the preferences of the two parties signiﬁcantly diverge?

As these questions suggest, and as noted earlier, a party’s policy risk payoﬀ from an allocation depends on two factors: (1) how distant, on the relevant issues, the party is ideologically from the coalition partners that gain control of the ministries, and (2) how important those issues are to the party. As these factors increase, the negative policy consequences experienced by the party (and its supporters) will become more severe, and/or the party has to devote greater resources towards

13 In SI Appendix E, we list the major ministries in our sample of countries, the policy dimensions assigned to them, and the typical issues on these dimensions for which ministers are responsible. 19 constraining its partner’s ministers in an eﬀort to avoid such consequences. We incorporate these factors into our dependent variable, which is constructed in the following steps:

(1) we calculate a dimension-speciﬁc policy risk payoﬀ for a coalition party c as the average

saliency-weighted distance between c and all the ministries (including those controlled by c

itself) that are responsible for that dimension (the ministries Md),

1 X ycd icd − imd , Md m∈Md

where ycd is the relative saliency that party c attaches to dimension d, icd is c’s policy position

14 on the dimension, and imd is the policy position of minister m on the dimension;

(2) we sum the dimension-speciﬁc payoﬀs across the set of (six) policy dimensions D to create a

multidimensional policy risk payoﬀ,

X 1 X ycd icd − imd ; Md d∈D m∈Md (3) ﬁnally, since we are interested in measuring the policy risk for a party given the number of

ministries ceded to other parties (i.e., we are interested in the level of policy risk a party has

accepted given the numerical constraints it has agreed to), we divide by the number of portfolios

controlled by the party’s partners, poc, thus obtaining the average multidimensional policy risk

payoﬀ per partner-controlled ministry:

1 X 1 X ycd icd − imd . poc Md d∈D m∈Md In short, the dependent variable, which we refer to as a party’s Portfolio-Adjusted Policy Risk

Payoﬀ, taps into a feature of portfolio allocation that parties presumably value highly—the distribution of policymaking authority—but whose details most supporters will be largely unaware of because understanding it requires knowledge that goes well beyond knowing how many ministries a party controls. Even knowing which ministries a party receives would be insuﬃcient. To evaluate the policy risks their party faces from a particular allocation, supporters need to know which ministries are responsible for which policy areas, how the ministries not received by their party are distributed

14 As noted in SI Appendix D, we scale the relative saliency score for a party such that a dimension of above-average importance to the party receives a score greater than 1.0, and a dimension of below-average importance receives a score less than 1.0. Each minister is assumed to have the same position as his or her party. 20 among its coalition partners, and the policy preferences of each of these parties in the areas under their control.

As stated in Hypothesis 2, we expect that parties that are, relative to their bargaining power, undercompensated in the numerical share of portfolios receive side payments in the form of a more favorable policy risk payoff. Thus, we require a measure of bargaining power. There are, of course, multiple approaches to assessing bargaining power. One alternative derives from the literature on power indices. These measures focus on the size of parties and assess each party’s “pivotality” across the set of winning coalitions. The downside of this approach is that it pays no attention to the policy preferences of actors, or other factors that potentially strengthen a party’s position in coalition negotiations. This may be sensible in a purely distributive setting, but is problematic in our context since coalition negotiations clearly depend on a host of factors beyond size, including the ideological positions of the potential coalition partners. Therefore, we take a different tack. An important source of leverage for parties in the process of government formation is their ability to join an alternative government to the one they are currently negotiating: Parties that have credible “exit options” from the current negotiations are more likely to be influential. Thus, an alternative approach to assessing bargaining power is to focus on parties’ ability to be part of (alternative) governments.15

There are multiple empirical models of coalition formation that would allow us to estimate the probability that a party can get into an alternative government. We rely on a recent model by Kayser,

Orlowski and Rehmert(N.d.)—hereafter, KOR—that builds on work by Martin and Stevenson(2001,

2010). Like these earlier studies, KOR use a conditional logit model to calculate the probability that a particular government is chosen (out of the set of all potential governments), where the probability in their model is a function of 9 size-related, policy-related, and contextual factors. Some notable advantages of the KOR speciﬁcation (versus the Martin and Stevenson speciﬁcations) are that it is

15 Of course, just as for the power index approach, there are limitations to using a party’s probability of being able to join an alternative coalition as a measure of bargaining power; for example, a party’s pivotality—which is central to power indices—may not be reﬂected in its “exit probability” if the party is a surplus member of many coalitions. Given these limitations, we also conduct our empirical analysis using a prominent power index—the normalized Banzhaf index—as an alternative measure of bargaining power. The results are very similar, as shown in SI Appendix J. 21 more parsimonious, excludes certain variables that are diﬃcult to measure reliably, and has a better predictive performance.16

We construct our measure of bargaining power in the following steps:

(1) using the KOR speciﬁcation, we predict the probability of formation for each potential gov-

ernment in each of our 308 bargaining situations, including the coalition that was actually

chosen;

(2) for each government party in the chosen coalition, we calculate the party’s probability of being

included in an alternative government by summing the formation probabilities of all non-

chosen potential governments in which that party is a member (we refer to this quantity as a

government party’s exit probability);

(3) we normalize each government party’s exit probability by dividing it by the sum of exit prob-

abilities across all government parties.

Thus, our measure of party bargaining power is simply its relative exit probability.17 Using this measure, we create our central covariate, Undercompensation in Portfolio Share, by subtracting the portfolio share received by a party from its bargaining power.

Again, we expect that any party that would receive—on the basis of its bargaining power—a share of portfolios that is less than its perceived “fair share” (i.e., its relative seat contribution) would be willing to trade oﬀ complex goods to its partners to achieve that fair-share allocation. What would such a tradeoﬀ look like in practice? Before we move to a full analysis, it is useful to consider a single episode of coalition bargaining. We focus here on the last Dutch government in our sample: the second cabinet led by Mark Rutte, which lasted from 2012 to 2017, and consisted of two parties, the VVD and the PvdA.

These parties were roughly equal in size. Given 14 ministerial posts in the cabinet, each party’s “fair share” (as implied by the relative size heuristic) was 7 posts. Each party received exactly that number.

However, while the parties were roughly equal in size, they were not equal in bargaining power: Given the composition of the legislature (which tilted towards parties of the right), the probability of VVD

16 In SI Appendix F, we present the results from our conditional logit model of government formation, using an updated version of the Martin and Stevenson(2010) coalition data set. We also describe the model variables in more detail. 17 In SI Appendix G, we illustrate the creation of this measure for a recent German government. 22

Table 2. Portfolio Allocation in Rutte II Government

Second Cabinet of Mark Rutte (2012–2017)

VVD PvdA

Prime Minister Deputy Prime Minister Economic Affairs Finance Security and Justice Foreign Affairs Defense Education and Culture Infrastructure and Environment Social Affairs Health and Welfare Interior and Kingdom Relations Housing and Civil Service Foreign Development Cooperation

Seat Implied Actual Bargaining Implied Share Portfolios Portfolios Power Portfolios

VVD 0.52 7 7 0.64 9 PvdA 0.48 7 7 0.36 5 becoming part of an alternative coalition was almost twice as high as the exit probability for the

PvdA. Thus, the Gamsonian allocation of portfolios left the PvdA, relative to its bargaining power, overcompensated with respect to the number of portfolios, while the VVD was undercompensated. Our argument implies that this numerical “bonus” received by the PvdA came at a price. Namely, since the most important issue for both parties in 2012 was how to improve the economy, a matter over which they were quite divided, we would expect the VVD to have taken most of the ministries with jurisdiction on economic matters, thereby lowering the risk that the PvdA could move policy too far away from the VVD’s preferred position.18

With two parties and 14 ministries, there are 3,432 possible ways to allocate portfolios such that each party receives seven ministries. In Figure4, we display the policy risk payoﬀs for each of these potential allocations for both parties. One important point to note is that the relationship between payoﬀs for the two parties is negative, meaning that switching ministries would typically (though not always) produce a loss for one party and a gain for the other. A more crucial point is that the actual

18 The saliency-weighted divisions between the parties on the economic regulation and state services dimension was almost 8 times their average level on the other dimensions. The two parties disagreed over several important issues, such as how quickly and by how much the budget should be cut, and whether there should be an increase in health care premiums. 23 6 8

→ Actual Bargain better

10 worse ← VVD Policy Risk Payoff 12 14 14 12 10 8 6 ← worse better → PvdA Policy Risk Payoff

Figure 4. Portfolio-Adjusted Policy Risk Payoffs Across Alternative Seat-Proportional Allocations in the Rutte II Government bargain that was struck—in line with the expectations of our theory—was much more favorable for the VVD than for the PvdA. Specifically, the VVD’s policy risk payoff was in the top 20% of its possible payoffs. Meanwhile, the payoff for the PvdA was in the bottom 15% of its possible payoffs: i.e., there were approximately 3,000 alternative ways to distribute the ministries (holding fixed the number of ministries received by each party at seven) that would have been more favorable for the

PvdA. Only three of its ministries dealt directly with economic policymaking (Finance, Education and Culture, and Social Aﬀairs), compared to ﬁve possessed by the VVD (Prime Minister, Economic

Aﬀairs, Infrastructure and Environment, Health and Welfare, and Housing).19

Is this case emblematic of a more general pattern? Before turning to our analysis, we need to consider a potential confounder, namely the ideological extremity of a party in relation to its coalition

19 Unlike the Prime Minister, the Deputy Prime Minister in the Netherlands has no formal policymaking role, and so this post is not assigned to any policy dimension. 24 partners. Naturally, a party that finds itself in a government in which it diverges widely from each of its partners on multiple issues should expect to face a higher baseline level of policy risk. If the party’s position vis-à-visits partners also affects its degree of undercompensation (through its impact on either or both of the covariate’s components, bargaining power or portfolio share), then not taking this factor into account could introduce significant bias into the analysis.

To confront this problem, we include a party-speciﬁc distance variable in our model, which we term

Distance from the Coalition Center of Gravity, and deﬁne as:

X X ycd icd − scicd .

d∈D c∈C The final term represents the coalition’s ideological “center of gravity” on an issue dimension d, defined as the weighted-average position of all parties in coalition C on that dimension, with icd representing the ideal point of each party and the weight sc corresponding to the proportion of seats each party contributes to the total controlled by the coalition. On each dimension, we measure the absolute distance between party c’s policy position and the coalition center of gravity, and then weight that distance by the relative importance of the dimension to the party, ycd. Finally, we sum these dimension- specific distances across our six policy dimensions to create the final party-specific measure.

In Table3, we present results from a multilevel random coefficients model. This type of model has several appealing features. First, it accounts for the fact that our party-level observations are nested (clustered) within bargaining situations. Policy risks may vary across bargaining situations for reasons not accounted for by the party-level covariates, inducing positively correlated errors between government parties. Failing to account for such correlations could yield estimates of the standard errors that are too small.20 Second, the model allows us to deal with possible heterogeneity in the effects of our covariates by providing estimates of both the overall (or average/fixed) intercept and slope coefficients of interest (shown in the top part of the table) as well as the extent to which the intercepts and slope coefficients at the level of the cluster deviate from the average estimates. Using the estimated variance components of the model (shown in the bottom part of the table), we can calculate best linear unbiased predictions of the random deviations and then use those to generate predicted

20 We discuss below the issue of possible negative correlation in risks. 25

Table 3. Eﬀect of Portfolio Undercompensation on Policy Risk

Explanatory Variables Estimates

Undercompensation in Portfolio Share (ups) -5.449 ∗∗∗ (0.717) Distance from Coalition Center of Gravity (dccg) 0.698 ∗∗∗ (0.035) Intercept (α) 4.910 ∗∗∗ (0.255)

σ2(ups) 61.638 (16.415) σ2(dccg) 0.149 (0.025) σ2(α) 14.027 (1.781) σ(ups, dccg) 0.966 (0.463) σ(ups, α) -13.975 (4.124) σ(dccg, α) -1.253 (0.186) σ2(residual) 2.797 (0.258)

Displayed are maximum likelihood coefficient estimates and standard errors from a multilevel random coefficients model (with no constraints imposed on the covariance matrix). Dependent variable: Portfolio-adjusted policy risk payoffs. N: 910 coalition parties (nested in 308 bargaining situations). A likelihood ratio test against a linear model with fixed coefficients leads us to reject the null hypothesis of no difference between the models (p < 0.001). Significance levels for level-one parameters: ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%.

random intercepts and random slope coefficients for individual bargaining situations.21 Finally, the model allows us to assess how much unexplained variation in policy risk payoffs is due to differences between parties within bargaining situations versus differences between bargaining situations.

Based on the results, we can conclude confidently (via a likelihood ratio test) that the multilevel random coefficients specification leads to a significant improvement in fit over a one-level model with

21 We allow parameter estimates to vary across bargaining situations because, in most cases, it is preferable to specify a general model and then “test down” (e.g., via t-tests or model goodness-of-ﬁt tests) to a more restricted version. Similarly, rather than impose the typical multilevel modeling constraint that random eﬀects are independent, we assume an unstructured covariance matrix, letting each variance and covariance component be uniquely estimated. 26

fixed coefficients and a fixed intercept (p < 0.001).22 We can also conclude that most of the unexplained variability in policy risk can be attributed to random (or unmeasured) differences between bargaining situations, rather than differences between parties. Specifically, the level-two variance par- titioning coefficient (VPC) is approximately 0.65, meaning that only 35% of the total residual variance is attributable to unmeasured differences between parties.23 6 30 4 20 2 0 Standardized Residuals 10 Predicted Policy Risk Payoffs 2 − 4 0 − −2 −1 0 1 2 0 10 20 30 Inverse Normal Actual Policy Risk Payoffs

Figure 5. Residuals and Predictive Fit for Policy Risk Model

But how large is this residual variance, i.e., how well does our model ﬁt the data? In Figure5, left panel, we present a quantile-normal plot in which the standardized residuals for our 910 coalition parties are compared against the values one would expect for a standard normal distribution (as represented by the solid 45◦ line). Most residuals stick fairly close to the line, indicating no serious departures from normality, and there are very few outliers (approximately 2% of cases in each tail).

22 Moreover, our model, which estimates the covariances between random effects, significantly improves fit over an alternative specification that constrains the covariances to be zero (p < 0.001). 23 The VPC at a given level of the model is simply the variance at that level divided by the total residual variance. In a multilevel model with random slopes, the level-two variance is a quadratic function of the covariates, so in our case: σ2(α) + (ups2) σ2(ups) + (dccg2) σ2(dccg) + (ups) 2σ(ups, α) + (dccg) 2σ(dccg, α) + (ups)(dccg) 2σ(dccg, ups). We set the two covariates equal to their means for our VPC calculation. 27

In the right panel, we plot our predicted policy risk payoffs against the actual policy risk payoffs for the 910 parties. In this panel, the dotted line is a 45◦ line, and the solid line is the linear fit from a regression of predicted policy risk payoffs on actual policy risk payoffs. Any deviation between the two lines suggests a systematic pattern in actual policy risk that is not being adequately explained by the model. Fortunately, the figure shows only a small difference between the lines: The solid line has an intercept of approximately 1.31 and a slope of 0.84, meaning that the model slightly over-predicts policy risk payoffs for parties with low risk and slightly under-predicts payoffs for parties with high risk. Nonetheless, the model appears to fit the data quite well overall, perhaps surprisingly so, since it includes only two covariates and their associated random effects.24

Of course, the most important results from Table3 concern the estimated eﬀects of these covariates.

Beginning with our control variable, we observe that, as expected, the more distant a government party is from the coalition’s ideological center of gravity, the higher its level of policy risk. That is, as a party becomes relatively more extreme, it is more likely to see the ministries not under its control fall into the hands of ideologically hostile partners.

More importantly, the results provide strong support for our central argument. Coalition parties that are undercompensated in their numerical share of portfolios (relative to their bargaining power) tend to receive signiﬁcantly more favorable policy risk payoﬀs than parties that are overcompensated.

In other words, the set of ministries that are not given to undercompensated parties, but rather to their partners, (a) tend to be those with jurisdiction on policy issues that are relatively less important to the undercompensated parties, and/or (b) tend to be assigned to partners with relatively similar policy positions. This supports our central claim that policy risk payoﬀs appear to be used as “side payments” to parties that are numerically undercompensated.

24 Although multilevel models can effectively solve the problem of residual positive correlation between observations in a cluster, they cannot solve the problem of residual negative correlation. Rather, appropriate level-one covariates must be included in the model in an effort to reduce residual negative correlation to a negligible amount. Regarding our two covariates, their values within clusters also happen to be negatively correlated, and this fact appears to account for much of the negative correlation in policy risk. That is, as we show in Figure5 and with our VPC calculation, the amount of residual variance is quite low overall and is mostly due to unmodeled differences between bargaining situations rather than between parties. Nonetheless, it would be heroic to assume that there is so little remaining residual negative correlation that it can cause no inferential problems. Fortunately, unmodeled negative correlation presents the opposite problem as unmodeled positive correlation—it results in an overestimation of standard errors, and thus an understatement of the parameters’ statistical significance (Norton et al. 1996, 920–24). 28

Of course, a critical question concerns the substantive significance of these side payments. To illustrate this, we calculate the predicted policy risk payoffs for two types of coalition parties in two different bargaining situations. In both situations, the parties are assumed to control approximately half the portfolios in their respective governments. But for one (the undercompensated party), this numerical payoff is considerably less than what is implied by its bargaining power, while for the other

(the overcompensated party), the payoﬀ is considerably more than its bargaining power.25 For each type of party, we predicted its policy risk payoﬀ using the overall intercept and slope estimates from

Table3 (holding distance from the coalition center of gravity at its sample mean), and then generated a distribution of 1,000 simulated predictions (drawn from a normal distribution with a mean equal to the predicted eﬀect and a standard deviation equal to the standard error of that eﬀect).

100 Overcompensated in Portfolio Share

Undercompensated in Portfolio Share 80 60 Median Median Frequency 40 20 0 11 10 9 8 7 6

← worse better → Policy Risk Payoff

Figure 6. Average Eﬀect of Portfolio Undercompensation on Policy Risk

25 To determine the levels of under/overcompensation, we used summary statistics from our sample of bargaining situations. Speciﬁcally, we examined the range of undercompensation for parties that received around half the portfolios in the cabinet (+/- 10%) and then assigned the undercompensated party the 90th percentile score from this subsample (+0.31), and the overcompensated party the 10th percentile score (-0.31). 29

We present the two distributions in Figure6. Clearly, there is a stark difference in expected payoffs between the parties. Specifically, for the party that is less powerful, but nonetheless receives half the portfolios, the figure shows that the median predicted policy risk payoff is over 50% higher (i.e., less favorable) than for the more powerful party. That is, the party that is undercompensated with respect to the raw number of portfolios can expect to translate its greater bargaining power into a significantly more attractive, albeit less directly observable, set of policy benefits.

These findings provide clear support for our argument. But there are two final issues we need to consider. The first concerns the presence of heterogeneity in the effects of the covariates, as captured by the estimated variance components. As noted earlier, we can use these estimates to predict random effects, which tell us how much the estimated intercepts and slopes in individual bargaining situations deviate from the overall (or average) estimates. In SI Appendix H, we present the estimated effect of the undercompensation variable (i.e., the estimated average effect across bargaining situations plus the situation-specific estimated random effect) for each of the 308 governments in the sample.26 We do find variation across bargaining situations in the impact of undercompensation on policy risk. There are a few cases in which the effect is in the opposite direction, and a few in which undercompensation has no significant effect. But in the overwhelming majority (approximately 90% of bargaining situations), the effect is statistically significant (p < 0.05) and in the expected direction. Notably, in approximately

25% of cases, the estimated eﬀect is over 35% larger in magnitude than the average eﬀect shown in

Table3.

The second issue relates to the fact that one component of our undercompensation variable— bargaining power—is itself an estimate produced by another model. As such, it is measured with error, which could lead to biased parameter estimates. Given the predictive success of the KOR model, we do not expect the amount of estimation error to be so great as to alter our conclusions.

However, this is ultimately an empirical question. Accordingly, we have chosen to conduct a sensitivity analysis using 100 alternative datasets based on the coeﬃcient estimates and standard errors from the

KOR model (see SI Appendix I for a more detailed description of our data generation procedure).

Each new dataset contains a new estimate of party bargaining power, and thus a new measure of

26 The estimates from Table3 also indicate heterogeneity in the eﬀect of the policy distance control variable, but we focus in the appendix only on our main variable of interest. 30 3 − 4 − 5 − 6 − Coefficient Estimate for 7 − Undercompensation in Portfolio Share 8 −

0 .4 .8 1.2 Estimation Error in Bargaining Power

Note: The dashed horizontal line is the estimated coefficient for Undercompensation in Portfolio Share from the model shown in Table 3, encompassed by a 95% confidence region. Circles represent the coefficient estimates from 100 simulated data sets (with 95% confidence bounds), arranged in ascending order of estimation error in bargaining power. The solid lines are lowess smoothing curves for simulated estimates greater than and less than the original coefficent estimate.

Figure 7. Impact of Measurement Error

undercompensation. For each dataset, we reestimate our model and compare the results to those from

Table3.

In Figure7, the dashed horizontal line represents the original coefficient estimate from Table3, with the shaded region corresponding to its 95% confidence interval. The 100 dots in the figure are the coefficient estimates for the undercompensation covariate (along with 95% confidence bounds) from the alternative datasets. For easier visualization, we have ordered the estimates according to the amount of measurement error in the datasets (calculated as the sum of squared deviations between the original and new estimates of bargaining power). Also displayed are two lowess smoothing curves, one for estimates above the original coefficient, and one for estimates below. As one might expect, the curves move away from the original coefficient as measurement error increases. However, even for values of measurement 31 error in the tails, the new coefficient estimates fall within the original estimate’s confidence region, and in all cases we can reject the null of no effect with a very high level of confidence.27

Conclusion

The negotiation of a coalition bargain constitutes one of the most consequential political events in multiparty parliamentary democracies. We have highlighted a central feature of such bargaining that has only received implicit treatment by scholars, but that has profound consequences for coalition negotiations: the fact that party elites must consider how the bargains they strike will be perceived by their supporters. The argument rests on two foundational assumptions. First, supporters vary in their political sophistication. Less knowledgeable supporters rely more heavily on simple heuristics to assess their party’s performance. Second, the goods that parties negotiate over vary in the degree to which they can be assessed by less knowledgeable supporters. Some aspects of the bargain are relatively easy to observe, while others are more complex and diﬃcult for less sophisticated supporters to evaluate. The combination of these features generates incentives for party leaders to strike bargains that distribute goods that less knowledgeable supporters are more likely to be aware of—and can assess with respect to some heuristic—in proportion to the expectations generated by their heuristic, and to use those goods that these supporters are less likely to be aware of as side payments to reconcile the overall bargain with the underlying bargaining power of the parties. Our analysis of the allocation of ministries in the process of government formation and the “policy risk” that emanates from this allocation provides clear initial support for the argument.

Our argument and findings have broad implications. Most immediately, it offers a way to reconcile the long-standing tension between the empirical regularity of Gamson’s Law and the theoretical expectation that coalition bargains should reflect party bargaining power. More importantly, the argument has profound implications for political accountability, for the incentives of parties to be responsive to the preferences of citizens, and thus for the quality of representation. The theory and findings suggest that what coalition governments appear to do (as reflected in the easily observable features of their bargains) will typically not be an accurate reflection of the actual influence of the coalition partners.

27 We also conduct an additional analysis, presented in SI Appendix J, in which we substitute a leading alternative index of bargaining power (the normalized Banzhaf index) for our model-derived measure. The results are very similar to what we report in Table3. 32

In return for allowing their weaker partners to “look good” with respect to those pieces of the bargain that supporters can easily evaluate, parties that are in a strong bargaining position are able to extract significant concessions in areas that are less amenable to supporter scrutiny. Put differently, the reality of who shapes coalition government outcomes may diverge from supporter perceptions on the basis of what they can easily observe. This raises obvious hurdles to the effectiveness with which supporters can hold parties accountable. It also implies—with respect to the quality of representation—that those interests represented by parties with strong bargaining positions exercise more influence than may be apparent on the basis of the “observable” aspects of coalition governance.

We close with a brief discussion of avenues for future work. First, there is obvious value in expanding empirical applications beyond portfolio allocations to other, less tangible objects of coalition bargaining

(such as budget allocations or policy compromises). More importantly, future work should move beyond the evidence we have presented here—which focuses on the behavioral implications of our argument for bargaining outcomes—to include an analysis of supporter (especially voter) behavior. Speciﬁcally, building on such work as that of Lin et al.(2017), Duch and Stevenson(2013), and Bowler, Gschwend and Indridason(N.d.), it is critical to investigate the following questions: To what extent do supporters employ heuristics to evaluate party performance under coalition governance? And to what extent does future support for a party depend on meeting supporter expectations induced by these heuristics?

There are also important directions for further theoretical development. One path relates to the

“observability” of goods. We have treated this as an exogenously given quality of the objects of coalition bargaining, and we think this represents a useful approximation. However, observability is also, within limits, subject to manipulation by parties—most obviously through prominent and clear public commitments to particular results that can be reasonably easily “checked” by supporters. The fact that party elites can attempt to shape observability opens up rich strategic possibilities that represent a fruitful area for further research. A second path is suggested by our empirical results. The model fits the data extremely well, but there remains unexplained variation in policy risk. As we have shown, this variation is mostly attributable to differences across bargaining situations, rather than differences between parties. This opens up interesting theoretical possibilities. One is that differences between bargaining situations are related to heterogeneity in voter knowledge about coalition outcomes: 33

If supporters are generally more aware of the policy implications of different portfolio distributions in some contexts, it may be more difficult for parties to use more qualitative aspects of portfolio allocation to achieve numerical proportionality. Institutional features of the bargaining environment may also play an important role. For example, the presence of written coalition agreements may be a significant factor that allows parties both to secure other side payments and to constrain policymaking in ways that interact with the particular allocation of portfolios (which is our focus here). Significantly, scholars are already making important theoretical and empirical progress in understanding how such agreements shape coalition governance (Müllerand Strøm 2008; Klüver and Bäck 2019). While the data that would be required to incorporate this dimension into the analysis are not yet available, moving in this direction is an obvious avenue for future work. 34

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45(4):635–65. Online Appendix

ONLINE APPENDIX

WHAT YOU SEE IS NOT ALWAYS WHAT YOU GET: BARGAINING BEFORE AN AUDIENCE UNDER MULTIPARTY GOVERNMENT

LANNY W. MARTIN ∗ GEORG VANBERG ∗∗

* Professor, Department of Social and Political Sciences, Dondena Centre for Research on Social Dynamics and Public Policy, Bocconi University. [email protected]. ** Professor, Department of Political Science, Duke University. [email protected]. 1 2

Contents

APPENDIX A: Technical Proof for the Edgeworth Box Analysis3 APPENDIX B: Sources for Coding Partisanship of Government Ministers9 APPENDIX C: Multilevel Model Estimation of Table 1 11 APPENDIX D: Measuring Issue Saliency and Positions on 6 Dimensions 12 APPENDIX E: Assignment of Government Ministries to Policy Dimensions 23 APPENDIX F: Model of Government Formation 27 APPENDIX G: Calculation of Bargaining Power (Example) 29 APPENDIX H: Heterogeneity in the Undercompensation Eﬀect 32 APPENDIX I: Measurement Error Sensitivity Analysis 49 APPENDIX J: Estimation of Table 3 using Normalized Banzhaf Index 50 References 52 3

APPENDIX A: Technical Proof for the Edgeworth Box Analysis

The purpose of this appendix is to provide the technical underpinnings for the Edgeworth Box analysis presented in Figures 1 and 2 in the main text. We proceed in two steps. First, we outline the payoff functions for the parties that give rise to the iso-support curves displayed in the figures. We then prove that, provided that less sophisticated supporters—including most voters—rely sufficiently on a heuristic to evaluate parties, any efficient bargain between the parties will allocate the simple good in line with the division implied by the voter heuristic. We do this in a general framework that eschews particular functional forms and imposes only general, standard conditions on payoff functions.

Payoff Functions. We assume that parties are motivated by securing the support of their target audiences, and act so as to maximize this support. Thus, they care about the outcomes of coalition bargaining indirectly, via the manner in which these bargains shape support. We assume that the cumulative support for a party—i.e., the party’s payoff—is an additive function of the backing secured from sophisticated and unsophisticated supporters, weighted by the relative importance of each support group to the party. Denote the relative importance of unsophisticated supporters by γ ∈ (0, 1) and the relative importance of sophisticated supporters by 1 − γ. (Typically, but not necessarily, importance may be tied to the relative size of the groups—this would especially be true with respect to voters.) We assume that the support that is secured from each group in response to a coalition bargain increases at a (weakly) diminishing rate as a party secures more of a good. Specifically, for each party and good x, there exists a support function s(x) that denotes the support secured by the party if it obtains share x of the good, where s0(x) > 0 and s00(x) ≤ 0. Note that this is a general functional form in keeping with standard modeling approaches for payoff functions: Support is monotonically increasing in x, but at a diminishing rate. A generic representation of this support function is displayed in Figure A1. Common functional forms that satisfy these conditions (and are therefore often used as utility functions in applications 4

Figure A1. Support Function - Sophisticated Supporters −→ Support

Share of simple good −→

in economics and political science) are the logarithmic function (e.g., s(x) = Log(x)), or a power function (e.g., s(x) = xa, where a ∈ (0, 1]). Recall that sophisticated supporters are aware of both the simple and complex goods in a coalition bargain, and do not rely on heuristics to make their support decision. Thus, support for the parties by sophisticated voters in response to a bargain Ω = {s, c}, which allocates share s ∈ (0, 1) of the simple good to Party A (with 1 − s going to Party B) and share c ∈ (0, 1) of the complex good to Party A (with 1 − c going to Party B) is given by:

Soph ∂s(j) ∂2s(j) • SA (Ω) = s(s) + s(c) where ∂j > 0 and ∂j2 < 0 for j ∈ {s, c} Soph ∂s(1−j) ∂2s(1−j) • SB (Ω) = s(1 − s) + s(1 − c) where ∂j < 0 and ∂j2 > 0 for j ∈ {s, c}.

Recall that unsophisticated supporters differ from sophisticated ones in two ways. First, they only observe the simple good, and therefore their support only depends on the allocation of the simple good. Second, these supporters rely on a heuristic to evaluate their party. This heuristic defines a division of goods between the parties such that support declines sharply if a party secures less than the share implied by the heuristic, and does not respond significantly once the heuristic threshold has been met. We model this heuristic in the following way. First, the parameter p ∈ (0, 1) denotes the division of the simple good implied by the voter heuristic. Second, we add two parameters to the support function for unsophisticated 5

Figure A2. Support Function - Sophisticated voters −→ Support

p Share of simple good −→

voters, which modify the slope of s(x). Speciﬁcally, the support function—which we display graphically in Figure A2—is given by:

  (1 − α)s(p) + αs(s) s < p  ∼Soph  (1) SA (Ω) = s(o) o = p   (1 − β)s(p) + βs(s) s > p

  (1 − β)s(1 − p) + βs(1 − s) s < p  ∼Soph  (2) SB (Ω) = s(1 − o) o = p   (1 − α)s(1 − p) + αs(1 − s) s > p.

The constant terms at the front of the function represent an intercept shift that ensures that the support function is continuous and passes through s(s) for s = p. (This feature is not critical to the argument.) The parameter α > 1 increases the slope of the support function to the left of p, with a steeper slope as α increases. The parameter β ∈ (0, 1) decreases the slope of the support function to the right of p, with the slope becoming more shallow as β approaches 0. 6

The payoﬀ (support) function for each party is given by the cumulative support obtained from sophisticated and unsophisticated supporters, weighted by their relative importance:

  (1 − γ)(s(s) + s(c)) + γ((1 − α)s(p) + αs(s)) s < p  (3) SA(Ω) = (1 − γ)(s(s) + s(c)) + γs(s) s = p   (1 − γ)(s(s) + s(c)) + γ((1 − β)s(p) + βs(s)) s > p

  (1 − γ)(s(1 − s) + s(1 − c)) + γ((1 − β)s(1 − p) + βs(1 − s)) s < p  (4) SB(Ω) = (1 − γ)(s(1 − s) + s(1 − c)) + γs(1 − s) s = p   (1 − γ)(s(1 − s) + s(1 − c)) + γ((1 − α)s(1 − p) + αs(1 − s)) s > p.

Efficient Bargaining. In this section, we show that if parties bargain efficiently, the coalition agreement that is reached will distribute the simple good in line with the heuristic used by unsophisticated voters. Suppose that—given the particular protocol employed—the relative bargaining power of the parties implies a bargain at Ω0 = (s0, c0). (We intentionally leave this bargaining protocol unspecified to highlight that the result does not depend on a specific protocol.) We need to demonstrate that if s0 6= p, the bargain is inefficient and the parties can engage in additional reallocations that increase the support of both parties. Specifically, the parties can shift some of the simple good to the party whose share of the simple good is below the share implied by the heuristic, and compensate the party who gives up the simple good by shifting some of the complex good to it. Note that if the marginal rate of substitution between the simple and the complex good (given by the ratio of marginal utilities) is larger for one party than for the other at a proposed bargaining outcome, the outcome cannot be efficient: The difference in the marginal rates of substitution implies that there is a mutually beneficial trade available. Recall that the slope of iso-support curves is given by the marginal rate of substitution. This implies that in the Edgeworth Box analysis presented above, at a bargain that is efficient, the iso-support curves of the parties must be just tangent. We want to show that—given the fact that 7 unsophisticated voters are employing a heuristic that focuses on whether their party’s share of the simple good corresponds to the threshold implied by their heuristic—this requires that o = p, i.e., the simple good is allocated in line with the unsophisticated voters’ heuristic. The proof proceeds by demonstrating that the marginal rates of substitution cannot be equal if s0 6= p. Case 1: x = {s, c} s.t. s < p. Given the support functions defined above, the marginal rates of substitution are given by:

∂SA(x) 0 ∂s (1 − γ + γα) s (s) (5) MRSA = = ∂SA(x) (1 − γ) s0(c) ∂c

∂SB (x) 0 ∂s (1 − γ + γβ) s (1 − s) (6) MRSB = = . ∂SB (x) (1 − γ) s0(1 − c) ∂c Note that for α sufficiently large, and β sufficiently small, the marginal rate of substitution for Party A must exceed the marginal rate of substitution for Party B; that is, the existing bargain is inefficient and the two parties can trade a portion of the complex good from Party A to Party B in return for an increase in Party A’s share of the simple good. Case 2: x = {s, c} s.t. s > p. Given the support functions defined above, the marginal rates of substitution are given by:

∂SA(x) 0 ∂s (1 − γ + γβ) s (s) (7) MRSA = = ∂SA(x) (1 − γ) s0(c) ∂c

∂SB (x) 0 ∂s (1 − γ + γα) s (1 − s) (8) MRSB = = . ∂SB (x) (1 − γ) s0(1 − c) ∂c 8

Note that for α sufficiently large, and β sufficiently small, the marginal rate of substitution for Party B must exceed the marginal rate of substitution for Party A; that is, the existing bargain is inefficient and the two parties can trade a portion of the complex good from Party B to Party A in return for an increase in Party B’s share of the simple good. Since an increasing α and declining β imply that unsophisticated voters evaluate the bargain more intensely with respect to the cutoff p, this is equivalent to saying that if the behavior of unsophisticated voters is sufficiently strongly tied to their heuristic, bargains that do not allocate the simple good in line with the voters’ heuristic are inefficient, and parties have opportunities for mutually advantageous trades. Translated into the Edgeworth Box framework, this result implies that the iso-support curves for Party A have a steeper slope than the iso-support curves for Party B when the simple good is below p and a more shallow slope than the iso-support curves for Party B if the simple good is above p. The iso-support curves are tangent only for bargains for which s = p. 9

APPENDIX B: Sources for Coding Partisanship of Government Ministers

In this appendix, we list the archival sources used to create the data on ministry assignments. The countries and years (and number of coalition governments) in the sample are as follows: Austria (1949–2016) [20], Belgium (1947–2011) [32], Denmark (1950–2014) [23], Finland (1945–2014) [41], France (1959–2017) [29], Germany (1949–2018) [25], Great Britain (2010) [1], Greece (1989–2015) [6], Iceland (1971–2016) [19], Ireland (1954–2011) [12], Italy (1946–2016) [38], Luxembourg (1959–2013) [13], the Netherlands (1946–2012) [23], Norway (1963–2009) [11], Portugal (1978–2011) [5], and Sweden (1951–2014) [10]. The years listed range from the formation year of the ﬁrst coalition appearing in the sample to that of the last. With a few exceptions, the data comprise all the multiparty governments that formed in these 16 democracies from the end of World War II until the last election year covered in the 2017 version of the Manifestos Project (MARPOR) dataset. Bargaining situations resulting in single-party, non-partisan, or caretaker administrations are excluded, as are governments in which all coalition parties ran on a single policy platform and those with government parties that are missing in the MARPOR data. In addition, bargaining situations in Luxembourg before 1959 and Iceland before 1971 are excluded because of missing information on a number of cabinet ministries. 10

Austria Republik Osterreich,¨ Parlament, Bundesregierungen seit 1918

Centre de Recherche et d’Information Socio-Politiques, Belgium Gouvernements F´ed´erauxdepuis 1944

Denmark Statsministeriet, Regerigen, Regeringer siden 1848

Finland Valtioneuvosto, Hallitukset ja Ministerit vuodesta 1917

AssembléeNationale, Les Gouvernements de la VèmeRépublique France (V) AssembléeNationale, Les DéputésFran¸cais depuis 1789

Schindler, Peter. 1999. Datenhandbuch zur Geschichte des Deutschen Germany Bundestages 1949 bis 1999. Baden-Baden: Nomos Verlagsgesellschaft. Das Datenhandbuch des Bundestages

Great Britain BBC News, “Cameron’s Government: A Guide to Who’s Who”

Greece General Secretariat of the Government, Governments from 1909 to Today

Althingi, Ministries since 1917 Iceland Althingi, Ministers since 1904

Department of the Taoiseach, Historical Information, History of Government Ireland Houses of the Oireachtas, Directory of Members

Italy Governo Italiano, Governi dal 1943 ad Oggi

Thewes, Guy. 2003. Les Governements du Grand-Duch´ede Luxembourg depuis 1848. Luxembourg: Service Information et Presse du Luxembourg Gouvernement Luxembourgeois. Le Gouvernement Luxembourgeois, Anciens Membres du Gouvernement

Netherlands Rijksoverheid, Regering, Inhoud, Kabinetten sinds 1945

Norway Norske Regjeringer Siden 1945

Guimarãis,Alberto Laplaine, Bernardo Diniz de Ayala, Manuel Pinto Machado, Portugal and Miguel FélixAntónio.2011. Os Governos da República: 1910–2010. Lisboa: s.n.). RepúblicaPortuguesa, Governos Anteriores

Sweden SverigesMinistrar.se 11

APPENDIX C: Multilevel Model Estimation of Table 1

Table C1. Random Intercepts Estimation

Explanatory Variables Estimates

Seat Contribution 0.790 ∗∗∗ (0.011) Intercept 0.068 ∗∗∗ (0.004)

σ2(Intercept) 0.000 (0.000) σ2(Residual) 0.004 (0.000)

Displayed are maximum likelihood coefficient estimates and standard errors from a multilevel random intercepts model. Dependent variable: Numerical share of cabinet ministries. N: 602 coalition parties (after 308 parties, one per bargaining situation, are randomly dropped from the analysis). Likelihood ratio test against linear model with a fixed intercept (Table 1) implies we cannot reject the null hypothesis of no difference between the models (p > 0.99). Significance levels : ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%.

Table C2. Random Coeﬃcients Estimation

Explanatory Variables Estimates

Seat Contribution 0.793 ∗∗∗ (0.012) Intercept 0.066 ∗∗∗ (0.005)

σ2(Seat Contribution) 0.006 (0.003) σ2(Intercept) 0.000 (0.000) σ(Seat Contribution, Intercept) -0.001 (0.001) σ2(Residual) 0.004 (0.000)

Displayed are maximum likelihood coefficient estimates and standard errors from a multilevel random coefficients model (with no constraints imposed on the covariance matrix). Dependent variable: Numerical share of cabinet ministries. N: 602 coalition parties (after 308 parties, one per bargaining situation, are randomly dropped from the analysis). Like- lihood ratio test against linear model with a fixed intercept and slope (Table 1) implies we cannot reject the null hypothesis of no difference between the models (p > 0.09). Significance levels : ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%. 12

APPENDIX D: Measuring Issue Saliency and Positions on 6 Dimensions

Using data on party election programs from the Manifestos Project (MARPOR), and the scaling approach developed by Lowe et al. (2011), we calculated issue saliency scores and policy positions for parties on six policy dimensions:

(1) Economic Regulation and State Services (2) Traditional Morality (3) Environmental Protection (4) Internationalism and European Integration (5) Social Cohesion and National Identity (6) Conﬂict and Military Power.

These dimensions overlap considerably with dimensions defined in several prominent expert studies, such as the pair of studies conducted by Laver and Hunt (1992) and Benoit and Laver (2006), as well as the Chapel Hill Expert Survey (Bakker et al. 2015). The MARPOR coding scheme classifies each “quasi-sentence” in a party’s electoral program into one of 56 mutually exclusive policy categories. Typically, some subset of the resulting category counts from a coded electoral program are aggregated and scaled to construct a more general—and presumably, substantively meaningful—index, such as the com- monly used left-right socioeconomic scale. Lowe et al. (2011) proposed a new scaling method (based on log-odds ratios), which improved on previous scales in several ways, to produce both saliency and position estimates on multiple dimensions. Specifically, their measure of the position of a party on a given dimension is defined as,

R + 0.5 ln , L + 0.5 and their measure of the saliency of the dimension for a party is deﬁned as,

R + L + 1 ln , N 13 where N is the total number of quasi-sentences in the manifesto, and R and L represent, respectively, the number of quasi-sentences in the party program assigned to the “right” and “left” sides of the policy dimension. (For instance, for the traditional morality dimension defined by Lowe et al., R was the number of quasi-sentences in a party program assigned to the MARPOR category “Traditional Morality: Positive,” while L was the number of quasi-sentences in the program assigned to the category “Traditional Morality: Negative.”1) Lowe et al. (2011) constructed several policy dimensions (which they defined a priori) from the MARPOR data set, using categories for each dimension that (a) deal with the same general issue (such as state-provided services) and (b) are inherently positional and confrontational (such as the categories “Welfare State Expansion: Positive” and “Welfare State Limitation: Positive”). We followed the same logic in constructing our a priori policy dimensions, some of which, as noted above, are similar (if not identical) to those from the Lowe et al. study. Specifically, the policy dimensions in our study are constructed from the MARPOR categories as follows.2

1 As shown in the latter equation above, the Lowe et al. (2011) scaling procedure produces issue saliency scores for a party that are on a logarithmic scale. For each party, we exponentiate this measure on each of the six dimensions and then create a relative saliency score for a dimension by dividing the dimension’s exponentiated measure by the average exponentiated measure across dimensions. Thus, if a policy dimension is of above-average importance to a party, it receives a relative policy saliency score greater than 1.0, while a dimension of below-average importance to the party receives a score less than 1.0. 2 The three-digit numbers in the tables refer to the MARPOR policy category codes. The “traditional morality” and “environmental protection” dimensions are identical to those constructed by Lowe et al. (2011), while the “economic regulation and state services” dimension is very similar to their “state involvement in economy” dimension. 14

(1) Economic Regulation and State Services

Left Right

403 Market Regulation + 401 Free Enterprise + 404 Economic Planning + 402 Incentives + 406 Protectionism + 407 Protectionism – 409 Keynesianism + 414 Economic Orthodoxy + 412 Controlled Economy + 505 Welfare State Limitation + 413 Nationalisation + 507 Education Limitation + 503 Social Justice + 702 Labour Groups – 504 Welfare State Expansion + 506 Education Expansion + 701 Labour Groups +

(2) Traditional Morality

Left Right

604 Traditional Morality – 603 Traditional Morality +

(3) Environmental Protection

Left Right

416 Anti-Growth Economy + 410 Economic Growth + 501 Environmental Protection +

(4) Internationalism and European Integration

Left Right

107 Internationalism + 109 Internationalism – 108 European Integration + 110 European Integration –

(5) Social Cohesion and National Identity

Left Right

301 Decentralisation + 302 Centralisation + 602 National Way of Life – 601 National Way of Life + 607 Multiculturalism + 605 Law and Order + 606 Social Harmony + 608 Multiculturalism – 15

(6) Conﬂict and Military Power

Left Right

103 Anti-Imperialism + 104 Military + 105 Military – 106 Peace +

To assess the construct validity of these dimensions, we performed a conﬁrmatory factor analysis to ensure that the MARPOR categories load on the latent predeﬁned policy dimensions in plausible ways—of particular importance is that the categories grouped within each “side” of the dimension (i.e., “left” or “right”) are correlated with the underlying dimension in the same direction and that the signs of the correlations across sides are in the opposite direction.3 The results are as follows.

(1) Economic Regulation and State Services

403 Market Regulation + 0.22 404 Economic Planning + 0.14 406 Protectionism + 0.05 409 Keynesianism + 0.06 412 Controlled Economy + 0.30 Left 413 Nationalisation + 0.37 503 Social Justice + 0.35 504 Welfare State Expansion + 0.23 506 Education Expansion + 0.09 701 Labour Groups + 0.35

401 Free Enterprise + -0.53 402 Incentives + -0.28 407 Protectionism – -0.17 Right 414 Economic Orthodoxy + -0.48 505 Welfare State Limitation + -0.38 507 Education Limitation + -0.14 702 Labour Groups – -0.13

(2) Traditional Morality

Left 604 Traditional Morality – 0.24

Right 603 Traditional Morality + -0.24

3 The factor analysis was performed using the full set of parties and elections (1,956 election-party observations) for all Western European parliamentary democracies covered by the 2017 version of the MARPOR dataset. 16

(3) Environmental Protection

416 Anti-Growth Economy + 0.43 Left 501 Environmental Protection + 0.45

Right 410 Economic Growth + -0.26

(4) Internationalism and European Integration

107 Internationalism + 0.25 Left 108 European Integration + 0.31

109 Internationalism – -0.22 Right 110 European Integration – -0.21

(5) Social Cohesion and National Identity

301 Decentralisation + -0.25 Left 602 National Way of Life – -0.16 607 Multiculturalism + -0.13

302 Centralisation + 0.11 601 National Way of Life + 0.33 Right 605 Law and Order + 0.42 606 Social Harmony + 0.02 608 Multiculturalism – 0.47

(6) Conﬂict and Military Power

103 Anti-Imperialism + 0.09 Left 105 Military – 0.46 106 Peace + 0.45

Right 104 Military + -0.14

Clearly, the degree to which the MARPOR categories are correlated with the predefined underlying policy dimensions varies quite a bit, but the loadings are all consistent with expectations, both within and between the “left” and “right” poles of each dimension. Just as important a task is to demonstrate that the position and saliency estimates for political parties on these six dimensions have face validity. To assess this (in a somewhat summary fashion), we used the Lowe et al. (2011) measures discussed above to generate position and saliency estimates for all the parties and elections examined in the factor analysis, 17 and then aggregated those estimates across parties and elections according to the MARPOR- defined party families to which the parties belong. The nine major MARPOR-defined party families are Ecologist (ECO), Communist (COM), Socialist (SOC), Liberal (LIB), Christian Democratic (CHR), Conservative (CON), Nationalist (NAT), Agrarian (AGR), and Eth- nic/Regionalist (REG). In the figures below, we simultaneously display the mean saliency and position estimates for party families over the postwar period, along with Hotelling T 2 confidence regions.4

Economic Regulation and State Services 1 −

COM SOC CON AGR

1.2 LIB − CHR

ECO 1.4

− REG

NAT Issue Saliency 1.6 − 1.8 − −3 −2 −1 0 Issue Position

Figure D1. Economic Regulation and State Services, by Party Family

Beginning with the Economic Regulation and State Services dimension, we see that most party families in postwar Western Europe have placed approximately the same amount of emphasis on economic issues. The most notable exceptions are Green parties, Regionalist parties, and Nationalists, all of which (as will be shown below) place almost equal stress on some other issue. In terms of position estimates, we see essentially the same pattern

4 Analogous to a univariate confidence interval, a confidence region is centered at the sample mean vector of the observed variables. The length of each axis of a region is longer the higher the variability in observed values of the corresponding variable and the smaller the sample size. The tilt of a region reflects the direction of the covariance between the plotted variables. 18

Traditional Morality 3 −

CHR 3.5 − AGR NAT

4 CON −

LIB

Issue Saliency ECO 4.5

− SOC COM REG 5 − −1 0 1 2 3 Issue Position

Figure D2. Traditional Morality, by Party Family

as revealed by most expert surveys of party economic stances, with the Communists, then Greens, then Socialists on the left of the spectrum, Agrarian and Christian Democratic parties on the center-right, and Liberal and Conservative parties farthest to the right. Estimates on the Traditional Morality dimension also appear consistent with typical assessments of party issue emphases and positions. No party family stresses this dimension as much as the economic dimension (note that the issue saliency estimates can be directly compared across figures). But there is significant differentiation between parties in terms of the importance of this dimension, which correlates positively with their positions. For example, Greens, Socialists, Communists, and Regionalists put relatively little stress on “morality” issues and are also on the relatively “permissive” side of the scale. They are joined by Lib- eral parties, which are known to be progressive on such issues as gay rights, abortion, gender equality, etc. On the other side of the dimension are party families that tend to stress this issue more, such as Agrarians, Conservatives, and Nationalists, all of whom tend to court ru- ral and/or religious voters with more traditional social views. Christian Democratic parties, with their obvious religious roots, are farthest to the right on this issue. 19

Environmental Protection 1.5

− ECO 2 −

AGR 2.5 −

REG CON

Issue Saliency SOC 3 COM LIB − CHR

NAT 3.5 −

−4 −3 −2 −1 0 Issue Position

Figure D3. Environmental Protection, by Party Family

The estimates on the Environmental Protection dimension show clear differences between Green parties and every other party family. Not surprisingly, Greens stress this issue more than any other type of party (stressing it as much as economic issues), and they tend to be extreme on the environmental protection side of the dimension. There is also differentiation between the other parties (though this perhaps gets somewhat lost in the figure because of the skew caused by the Green party family estimates). For example, Communists are more pro-environment than Socialists, which are more pro-environment than Conservatives. Estimates for the Internationalism and European Integration dimension are also not that surprising. Most mainstream parties cluster together on the pro-internationalism and pro- integration side of this dimension. These parties are separated from three party families that either tend to talk frequently about national sovereignty, such as Nationalists, or have hostile attitudes towards the European Union. Agrarian parties (which are most prevalent in Scandinavia) have often taken positions against further EU integration, as have Commu- nist parties, which typically portray the EU as a vehicle for harsh free-market capitalism. Notably, this is the only issue on which Nationalists and Communists share common ground. 20

Internationalism and European Integration 2.8 −

ECO 3 −

SOC NAT CHR LIB COM 3.2 − CON REG AGR Issue Saliency 3.4 − 3.6 − −3 −2 −1 0 Issue Position

Figure D4. Internationalism and European Integration, by Party Family

Social Cohesion and National Identity 1.5 −

REG

NAT 2 −

AGR CHR CON 2.5

− LIB

ECO

Issue Saliency SOC 3

− COM 3.5 − −2 −1 0 1 2 3 Issue Position

Figure D5. Social Cohesion and National Identity, by Party Family 21

On the Social Cohesion and National Identity dimension, the clearest differences are between Ethnic/Regionalist parties and Nationalists. Both party families emphasize these issues nearly as much as economic issues. Nationalists tend to make positive statements about national identity, as well as negative statements about cultural diversity, and they tend to take a zero-tolerance approach to law and order issues (which is intimately connected to their hostile views towards immigrant communities and ethnic minorities). In contrast, regionalist parties highlight the virtues of multiculturalism and advocate for greater autonomy for minority groups, especially where they are geographically concentrated. Finally, estimates on the Conflict and Military Power dimension differentiate party families that extol the virtues of a strong military from those that advocate peaceful solutions to international problems, such as Green parties or (to a lesser extent) Socialists, or parties that tend to associate large militaries with (capitalist) imperialism, such as Communist parties (which stress this issue more than any other party family). Agrarians, Liberals, and Christian Democratic parties are relatively centrist on this dimension, whereas Conservative and Nationalist party families take very similar stances on the right (both advocating greater military strength). In sum, at least with respect to broadly-defined party families, the saliency and position estimates on the six predefined policy dimensions do appear to have significant face validity. A more extensive investigation is warranted, nonetheless, to assess whether the estimates accurately describe the positions of individual parties and track changes in issue priorities and policy positions over time. 22

Conflict and Military Power 3 −

COM 3.5 − NAT CON SOC AGR LIB

ECO CHR 4 Issue Saliency −

REG 4.5 − −3 −2 −1 0 1 Issue Position

Figure D6. Conﬂict and Military Power, by Party Family 23

APPENDIX E: Assignment of Government Ministries to Policy Dimensions

Matching policy dimensions to specific ministries obviously requires knowledge of ministerial competences. Bäck, Debus and Dumont (2011), in their classification of 13 ministerial posts that have been present (more or less) in all Western European countries in the post-war period, followed what they described as a “maximalist” approach, in which they assigned numerous MARPOR categories to a ministry “to get the widest possible picture of the policy jurisdiction of the portfolio” (Bäck, Debus and Dumont 2011, 453).5 They also allowed for the repetition of categories across ministries. We follow a similar strategy, although since we have predefined policy dimensions, we associate ministers with those rather than with MARPOR categories.6 We have classified ministries onto specific policy dimensions based on the sorts of issues that fall within their particular remit, which we assessed based on information gathered from a variety of sources, such as historical descriptions provided by the ministries themselves, formal legislative documents detailing the organization of the government and policy competences of each department, and the types of government bills and directives introduced by the ministers in the legislature. Ministries that have significant policymaking responsibility in different policy areas are assigned to multiple policy dimensions. In this appendix, we list (a) the major ministries in our sample of countries (necessarily by broad policy area rather than by specific names, since these vary dramatically across countries and years), (b) the policy dimensions assigned to them, and (c) the typical sorts of issues on these dimensions for which ministers are primarily responsible. Not all ministries can be assigned to these policy dimensions. For example, those ministers without portfolio who are not tasked with a specific policy area cannot be assigned to any dimension. The

5 The portfolios included in their study were Foreign Affairs, Interior, Justice, Finance, Economic Affairs, Defense, Labor, Education, Health, Agriculture, Industry, Environment, and Social Affairs. 6 A fundamental premise of our argument, unlike that of Bäck, Debus and Dumont (who were testing a saliency theory of party competition), is that the utility a party derives from receiving (or not receiving) a ministry is a function of the distance between the party’s ideal point and the (expected) policies produced by the coalition party controlling the ministry. Naturally, to measure distance between parties, we have to define a space on which we can place them; the role of the MARPOR categories is to give substance to that space (i.e., coding positions using these categories allows us to say what “further right” or “further left” actually means with respect to positions on the corresponding dimension). 24 post of Prime Minister represents a special case. Even though prime ministers control no government department, per se, it is plausible to think that they could insert themselves into the affairs of those departments, particularly on the issues they care a lot about, since (at least formally) all ministries are accountable to them. Accordingly, we assign prime ministers to all six policy dimensions. 25

Policy Dimensions and Typical Issues Ministerial Posts

Finance/Budget/Treasury (1) Economic Regulation and State Services Social Aﬀairs/Welfare Regulation of industry and markets, privatization, Health state-subsidized social services and insurance Labor schemes (pensions, disability, health, unemployment), Industry/Enterprise/Economic Aﬀairs housing, social assistance, income and sales taxes, Energy minimum incomes, collective bargaining Economic Planning Education Housing Transport/Telecoms/Public Works Agriculture/Fisheries/Forests Environment

Justice (2) Traditional Morality Social Aﬀairs Gay rights, same-sex marriage and adoption, Family gender equality, contraception, abortion, Health divorce, euthanasia Women’s Aﬀairs

Environment (3) Environmental Protection Energy Air, soil, and water pollution, nuclear power, Agriculture/Fisheries/Forests emissions standards, sustainable industrial growth, Industry/Enterprise/Economic Aﬀairs climate change 26

Foreign Aﬀairs (4) Internationalism and European Integration Foreign Trade European integration, international cooperation, Foreign Aid foreign trade, international human rights, EU Aﬀairs development aid

Justice (5) Social Cohesion and National Identity Interior Immigration, law and order, civil rights, Immigration and Identity decentralization, minority protections Regional and Local Government

Foreign Affairs (6) Conflict and Military Power Defense Military conflict, nuclear arsenal, national defense, Foreign Aid decolonization, colonial relations Overseas Territories 27

APPENDIX F: Model of Government Formation

To construct our measure of bargaining power (see the main text, also Appendix G), we rely on a model developed in a recent study by Kayser, Orlowski and Rehmert (N.d.)— hereafter, KOR—that builds on previous work by Martin and Stevenson (2001, 2010). Like these earlier studies, KOR use a conditional logit model to calculate the probability that a particular coalition is chosen (out of the set of all potential coalitions), where the probability is modeled as a function of 9 size-related, policy-related, and contextual factors. We present the conditional logit model estimates below. The size variables measure whether the largest party is in the potential coalition, whether the potential coalition controls a minority of legislative seats, whether it is minimal winning, and the number of parties it contains. The policy variables measure the ideological range of the potential coalition, whether it contains the median legislator, and the presence of anti- establishment sentiment. Finally, the contextual variables measure whether the potential coalition is the incumbent and the extent to which parties in the potential coalition have a shared history of working together. While we use the set of variables suggested by KOR, we continue to use the Martin and Stevenson measures for several of them. Speciﬁcally, we use the Martin and Stevenson (2010) measures for the three ideological variables (which they construct using MARPOR data), as these are more established (and more ﬁne-grained) than those used by KOR. And we use the Martin and Stevenson (2010) measure of cabinet history (or “familiarity”), which we see as more substantively grounded than the KOR measure. 28

Table F1. Determinants of Government Formation

Explanatory Variables Estimates

Largest Party in Coalition 1.199 ∗∗∗ (0.166) Minority Government -1.481 ∗∗∗ (0.233) Minimal Winning Coalition 0.644 ∗∗∗ (0.162) Number of Parties in Coalition -0.616 ∗∗∗ (0.084) Ideological Divisions in Coalition -0.026 ∗∗∗ (0.004) Median Party in Coalition 0.409 ∗∗∗ (0.145) Anti-System Presence in Coalition -0.041 ∗∗ (0.021) Status Quo 2.561 ∗∗∗ (0.138) Familiarity 1.586 ∗∗∗ (0.401)

Displayed are maximum likelihood coeﬃcient estimates and standard errors from a conditional logit model. Dependent variable: Binary indicator for whether a potential government was chosen. N: 498 bargaining situations (163,998 potential governments). Signiﬁcance levels : ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%. 29

APPENDIX G: Calculation of Bargaining Power (Example)

As noted in the main text, we construct our measure of government party bargaining power in the following steps:

(1) using the coeﬃcients from the KOR model (SI Appendix F), we predict the probability of formation for each potential government in each of our 308 bargaining situations, including the coalition that was actually chosen; (2) for each government party in the chosen coalition, we calculate the party’s probability of being included in an alternative coalition by summing the formation probabilities of all non-chosen potential coalitions in which that party is a member; (3) we normalize each government party’s exit probability by dividing it by the sum of exit probabilities across all government parties.

In this appendix, we illustrate how to follow these steps to construct our bargaining power measure using a simple example: Germany following the 2002 elections, which produced a legislature with only 5 parties. In Table G1, we list all 31 potential governments that could have formed after this election (column 1), highlighting the chosen one in bold: the two- party coalition of the SPD and the Greens (the SchröderII cabinet). In column 2, we list the seat shares of all potential governments (the first five rows in the data are single-party governments, and thus reflect the individual seat shares for the 5 parties), and in the note to the table, we list the MARPOR left-right party positions.7 Columns 3–11 display the characteristics of the potential governments in the order they are presented in SI Appendix F. Column 12 indicates the chosen government, and column 13 lists the predicted probability of formation in Step (1) above. In the conditional logit model, the predicted probability of coalition i being selected in a given bargaining situation is,

P exp( k Xikβk) πi = P P , i exp( k Xikβk)

7 Although these variables are not predictors in the government formation model, we list them because they are building blocks for several of those covariates: largest party status, minority status, minimal winning status, ideological divisions, and median party status. 30 where βk refers to the vector of coeﬃcients from SI Appendix F, and Xik represents the associated vector of values of the k variables for potential coalition i. The denominator, which sums the numerator across all potential coalitions in the bargaining situation, assures that the predicted probabilities sum to one in the bargaining situation. In Step (2), for each government party (here, the SPD and Greens) we sum the predicted formation probabilities in column 13 across all potential coalitions in which the party is a member excluding the chosen one. Thus, this is each party’s exit probability. For example, for the Green party, the probabilities across the 15 alternative governments in which it is a member sum to about 0.07, meaning that it has roughly a 1 in 14 chance of getting into another government. For the SPD, the probabilities across the 15 alternative coalitions in which it is a member sum to slightly more than 0.17, meaning that it has roughly a 1 in 6 chance of getting into another government. In Step (3), we normalize the measure so that it sums to one (thereby putting it on the same metric as portfolio share, the other component of the undercompensation variable).

.07 Thus, the bargaining power of the Greens is approximately .24 = 0.29, while for the SPD, it .17 8 is approximately .24 = 0.71.

8 We should note that an alternative measure of bargaining power, the normalized Banzhaf index (discussed in footnote 27 in the main text; see also SI Appendix J), indicates that the SPD and Greens are equal in power, as they each belong to the same number of minimal winning coalitions. Our measure, however, accounts for the fact that the SPD has several other characteristics that have been shown empirically to be advantageous in coalition bargaining: it is ideologically central (as it is the median party), and it is the largest legislative party (making it more likely to be appointed the formateur). 31 APRprycds 11 B0Gen) 12 PSLf) 12 SD,440(D) 12 CUCU.MRO etrgtscores: left-right MARPOR (CDU/CSU). (20.76). 41521 41521 (FDP), (4.59), 41420 41420 (SPD), (4.10), 41320 41320 (PDS/Left), (-21.33), 41221 41221 (B90/Greens), (-13.43), 41113 41113 codes: party MARPOR 11 12 12 12 12 20 .2 .5 0.002 0.003 0.003 0.001 0.011 0.003 0 0 0.000 0.006 0 0.007 0 0.003 0 0 0.002 0.357 0.422 0 0 0.007 0.359 0 0.013 0.539 0 0.002 0 0 0.425 0.413 0 0.002 0.000 0 0.722 0.541 0 0.046 0.014 0 0.496 0 0.012 2.229 0 1.615 0 0.725 0 0.001 0 2.229 0 0.545 0 0 0.002 0 2.229 0.416 0 0.007 0 0.009 1 1.615 0 2.229 0.548 1 0 0.008 0.007 1.184 0 2.229 0.694 1 0 0.034 0.001 1.615 0 0.732 0.484 0 42.09 0 1.615 0 42.09 0.500 1 0.696 1 0.007 0 0 0.007 0.003 2.229 0 34.19 0.734 0 1 0 0 0.778 0 2.229 0 42.09 0.984 1 0 0 0 2.229 0 16.66 42.09 1 5 4 0.922 0 2.229 42.09 0 25.92 0.984 0 4 0 0 1 1.009 0 2.229 42.09 0.703 1 1 4 1.615 2.229 25.92 0.503 1 1 0 3 4 1 1.615 0 0 34.19 0 0 3 4 1.184 0 34.19 0 0 0 0 3 0.932 1 0 18.02 1 0.705 1 1 1.184 0 3 0 1.615 42.09 1 0 0 0 0 3 0 2.229 16.17 25.92 0 0.456 0 0 0 3 1 0 2.229 16.66 25.43 0 0 3 0 1.009 0 0 0.492 1 1.615 0 3 1 0 0 42.09 0 1 2.229 0 2 0 3 2.229 1 0 0 1 1.184 0 25.92 2 3 2.229 0 0 25.43 0 0 2 0.909 1 1 1 34.19 1 1 0 2 0.997 0 1 0 18.02 0 0 1 0 0 0 0.584 41521 0 2 0 41420 1 41320 1 0 0.905 2 0.922 41221 0 41113 0 41521 1 0 41420 0 17.53 0.493 7.893 2 0.589 41320 41221 0 41521 0 41420 0 0.831 2 41320 1 41113 1 41521 0 1 41420 1 0.498 41221 0 0 0 41113 0 41521 1 41320 0 0.580 41221 2 1 1 41113 2 41420 0 41320 1 1 0.919 41221 1 41113 0 0 41521 0 0.585 41420 41320 1 1 1 0 1 41521 0.506 41420 1 1 41221 1 41521 0.489 1 0.172 41320 0 0 0 41221 0 0 41420 0.828 0.511 41320 1 41221 41521 0.494 0 41420 1 41113 1 0 41521 0.415 41320 0 0 41113 0 1 1 41420 0.0813 41320 1 41113 0 41521 0.420 41221 41113 0 Formation 41420 0.502 1 41221 41113 1 1 41320 0.169 0 0 41221 Chosen 41113 1 0.411 41521 41420 0.507 Familiarity 0.0779 0.0945 41521 0 41320 Status 0.416 0 41420 Anti-System 41320 Median 41521 0.00332 41221 Ideological 0.0912 41420 41221 of Number 41320 41221 Minimal 41521 Minority 41113 Largest 41420 41113 Seats 41320 41113 41221 41113 41521 41420 41320 41221 41113 Coalition at inn ate iiin at rsneQoGvrmn Probability Government Quo Presence Party Divisions Parties Winning Party al G1. Table oeta oltosi emn,2002 Germany, in Coalitions Potential 32

APPENDIX H: Heterogeneity in the Undercompensation Effect

A multilevel random coefficients model allows us to address possible heterogeneity in the effects of the covariates by providing estimates of both the overall (or average/fixed) intercept and slope coefficients of interest as well as the extent to which the intercepts and slope coefficients at the level of the cluster deviate from the average estimates. Using the estimated variance components of the model, we can calculate best linear unbiased predictions (BLUPs) of the random deviations, and then use the BLUPs to generate predicted random intercepts and random slope coefficients for individual bargaining situations. In the graphs below (which are arranged alphabetically by country, and chronologically by government), we display predicted policy risk payoffs (on the y-axis) for the 910 parties in our sample of 308 bargaining situations. To generate the predictions, the theoretical variable (Undercompensation in Portfolio Share [ups]) is set to the actual value for each government party (on the x-axis), and the control variable (Distance from the Coalition Center of Gravity [dccg]) is set to its mean value across the full sample. Letting α represent the intercept, β the coefficient on the theoretical variable, and γ the coefficient on the control variable, the predicted policy risk payoff for a party c in a bargaining situation s is simply:

BLUP BLUP BLUP (α + αs ) + (β + βs )upsc + (γ + γs )dccgc.

Inside the plot region of each graph is the predicted random coeﬃcient estimate for Under-

BLUP compensation in Portfolio Share—i.e., (β + βs ), the ﬁxed intercept plus the situation- speciﬁc random deviation—which describes the slope of the dashed line. Austria

1, Figl III 2, Raab I 3, Raab II 4, Raab III 5, Gorbach I 20

15 -10.353 *** -10.906 *** -9.621 *** -14.918 *** -8.737 *** 10 5

6, Gorbach II 7, Klaus I 8, Sinowatz 9, Vranitzky I 10, Vranitzky II 20

15 -8.781 *** -13.547 *** -13.547 *** -3.63 *** -6.846 *** 10 5

11, Vranitzky III 12, Vranitzky IV 13, Vranizky V 14, Klima 15, Schüssel I 20 15 -14.694 *** -12.35 *** -13.632 *** -8.166 *** -10.122 *** 10 5

Predicted Policy Risk PayoffsRisk Policy Predicted 16, Schüssel II 17, Gusenbauer 18, Faymann I 19, Faymann II 20, Kern 20 15 -11.318 *** -11.575 ***

10 -5.421 *** -1.408 *** -.236 5 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5

Undercompensation in Portfolio Share

Note: The variable Distance from Coalition Center of Gravity is set to its mean sample value. Displayed in the plot region of each graph is the random coefﬁcient estimate for Undercompensation in Portfolio Share. Signiﬁcance levels: * : 10% ** : 5% *** : 1%. Belgium

21, Spaak II 22, Eyskens 23, Van Acker IV 24, Eyskens III 25, Lefevre 26, Harmel -15.126 *** 15 8.169 *** -3.637 *** -19.403 *** 3.911 *** -3.244 *** 10 5

27, Van den Boeynants I 28, Eyskens IV 29, Eyskens V 30, Leburton 31, Tindemans 32, Tindemans II 15

-3.656 *** -3.54 *** -5.708 *** -4.031 *** 10 -2.413 *** -.655 *** 5

33, Tindemans III 34, Tindemans IV 35, Van den Boeynants II 36, Martens I 37, Martens II 38, Martens III 15

-6.196 *** -4.212 *** -5.984 *** -5.369 *** 10 -5.542 *** -5.823 *** 5

39, Martens IV 40, M Eyskens 41, Martens V 42, Martens VI 43, Martens VII 44, Martens VIII 15

-6.929 *** -4.298 ***

10 -3.938 *** -5.441 *** -5.445 *** -1.749 *** 5

45, Dehaenen I 46, Dehaene II 47, Verhofstadt I 48, Verhofstadt II 49, Leterme I 50, Van Rompuy 15

-4.102 *** -6.767 *** -6.753 *** 10 -4.634 *** -5.578 *** -6.675 *** Predicted Policy Risk PayoffsRisk Policy Predicted 5 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5

51, Leterme II 52, Di Rupo 15 -6.676 *** -2.742 *** 10 5 -.5 0 .5 -.5 0 .5

Undercompensation in Portfolio Share

53, Eriksen I 54, Eriksen II 55, Hansen II 56, Kampmann I 57, Kampmann II -29.6 ***

20 13.222 *** -19.703 *** 15 -5.296 *** -1.257 *** 10 5

58, Krag I 59, Baunsgaard 60, Jorgensen IV 61, Schlüter I 62, Schlüter II

20 -22.811 *** -8.398 ***

15 -3.184 *** -3.886 *** -4.8 *** 10 5

63, Schlüter III 64, Schlüter IV 65, Schlüter V 66, Rasmussen I 67, Rasmussen II 20 15 -2.636 *** -4.601 *** -4.559 *** -8.758 *** -9.153 *** 10 5

68, Rasmussen III 69, Rasmussen IV 70, A Rasmussen I 71, A Rasmussen II 72, A Rasmussen III 20

15 -7.212 *** -3.314 *** -1.583 *** -3.752 *** 1.246 *** 10 5

Predicted Policy Risk PayoffsRisk Policy Predicted -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2

73, L Rasmussen I 74, Thorning-Schmidt I 75, Thorning-Schmidt II 20 -8.936 *** 15 -9.226 *** -5.23 *** 10 5 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2

Undercompensation in Portfolio Share

76, Paasikivi IV 77, Pekkala 78, Kekkonen I 79, Kekkonen II 80, Kekkonen III 81, Kekkonen IV 82, Törngren

15 -14.276 *** -16.647 *** 3.207 *** -13.026 *** -4.193 ***

10 -3.845 *** -4.694 *** 5

83, Kekkonen V 84, Fagerholm II 85, Sukselainen Ic 86, Sukselainen Ib 87, Fagerholm III 88, Karjalainen I 89, Virolainen

15 -10.248 *** -10.001 *** -8.271 *** -7.084 *** -5.551 *** -1.868 *** -5.783 *** 10 5

90, Paasio I 91, Koivisto I 92, Karjalainen Iia 93, Karjalainen Iib 94, Sorsa I 95, Miettunen II 96, Miettunen III

15 -16.84 *** -8.789 *** -13.191 *** -4.732 *** -2.775 ***

10 -3.541 *** -3.169 *** 5

97, Sorsa II 98, Sorsa III 99, Koivisto II 100, Sorsa IV 101, Sorsa V 102, Sorsa VI 103, Holkeri a 15

-9.557 *** -8.472 *** -.273 -3.981 ***

10 -2.004 *** -4.155 *** -1.135 *** 5

104, Holkeri b 105, Aho a 106, Aho b 107, Lipponen 108, Lipponen II 109, Jäätteenmäki I 110, Vanhanen I 15 -14.919 *** -.982 *** -6.514 *** -8.075 *** -6.711 ***

10 -6.148 *** -6.325 *** Predicted Policy Risk PayoffsRisk Policy Predicted 5 -.2 0 .2 .4

111, Vanhanen II 112, Kiviniemi 113, Katainen I 114, Katainen II 115, Stubb I 116, Stubb II 15

-3.648 *** 10 -7.603 *** -5.502 *** -4.254 *** -4.324 *** -3.387 *** 5 -.2 0 .2 .4 -.2 0 .2 .4 -.2 0 .2 .4 -.2 0 .2 .4 -.2 0 .2 .4 -.2 0 .2 .4

Undercompensation in Portfolio Share

117, Debré 118, Pompidou I 119, Pompidou II 120, Pompidou III 121, Pompidou IV 122, Couve de Murville -7.978 *** 12 -7.068 *** 10 -8.635 *** -5.674 ***

8 2.631 *** 4.47 *** 6 4

123, Chaban Delmas 124, Messmer I 125, Messmer II 126, Chirac I 127, Barre I 128, Barre II -6.725 *** 12 -8.722 ***

10 -1.918 *** -5.184 *** -1.962 *** 8 1.656 *** 6 4

129, Mauroy II 130, Chirac II 131, Balladur 132, Juppé 133, Jospin 134, Raffarin II -13.644 *** 12 4.319 *** -.163 10 -5.642 *** -2.028 *** 8 5.283 *** 6 4

135, de Villepin I 136, Fillon I 137, Fillon II 138, Fillon III 139, Ayrault I 140, Ayrault II -13.553 *** 12

10 -2.222 *** -4.573 *** 8 -.098 -1.969 *** -1.714 *** 6 4

Predicted Policy Risk PayoffsRisk Policy Predicted -.5 0 .5

141, Valls I 142, Valls II 143, Valls III 144, Cazeneuve 145, Philippe II 12 10 -5.053 *** -5.213 *** -3.602 *** -3.613 *** 8 -.946 *** 6 4 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5

Undercompensation in Portfolio Share

146, Adenauer I 147, Adenauer II 148, Adenauer III 149, Adenauer V 150, Adenauer VII

20 -16.392 *** 15 -3.271 ***

10 -.741 *** -2.324 *** 1.184 *** 5

151, Adenauer IX 152, Erhard I 153, Erhard II 154, Kiesinger 155, Brandt I 20 15 -2.353 *** -1.098 *** 1.412 ***

10 1.024 *** -2.434 *** 5

156, Brandt II 157, Schmidt I 158, Schmidt II 159, Schmidt III 160, Kohl I 20 15 -5.184 *** -6.58 *** -11.125 *** -4.134 *** -4.553 *** 10 5

161, Kohl II 162, Kohl III 163, Kohl V 164, Kohl VI 165, Schroeder 20 -21.263 *** 15 -4.882 *** -6.328 *** -7.345 *** -4.28 *** 10 5 Predicted Policy Risk PayoffsRisk Policy Predicted

166, Schröder II 167, Merkel I 168, Merkel II 169, Merkel III 170, Merkel IV 20 15 -5.89 *** -4.596 *** 1.254 *** -2.261 *** -3.389 *** 10 5 -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4

Undercompensation in Portfolio Share

171, Cameron I 7.165 7.16

-3.376 *** 7.155 Predicted Policy Risk PayoffsRisk Policy Predicted 7.15

-.002 -.001 0 .001 .002

Undercompensation in Portfolio Share

172, Zolotas 173, Papademos I 174, Papademos II

10 -7.105 *** 9 -8.01 *** -5.242 *** 8 7 6

175, Samaras I 176, Samaras II 177, Tsipras I 10 9

8 -2.89 *** Predicted Policy Risk PayoffsRisk Policy Predicted -4.488 ***

7 -1.26 *** 6 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2

Undercompensation in Portfolio Share

178, Johannesson I 179, Hallgrimsson 180, Johannesson II 181, Thoroddsen 182, Hermansson I

10 -8.254 *** -4.124 ***

8 -.496 ** .266 -3.405 *** 6 4

183, Palsson 184, Hermansson II 185, Hermansson III 186, Oddsson I 187, Oddsson II -4.468 *** 10 -1.201 *** -5.775 *** -5.272 ***

8 .809 *** 6 4

188, Oddsson III 189, Oddson IV 190, Ásgrímsson 191, Haarde I 192, Haarde II

10 -4.81 *** -1.124 *** -3.522 *** -1.996 *** -1.821 *** 8 6 4 -.5 0 .5

Predicted Policy Risk PayoffsRisk Policy Predicted 193, Sigurdardottir I 194, Sigurdardottir II 195, Gunnlaugsson 196, Johannsson 10 -6.97 *** -6.946 *** -6.946 ***

8 -1.036 *** 6 4 -.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5

Undercompensation in Portfolio Share

197, Costello II 198, FitzGerarld I 199, FitzGerald II 200, Haughey IV 25 20 -23.566 ***

15 -19.204 *** -9.492 ***

10 -2.789 *** 5

201, Reynolds I 202, Reynolds II 203, Bruton 204, Ahern I 25 20 15 -12.292 *** 2.145 *** -4.18 *** 10 -3.756 *** 5

205, Ahern II 206, Ahern III 207, Cowen 208, Kenny I 25 Predicted Policy Risk PayoffsRisk Policy Predicted 20 15

-10.142 *** -11.735 *** 10 -1.904 *** .162 5

-.5 0 .5 -.5 0 .5 -.5 0 .5 -.5 0 .5

Undercompensation in Portfolio Share

209, De Gasperi II 210, De Gasperi III 211, De Gasperi IV 212, De Gasperi V 213, De Gasperi VI 214, De Gasperi VII 215, Scelba

20 -24.255 *** 15 -8.624 *** -10.641 *** -3.689 ***

10 2.57 *** -2.439 *** -2.604 *** 5

216, Segni I 217, Fanfani II 218, Fanfani IV 219, Moro I 220, Rumor I 221, Rumor III 222, Colombo 20 15 -5.739 *** -4.051 *** -5.841 *** -5.093 *** -8.624 *** 4.048 *** -.403 * 10 5

223, Andreotti II 224, Rumor IV 225, Rumor V 226, Moro II 227, Andreotti IV 228, Cossiga I 229, Cossiga II 20 15 -4.844 *** -9.762 *** -.154 -3.13 *** -2.606 *** 10 -3.278 *** -2.37 *** 5

230, Forlani 231, Spadolini 232, Fanfani V 233, Craxi 234, Goria 235, De Mita 236, Andreotti V 20 15

-4.054 *** -3.542 *** -4.546 *** 10 -1.936 *** -9.828 *** -2.433 *** -6.439 *** 5

237, Andreotti VI 238, Amato 239, Ciampi b 240, Prodi 241, Berlusconi IV 242, Letta I 243, Letta II 20 -13.95 *** -14.857 *** 15 -14.294 *** -7.471 *** -4.914 *** -10.691 *** -3.033 *** 10 Predicted Policy Risk PayoffsRisk Policy Predicted 5 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2

244, Renzi I 245, Renzi II 246, Gentiloni -22.28 *** 20 -24.61 *** -22.25 *** 15 10 5 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2

Undercompensation in Portfolio Share

247, Werner I 248, Werner II 249, Werner III 250, Thorn

12 -3.85 ***

10 -.651 *** 4.583 *** -2.492 *** 8 6

251, Werner IV 252, Santer I 253, Santer II 254, Santer III

12 -8.462 ***

10 -3.651 *** 1.05 ***

8 -1.677 *** 6

255, Juncker 256, Juncker II 257, Juncker III 258, Juncker IV 12

10 1.312 *** -.34 1.029 ***

8 -1.264 *** 6

-.5 0 .5 -.5 0 .5 -.5 0 .5

Predicted Policy Risk PayoffsRisk Policy Predicted 259, Bettel 12

10 3.808 *** 8 6

-.5 0 .5

Undercompensation in Portfolio Share

260, Beel I 261, Drees I 262, Drees II 263, Drees III 264, Drees IV 12 -6.415 *** -3.528 *** 10 -4.859 *** -3.689 ***

8 3.183 *** 6

265, De Quay 266, Marijnen 267, Cals 268, De Jong 269, Biesheuvel I 12

10 -4.454 *** .465 ** -4.242 *** 8 -3.22 *** -2.172 *** 6

270, Den Uyl 271, Van Agt I 272, Van Agt II 273, Lubbers I 274, Lubbers II 12

10 -4.146 *** -6.763 *** -4.868 *** 8 -4.485 *** -2.283 *** 6

275, Lubbers III 276, Kok I 277, Kok II 278, Balkenende I 279, Balkenende II 12

10 -8.53 *** -3.426 *** -3.637 *** -8.289 *** -6.612 *** 8 6

Predicted Policy Risk PayoffsRisk Policy Predicted -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4

280, Balkenende IV 281, Rutte I 282, Rutte II

12 -14.759 *** -9.743 *** 10

8 -2.315 *** 6

-.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4

Undercompensation in Portfolio Share

283, Lyng 284, Borten I 285, Borten II 286, Korvald 12 10

-7.528 *** -11.495 ***

8 -4.505 *** -3.217 *** 6

287, Willoch II 288, Willoch III 289, Syse 290, Bondevik I 12

10 -8.803 *** -6.102 *** -5.224 *** 8 2.501 *** 6

-.4 -.2 0 .2

291, Bondevik II 292, Stoltenberg II 293, Stoltenberg III 12 Predicted Policy Risk PayoffsRisk Policy Predicted 10 -7.887 *** -4.245 *** -7.345 *** 8 6

-.4 -.2 0 .2 -.4 -.2 0 .2 -.4 -.2 0 .2

Undercompensation in Portfolio Share

294, Soares II 295, Soares III 296, Barroso 9 -6.182 *** -7.548 ***

8 -2.582 *** 7 6 -.2 0 .2 297, Lopes 298, Coelho I 9 8 Predicted Policy Risk PayoffsRisk Policy Predicted -2.717 *** -2.565 *** 7 6 -.2 0 .2 -.2 0 .2

Undercompensation in Portfolio Share

299, Erlander III 300, Erlander IV 301, Erlander V 302, Fälldin I

12 -8.107 ***

10 .702 *** -1.041 *** -3.022 *** 8 6

303, Fälldin II 304, Fälldin III 305, Bildt 306, Reinfeldt I 12 10 -4.701 *** -6.083 *** 8 -.426 * -.042 6

-.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4

307, Reinfeldt II 308, Löfven I 12 Predicted Policy Risk PayoffsRisk Policy Predicted 10

8 -1.93 *** -4.23 *** 6

-.4 -.2 0 .2 .4 -.4 -.2 0 .2 .4

Undercompensation in Portfolio Share

APPENDIX I: Measurement Error Sensitivity Analysis

One component of our undercompensation variable—bargaining power—is itself an estimate produced by another model (specifically, the model of government formation shown in SI Appendix F). As such, it is clearly measured with some degree of error, which could lead to biased parameter estimates in our model of policy risk. Our preferred approach to dealing with the issue of measurement error is to conduct a sensitivity analysis (see, e.g., Blackwell, Honaker and King 2017), which we do in three steps. First, we create a number of multiple alternative datasets based on the point estimates and standard errors from the government formation model. More specifically, for each of the 9 government formation model covariates shown in SI Appendix F, we randomly draw a coefficient estimate from a normal distribution that has a mean equal to the corresponding covariate’s coefficient estimate and a standard deviation equal to its standard error, and we then use these new estimates to generate new predictions of coalition formation probabilities. Second, using these new predictions, we calculate for each government party new relative exit probabilities (i.e., new estimates of bargaining power), and consequently new estimates of Undercompensation in Portfolio Share. We repeat these two steps 100 times to produce 100 alternative datasets. Third, we reestimate our model on each of these datasets and compare the results to those from Table 3 in the main text. We present the results of the sensitivity analysis in Figure 7 in the text. 50

APPENDIX J: Estimation of Table 3 using Normalized Banzhaf Index

In this appendix, we conduct an ancillary analysis in which we substitute a leading alternative index of bargaining power for our model-derived measure. Speciﬁcally, we compute the normalized Banzhaf power index for the 910 parties in our sample, which is equal to the number of times a party is a pivotal member in the set of winning (i.e., majority) coalitions in the legislature divided by the total number of times any party is pivotal (this ratio is then normalized so that it sums to unity across government parties). We then recreate our undercompensation variable by subtracting portfolio share from the normalized Banzhaf index of bargaining power. In Table J1 below, we present estimates from our multilevel model using this alternative power measure (note, however, that we have to assume two restrictions on the covariance parameters in this case, as noted in table). Although we prefer our more comprehensive measure of bargaining power for substantive reasons, we are reassured by the striking simi- larity between the results using the normalized Banzhaf index and those from Table 3 in the main text. 51

Table J1. Eﬀect of Portfolio Undercompensation on Policy Risk

Explanatory Variables Estimates

Undercompensation in Portfolio Share (Banzhaf index) (upsb) -5.684 ∗∗∗ (1.005) Distance from Coalition Center of Gravity (dccg) 0.797 ∗∗∗ (0.039) Intercept (α) 3.661 ∗∗∗ (0.295)

σ2(upsb) 88.024 (16.967) σ2(dccg) 0.098 (0.020) σ2(α) 10.531 (1.727) σ(dccg, α) -0.998 (0.171) σ2(residual) 4.076 (0.354)

Displayed are maximum likelihood coefficient estimates and standard errors from a multilevel random coefficients model (with no constraints imposed on the covariance matrix, except for σ(upsb, α) and σ(upsb, dccg), which are not estimable and are thus constrained to zero). Dependent variable: Portfolio-adjusted policy risk payoffs. N: 910 coalition parties (nested in 308 bargaining situations). A likelihood ratio test against a linear model with fixed coefficients leads us to reject the null hypothesis of no difference between the models (p < 0.001). Significance levels for level-one parameters: ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%. 52

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