Why Democracies May Actually Be Less Reliable Allies

Erik Gartzke Columbia University Kristian Skrede Gleditsch University of California, San Diego

Recent research builds on the observation that democracies have more durable alliances to argue that democracies make more reliable allies. This need not be the case. Alliances serve as commitment devices, adding ex ante credibility to states’ claims about ex post behavior. Variation in alliance durability must reflect differences in the desirability of formalizing alignments. Put simply, democracies are “most improved” by formal commitments. We offer two related explanations for why democracies might actually be less reliable alliance partners. Information costs for participating in policymaking and the advantages of organized interest groups combined with distributional incentives generated by the periodic turnover of governments may conspire to make informal commitments on the part of democracies problematic. Determining the net effect of democratic virtue and vice is best done empirically. We test alliance reliability by focusing on intervention, rather than on the duration or the number of commitments. Our results suggest that democracies make less reliable allies.

ontemporary wisdom in international relations contingent and thus leading to less reliability as partners holds that democracies make more reliable al- than stable autocracies (Kennan 1996, 135–36). Claims of Clies. Public review and ratification of interna- democratic reliability also appear to be in logical tension tional agreements, combined with respect for interna- with explanations for the democratic peace that empha- tional law, are said to fashion formal commitments that size the ability of citizens to veto the mobilization deci- are effectively binding on democracies. As evidence, re- sions of political elites. searchers point out that democracies tend to ally together The recent contest in Iraq highlights the impact of and that alliances involving democracies are more durable regime type on foreign policy. Bush administration offi- (see Cowhey 1993; Gaubatz 1996; Reed 1997). This view cials initially sought significant assistance from U.S. allies. of the effectiveness of democratic commitments repre- Contrary to the notion that democratic publics encourage sents a remarkable break with the more pessimistic con- adherence to international commitments, popular oppo- ception that held sway previously. Earlier observers of- sition to U.S. plans for a war led many continental democ- ten argued that democracies are “mercurial.” Executives racies to interpret their NATO obligations as narrowly as in democracies are necessarily reliant on shifting public possible.1 Similarly, while the “Arab street” voiced em- opinion and transient coalitions, making commitments phatic condemnation of U.S. policy, democratic Turkey,

Erik Gartzke is Associate Professor of Political Science and the Saltzman Institute of War and Peace Studies, Columbia University, Inter- national Affairs Building Room 1326, 420 West 118th Street, New York, NY 10027 ([email protected]). Kristian Skrede Gleditsch is Assistant Professor of Political Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0521, and Research Affiliate, Centre for the Study of Civil War, International Peace Research Institute Oslo (PRIO) ([email protected]). We thank Scott Bennett, Bruce Bueno de Mesquita, John Conybeare, Havard˚ Hegre, Pat James, Dong-Joon Jo, Kelly Kadera, Andrew Kydd, David Lalman, James Morrow, Michael Mousseau, Forrest Nelson, Hilde Ravlo, Dan Reiter, David Rousseau, Michael Simon, Alastair Smith, Gerald Sorokin, Maura Stevenson, Wayne Steger, Richard M. Tucker, and Michael D. Ward. Special thanks are due to Brett Ashley Leeds for estimating our model on the new, unreleased post-1944 version of the Alliance Treaty Obligations and Provisions (ATOP) data. Erik Gartzke would like to thank the Institute for Social and Economic Research and Policy (ISERP) at Columbia University for financial support. 1In February 2003, for example, NATO members exhibited severe disagreement over a plan to dispatch military equipment to Turkey. Ankara took the unprecedented step of invoking article 4 of the NATO treaty, which requires members to “consult together when, in the opinion of any of them, their territorial integrity, political independence or security is threatened.” France, Germany, and Belgium blocked assistance on the grounds that there was no threat to Turkey. U.S. authorities charged that opponents had given way to domestic public opinion and neglected their NATO duties. U.S. Secretary of Defense Rumsfeld complained of a “truly shameful” dereliction of NATO’s obligation to defend Turkey, and U.S. NATO Ambassador Burns declared that “NATO is now facing a crisis of credibility.” American Journal of Political Science, Vol. 48, No. 4, October 2004, Pp. 775–795

C 2004 by the Midwest Political Science Association ISSN 0092-5853

775 776 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH a close ally of long standing, was the lone U.S. ally in the the determinants of alliance behavior suggests a com- region to refuse all U.S. requests.2 plex relationship between regime type and reliability in The Anglo-French response to German annexation which democracies offer both benefits and burdens as of Czechoslovakia in 1939 provides the classical example security partners. We believe that existing accounts suf- of democratic unreliability. Czechoslovakia and France fer in at least two ways. First, the literature ignores the had concluded a defense pact, while Britain had publicly possibility that states have different incentives to ally. Dif- guaranteed the integrity of Czechoslovakia. Although the ferences in alliance behavior by regime type could be due German attack in principle should have precipitated a to variation in supply (democracies are more reliable, and war among the three powers, neither Britain nor France thus more sought after as allies) or demand (democracies replied with force. France tendered a letter of protest af- are less reliable, and so have more need to institutional- ter Hitler moved to occupy all of Czechoslovakia. Britain ize their security partnerships). If regimes differ in their offered the legal ruse that it was not obliged to intervene utility for alliances more than they differ in their abil- since the declaration of Slovak independence terminated ity to honor commitments, then democratic alliance be- thestatewhoseterritorialintegrityithadguaranteed.Pop- havior may reflect relative unreliability. Second, existing ular opposition to war thwarted the ability to maintain arguments exaggerate democratic virtues. Popular rati- security commitments by the two democracies, leading fication of alliance treaties may augment commitment, to abandonment of Czechoslovakia.3 but other features of democracy hinder reliability. Effec- Just as World War II was preceded by failed demo- tive monitoring of government requires knowledge of the cratic commitments, the previous “great war” was pre- relationship between policies and outcomes. Yet, the pay- cipitated in part by ambiguity over Britain’s obligation off for being attentive to policy evaporates as individual to France. A number of signals led German planners to votes become inconsequential in the large selectorates that discount British resolve to intervene (Lebow 1981; Levy characterize democracy.4 Although the broader public is 1990). Word that British Foreign Secretary Grey had au- attentive during crises, organized interests are likely to thorized preliminary talks with French military officials have disproportionate influence over the abstruse details designed to develop a contingency plan for joint mobiliza- of treaty provisions. The relative impact of public opinion tion resulted in calls for his resignation. Grey was forced to and interest groups fluctuates along with issue salience, so publicly disavow British support for France, even though that commitments stand different tests at different times the entente clearly contemplated such an effort (Fergu- in democracies. Similarly, regular leader replacement en- son 1999, 56–81). In spite of formal guarantees of Belgian courages incumbents to institutionalize policy.5 While in- neutrality dating back to 1839, public opposition in the stitutions buttress the status quo, tensions between the in- U.K. to the draft and to any increase in defense spending terests of the administration that forges an alliance and led German officials to expect that British involvement the government that chooses whether to honor an agree- in the war could be made redundant by rapid mobiliza- ment can lead democracies to be more brittle as security tion and decisive defeat of France (the Schlieffen plan). partners. Reiter and Stam argue that “[t]he events of the July cri- As the preceding anecdotes suggest, governments that sis leading to World War I clearly illustrate the problem are answerable to popular preferences face a dilemma that democracies face: potential aggressors do not believe when confronted by unpopular alliance commitments. that democracies’ commitments to come to the aid of one Attending to domestic demands will occasionally anger another are credible” (2002, 101). strategic partners, while contradicting the wishes of cit- Contemporary optimism about democratic alliance izens is only ever easy when the public has little say. We behavior is probably a healthy response to the excessive develop two formal models of reliability and regime type pessimism of the past. Still, a thorough examination of based on reselection of governments and special interests. The net effect of the perceived advantages and the less 2Saudi Arabia and the Persian Gulf autocracies chose to interpret their treaty obligations differently, providing access, basing rights, and other support, without which U.S. plans would have foundered. 4Bueno de Mesquita et al. (1999) examine how varying the size of

3 selectorates and of winning coalitions influences policy. They argue Bullock argues that Hitler’s “skill in diagnosing the state of pub- that large winning coalitions (i.e., democracies) make it harder to lic opinion” allowed him to anticipate that “France and Great buy off constituents with private goods (side payments, etc.). Britain, in their anxiety to avoid war, were prepared to go to great lengths to prevent the Czechs invoking the guarantees they had 5Alliances often exist for long periods. Democratic leaders are gen- been given” (1955, 402–3). A leader in The Times suggesting that erally in office for shorter periods than autocrats (see Bueno de Czechoslovakia should cede the Sudetenland to Germany signaled Mesquita and Siverson 1995). Autocratic successors are also often widespread opposition to war. This effect of mass media is inten- proteg´ es´ of the autocrat, binding identities together and internal- tionally precluded in autocracies (see Van Belle 1997). izing reputation across generations. REGIME TYPE AND ALLIANCE COMMITMENT 777 sanguine notion of “mercurial” democracies is difficult wield disproportionate influence in democratic politi- to ascertain deductively. Instead, we let empirical analysis cal processes by providing needed resources to leaders. adjudicate the respective impact of countervailing forces Special interests will be most influential when salience is affecting alliance reliability. We find that democracies are skewed (some groups care intensely about an issue while less likely than other regimes to intervene in wars on behalf most others do not), or when policy involves complex of allies. technical issues where the price of informed participa- The elements of our two related arguments will be fa- tion is relatively high. A change in the salience or com- miliar to any student of political science. Arrow’s (1951) plexity of issues, however, will alter political participation possibility theorem tells us that it is impossible to prevent and shift winning policy outcomes. Advocates have an in- cycling over policy in any representative system. Over centive to formalize policy to block the impetus toward time, the social preference changes, even if individuals policy change following changes in political salience or preferences remain the same. Institutions limit the ef- the cost of participation. Special interests will play an im- fectsof cycling,butonlybysomewhatarbitrarilyassigning portant role in fashioning alliance commitments when winners and losers in the political process. Determining the salience of such issues is relatively low, but salience the rules by which decisions are made is thus inherently will increase when alliance commitments are called upon. strategic. Of course, the same should be true in foreign Efforts to institutionalize temporary political advantage policy.Alliancecommitmentsthatconstrainfuturechoice cannot be absolutely irreversible without contravening making limit the tendency of democratic policies to cy- majority rule. The ability of special interests to leverage cle unpredictably, but they can do so only by limiting the foreign policy through formal commitments also means responsiveness of a government to its citizens. that democratic alliances are subject to domestic opposi- We accept that alliance commitments increase the tion, and thus to failure. probability that alignments will be upheld. However, this In the sections that follow, we first review the relevant begs the critical question of the baseline. Institutional- literature on alliances and democracy. Wethen discuss our izing agreements limits cycling, but only to the extent argument, presenting elements of two game theoretical that it limits representation. Institutions are most de- models that formalize our claims about democratic poli- sirable in situations where those in power fear that fu- tics and alliance commitments. In an empirical section, we ture choices challenge status quo interests. Democratic test alliance reliability using interventions by third-party cycling means that the informal promises of incumbent allies in interstate wars. governments must be treated with some suspicion by foreign powers. There is simply little reason for subse- quent governments to feel bound by the weak commit- Linking Regime Type ments of previous administrations. The prospect that and Alliance Reliability future governments will prefer dissimilar policies, and the effect of institutions in constraining choice, make Why should one expect the behavior of countries in al- it appealing for incumbent administrations in democ- liances to differ by political regime type? Linkages be- racies to formalize their preferred policies, foreign or tween alliance behavior and domestic politics have re- domestic. Democracies will tend to formalize interna- ceived considerable attention in the wake of research on tional agreements in an attempt to generate greater sta- the democratic peace. Siverson and Emmons (1991) find bility and to overcome cycling, but this will only produce that democracies are more likely to ally between 1946 and more reliable allies to the degree that democratic govern- 1965, though not during other historical periods. Simon ments are unresponsive to shifting popular preferences. and Gartzke (1996) argue that dissimilar regimes appear We find it implausible that democracies pay less attention to prefer to co-ally. Lai and Reiter (2000) report that sim- to the evolving preferences of their constituents than do ilar regimes are less likely to ally prior to World War II, autocracies.6 but that democracies co-ally more often during the Cold Research on special interest groups and issue salience War. suggests a second way to explain change that leads to Some researchers assert that institutional features democratic unreliability. Special interest groups often make democracies generally more likely to honor commit- ments. Cowhey argues that a system of division of powers, with each branch having a veto over policy, “makes it po- 6 Schelling (1960) makes it clear that commitment involves an in- tentially harder to initiate new commitments but easier to ability to alter one’s policies. For democracies to be more reliable, their leaders must be more tightly bound by prior agreements and maintain them” (1993, 306). Gaubatz (1996) holds that less responsive to constituents than autocrats. institutional constraints make democracies better able to 778 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH keep security commitments. Public debate over policies analysis with more advanced estimation techniques and in democracies mobilizes popular support. Democracies improved research design. by their nature must deliberate in a manner making com- We are skeptical as to whether these empirical tests mitments more complete. The “transparency” of liberal of alliance durability provide a basis for concluding that commitments and the role of democratic institutions in democracies are more reliable allies. Bennett’s test con- binding citizens to their promises are seen as key factors siders democracy as an attribute of an alliance, summed making democracies more reliable. over all alliance members and years of existence, and of- A final argument linking democracy and alliance fers at best limited evidence that democratic alliances commitments involves the role of the mass public in hold- last longer. The second set of tests seem weakly related ing leaders accountable for their actions. The need for to the theoretical rationale, presented as monadic state- democratic leaders to maintain public approval makes it ments about democracies, as they consider the dyadic difficult to act contrary to public opinion. Fearon (1994) duration of a democracy’s alliance with another democ- develops a crisis bargaining model where liberal leaders racy, not their ability to commit to stable alliances with can signal resolve through the “audience costs” they may other states. Gaubatz (1996), for example, finds no evi- incur for backing down in international crises. Such audi- dence that the duration of a democratic state’s commit- ence costs can enhance the reliability of informal and for- ment to an ally in general differs from that of autocracies. mal commitments. Smith argues that democracies “face Gaubatz surmises that the dyadic nature of the relation- higher domestic costs for failing to honor alliance com- ship between democratic institutions and alliance dura- mitments ...[and] should be more reliable alliance part- bility stems from “the distinctive preferences democratic ners” (1996, 28–29). states may hold for maintaining their relationships with Existing studies have attempted to measure alliance each other or ...the institutional elements that develop in performance or reliability in several ways. One line of the relationships between democratic states” (1996, 135). research examines alliance durability as an indicator of Institutionalized organizations tend to perpetuate them- performance. Morrow (1991) develops a theory on al- selves, and alliances that have lasted a long time are more liance formation based on tradeoffs between autonomy likely to endure (see Bennett 1997). This is sometimes and security (see also Altfeld 1984). Based on his theory, offered as an explanation for why NATO persists in the he reasons that asymmetric alliances, where one part- seeming absence of enemies (e.g., Haftendorn, Keohane, ner seeks greater security while the other seeks more and Wallander 1999). But duration in this sense is not nec- autonomy, should prove more durable than symmetric essarily indicative of the strength of commitments or the alliances. He finds that alliances between militarily weak security provisions of the alliance. Finally, since a democ- and strong states endure an average of three-and-a-half racy/nondemocracy dichotomy ignores differences in po- years longer than symmetric alliances (Morrow 1991, litical orientation among autocracies and many changes 922). that may result in realignment, these tests are probably Recent research on democracy and commitment has biased in favor of democratic similarity.7 Durable auto- used alliance duration as a measure of the strength of crats may have alliance commitments that are as stable as commitments. Bennett (1997) tests whether democracy democracies. Overall, we conclude that the existing stud- enhances the duration of alliances at the level of the al- ies on durability yield little evidence that democracies are liance itself. Bennett assesses the extent of democracy by generally better able to commit than other states. “the proportion of alliance member-years in which allies Other researchers assess alliance performance or were liberal” (1997, 868). Although he finds some evi- reliabilitybyexaminingwhetheralliesfulfillmilitarycom- dence that more democratic alliances tend to last longer mitments during contests. In an analysis of the Cor- than less democratic alliances when using the Doyle relates of War (COW) project’s alliance and war data, democracy measure, there is no support for a relation- Sabrosky (1980) finds that allies often fail to assist part- ship between durability and regime type using the Maoz ners in wartime. He concludes that alliances are generally and Russett (1993) joint democracy index based on the Polity data. 7Although institutional change may augur change in political ori- Other studies examine durability in alliance dyads. entation and realignment (see Siverson and Starr 1994), changes in political orientation need not result in institutional change. Many Gaubatz (1996, 128–33) tests whether democracies are major political changes are not reflected in measures of democracy better able to commit by looking at the duration of al- such as the Polity data. For example, when the Shah fell in 1979, liances. His analysis indicates that alliances in democratic Iran ended its membership in an entente with Turkey, the United Kingdom, Pakistan, and the United States. Iran’s Polity score in- dyads tend to last longer than in dyads where at least creases from a value of 1 before the revolution to 2 and does not one party is autocratic. Reed (1997) replicates Gaubatz’s reflect the dramatic change in orientation. REGIME TYPE AND ALLIANCE COMMITMENT 779 unreliable as deterrence mechanisms. Leeds, Long, and ing empirical studies—if not necessarily the conventional Mitchell (2000) note that alliances often entail commit- wisdom—are consistent with the argument we advance ment to actions other than intervention, such as consulta- in this article. Both the ATOP and the COW alliance data tion in the event of certain contingencies. Even commit- indicate that democratic states are less likely to fulfill their ments to intervene are often highly specific: a state may alliance commitments in wars than autocratic states over for example only be required to help its ally in the event the period 1816–1991. Unlike the earlier studies, how- of attack by particular third parties. Using new data that ever, we offer an explanation for why democracies face codes the specific commitments and contingencies, enti- problems in carrying out commitments. tledTheAllianceTreatyObligationsandProvisions (ATOP) Looking at crisis behavior has some advantages over project, Leeds, Long, and Mitchell (2000) offer a more op- measures of duration, as intervention more clearly con- timistic view of alliance effectiveness, as allies carry out stitutes situations where alliance commitments or pledges their commitments about 75% of the time over the period of support come into play. However, as some researchers 1816–1944. However, Leeds and Gigliotti-Labay (2003, point out, looking at alliance behavior in disputes may 31) find substantially lower reliability for commitments be vulnerable to selection problems relating to the abil- to intervene in the ATOP data for the period 1816–1991, ity of alliances to deter aggression. Smith (1995; 1996) as allies only intervene in defense of their partners 52% argues that potential aggressors possess rational expec- of the time. tations about the reliability of a state’s alliance partners. A number of recent studies examine the relationship Reliable allies discourage aggression while unreliable part- between democracy, alliances, and intervention in war. ners do not, hence the sample of disputes involving al- Werner and Lemke (1997) assess whether regime simi- liances overrepresents alliance failures. For selection to larity and alliances significantly predict intervention pat- influence our inferences about the behavior of the relia- terns in third-party disputes. Their analysis shows that bility of democracies in alliances, the share of “unreliable intervening states tend to join the side with the more sim- partners” among targeted alliances must differ systemati- ilar regime type and with which they share alliances. How- cally by regime type. We address the issue of selection bias ever, although formal alliance commitments discriminate in greater detail in our analysis, but find no evidence that which side autocracies intervene on, defense pacts do not selection bias can account for our results. exertstatisticallysignificanteffectsfordemocracies(1997, 538–39). Werner and Lemke consider only those states that actually intervene in ongoing wars and overlook all Theory: Regime Type states that potentially could have joined but decide not and Alliance Unreliability to intervene. Hence, their study cannot establish whether democracies are generally more or less likely to support We have noted that existing work on regime type and allies or other democracies in conflict. In another study, alliance performance is based on evidence of duration Reiter and Stam conclude that “democracies are not more that we find unpersuasive for demonstrating reliability or likely to intervene to save targeted democracies”,evenif presents results suggesting that democracies may not be the two democracies are allied (2002, 91, 106–13). Smith more reliable partners. In this section, we offer two ver- (1996) tests the proposition that democracies are more sions of a theory of democratic unreliability. We start by likely to honor alliances by intervening on the side of al- discussing some deficiencies in the treatment of alliances lies in ongoing wars. His empirical findings, however, con- in earlier research. tradict the hypothesized relationship, suggesting instead that democracies are less likely to honor commitments. A Alliances, Principal-Agency, dummy variable for democracy generally has a negative and Democracy and significant coefficient, indicating that democracies are less likely to assist their allies (see Tables 3 and 6, A major shortcoming in existing studies of regime type and Appendix Table 3a). Leeds (2003) finds that demo- and alliance behavior is the incomplete treatment of state cratic allies are more likely to intervene in the ATOP data motives. If democracies have more or more durable for- for the period 1816–1944. However, Leeds and Gigliotti- mal alliances, then it is likely that they use alliances in Labay (2003, 17)—using ATOP data for the longer period different ways than other regimes. 1816–1991—find that only 34% of the leaders of demo- States often make promises that later they prefer cratic systems who find an alliance invoked by war ful- not to keep. Commitment problems arise when incen- fill their commitment, in comparison to 57% of leaders tives ex ante to make promises about ex post behavior in nondemocratic systems. Hence, the findings in exist- clash with the incentives ex post to act on promises made 780 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH ex ante. A simple promise of security assistance may suc- operate, then they may more often align.10 Yet, if democ- ceed in deterring foreign aggressors or mollifying friendly racies are better able to cooperate through alignments, states. Yet, the incentives to avoid the costs of using force they should have less need for formal alliances. Similar can make potential challengers and partners suspicious interests predict alignment, but whether alignments re- of such promises. The pooling of genuine and insincere sult in alliances depends on whether states need to bolster promises in informal security agreements (alignments) their commitments. We argue that attributes of demo- can undermine deterrence and lead to bargaining failures. cratic institutions make democracies more reliant on for- Military alliances act as commitment devices, en- mal commitments than other regime types. The fact that hancing the credibility of promises to intervene by more democracies rely on formal alliances, then, should not closely tying a state’s reputation for reliability to its ac- be seen as an indicator of strength, but rather as a sign tions.8 The value of a reputation potentially forces states of the prevalence of problems with informal democratic to abide by commitments that might otherwise not be car- commitments. ried out. States that abandon commitments find it more The agency inherent in democracy exacerbates the difficult to conduct credible diplomacy through words problem of commitment, since the actor promising ac- and may need to resort more often to military deeds. This tion is likely to differ from the actor who must act. In gives states an incentive to honor commitments, particu- democracies, elections serve as the primary instrument of larly when agreements are formally documented. control, threatening executives with replacement should Existing studies have tended to treat alliances as con- they stray from the popular will (Smith and Hayes 1999). tracts between friends or expressions of similar interests. Periodic replacement of leaders enhances representation, There is a risk of conflating alignments, or informal com- but also separates the actors making commitments from mitments, with formal alliance commitments. If states are those who ultimately determine whether to honor com- unequivocal about their commitment to one another and mitments. Principal-agency is an efficient political mech- can cooperate informally, then there is less need for formal anism. It allows agents to specialize in government and promises to commit. Warring states eventually sign peace leaves the principal free to engage in other tasks. How- treaties precisely because enemies find value in detailing ever, this also means that agent preferences are imperfectly what friends take for granted. Alliances require formal- constrained by the principal, and the large selectorates in ization because parties have partly differing interests and a democracy imply a collective action problem. Members need to clarify their basis for cooperation (Morrow 1991, of the selectorate can only evaluate leader performance 2000). Forming alliances imposes costs on members, such once they are informed about the relationship between as autonomy loss, costs of integration, and higher vulner- policies and likely outcomes. Monitoring costs thus serve ability if abandoned to fight alone. Demonstrating a will- as an effective curb on the level of political participation. ingness to bear such costs can make commitments more Media and policy entrepreneurs can lower the cost of in- credible.9 formation, but the marginal product of being informed Many claims about democracy and cooperation ac- is extremely small under large constituencies. tually pertain to alignment rather than formal alliances. Formal commitment devices enhance the credibil- If democracies or similar regimes are better able to co- ity of commitments by linking promises more closely to actions. The more attenuated nature of democratic com- mitments implies a weaker link between reputation and 8Fearon (1997) differentiates between “tying hands” (commit- ment) and “sunk costs” (signaling). We see these as linked since action. Agency between leaders and their constituents, sunk cost alliances attach state reputation to ex post behavior. large selectorate size, and shifting coalitions can lead to 9A reviewer notes that our argument is akin to suggesting that peo- an inherent dynamism in policy formation that in turn ple who really love each other do not need to marry. Economists makes it more difficult for democracies to credibly com- such as Becker (1981) make precisely this point. Marriage indeed mit. Since democracies must be responsive to be demo- formalizes an underlying (informal) relationship. Lovers may pro- fess undying (and uncommitted) affinity, but individuals in a com- cratic, democracies fluctuate more in their policies than petitive mating market often face incentives to renege at some later politically stable autocracies. date. Marriage makes it more costly and difficult to part, but if Democratic institutions exist in large part to ad- there is love and loyalty to the point that two parties have undis- tinguishable preferences, then marriage can do little to improve dress the tension generated by the difference in interests outcomes. Indeed, men and women who are romantically involved between principals and agents. If democracies rely on often hesitate to suggest formal obligations precisely to avoid giving institutions in domestic decision making to address the impression that one harbors doubts about the relationship or the other’s commitment. A stable marriage may display additional advantages (e.g., joint ownership, joint cooking for two is more 10Leeds (1999) shows that similar regime types cooperate more than efficient, etc.), but these can be achieved without a formal contract. heterogeneous dyads. REGIME TYPE AND ALLIANCE COMMITMENT 781 collective action problems, then formal international temporarily hold power. If an incumbent administration agreementsshouldbeinterpretedasservingasimilarsetof chooses to renege on an alliance commitment, society as purposes. Formal agreements are developed when norms a whole may suffer from damage to the state’sreputa- are unlikely to suffice. Similarly, alliances are evidence of tion, while private benefits of abandonment (not having commitment problems, rather than a sign of reliability. to fight, continuing trade, etc.) can accrue to the incum- bent administration and its supporters. Democratic Cycling and Alliances are designed to overcome commitment Alliance Unreliability problems by making it costly for states to aban- don security partners. Intervention, however, is invari- Where modern researchers focus on cycling—the ten- ably subject to a state’s decision to honor its com- dency for winning coalitions to shift interminably—as mitments. Autocratic leaders face few limitations on a source of policy instability, Madison (1961 [1787]) in the use of force and thus have slightly less need to Federalist No. 10 saw a virtuous means of blunting the ally because they are less likely to make commitments tyranny of majorities. Cycling means that commitments that they do not expect to fulfill. High-value democratic are subject to future challenge in a democracy. Institu- coalitions have additional incentives to ally to encour- tions can minimize the effect of cycling by making poli- age subsequent administrations to intervene. Democratic cies “sticky,” and limit the ability of succeeding coalitions alliances can thus be interpreted as attempts to induce to replace existing policies. Gaubatz (1996) and others greater policy stability across time and space. identify this status quo bias as a feature of democratic We expect that the foreign policies of democracies institutions that enhance commitments. Yet, to be repre- display inherent instabilities that are particularly likely to sentative, institutions must allow popular preferences to show up in the change from decisions on alliance for- guide the selection of leaders and policies. Representative mation to decisions on intervention. For an ally, cycling democracy balances majority rule with protection of mi- necessarily makes democracies less predictable (and thus nority interests. Elections poll the public will, but only at less reliable) as a partner. When most needed, democra- relatively arbitrary points in time. Stability is achieved by cies may simply fail to show up.11 making government less responsive to the popular will. Democratic institutions thus embody a tension between Democratic Interest Groups populism and continuity, in which neither objective can and Alliance Unreliability be fully realized (see, e.g., Shepsle and Weingast 1981). Institutions limit change so that even policies not Even without cycling, political participants must be in- strictly preferred by a majority of citizens are often main- formed about foreign policies and outcomes and be will- tained. But although existing policies are maintained as ing to actively exert influence. Principal-agent analogies long as no significant momentum arises to revise policy, such as the two-level games metaphor rely on constituents the prospects of substantial cost (war, military mobiliza- to monitor and act (e.g., Putnam 1988). Although citizens tion) can clearly challenge status quo policies. Time and can display strong attitudes on some foreign policy issues, cycling yield coalitions weakly opposed to a given com- most of what we know about public opinion suggests that mitment, but unwilling to invest in the effort to annul citizens are often poorly informed and display little inter- the status quo. In a crisis, however, weak preferences turn est in foreign policy compared with domestic issues (e.g., into strong preferences. Wars are costly, so citizens have Aldrich et al. 1989; Sullivan and Borgida 1989; Almond incentives to reconsider commitments, even if interven- 1960). Information about foreign policy clearly fluctuates tion is “the law.” Further, winning coalitions can rarely be with issue salience and motivation. Complex foreign pol- projected much into the future, since even a small number icy issues such as the details of treaties are bound to be of issues yields a large number of possible winning coali- less carefully followed than the decision to go to war. tions. Whether liberal institutions are sufficiently robust Information and transactions costs impose a high to compensate for the effects of policy cycling in democ- threshold on political participation. The marginal value racies is then open to question. International commitments impose reputation costs 11Democracies could offer other advantages that balance unrelia- on states that abandon allies. The agency problem in bility, for example by offering more power and resources if they democracies, however, can make it particularly difficult do intervene (see Bueno de Mesquita et al. 1999; Choi 2003; Lake 1992). Reiter and Stam (2002) find that democracies do not win to rely on reputation as an enforcement mechanism. Rep- wars because of greater resources, although this does not directly utations are associated with states, not the coalitions that address aid to allies. 782 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH of voting decreases with selectorate size, while the costs of crats tend to believe that democracies’ requisite needs to attempting to influence policy are often flat or increase. generate public consent handcuff their leaders, prevent- Even very modest transactions costs can be prohibitive ing them from taking swift military action to defend their in large selectorates. Indeed, rational voting theory con- national interests” (2002, 101). cludes that it is often irrational for ordinary voters to cast a Key assumptions about public opinion and domestic ballot (Austen-Smith 1993). When the salience of issues is politics in the existing literature on regime type and al- low, high-value constituents can disproportionately influ- liance reliability seem questionable. Citizens are assumed ence decision making. Leaders who allocate public policy to actively participate in an alliance decision and then to maximize the probability of reelection can help them- deem the outcome binding on subsequent behavior. Op- selves more by catering to interest groups that supply positionpartiesmustrefrainfromseekingpoliticaladvan- campaign resources (Denzau and Munger 1986). Orga- tage by challenging intervention decisions. Voters must be nized groups have an informational advantage that lim- informed and actively involved in the minutia of fashion- its the ability of the median voter to effectively moni- inganalliancetreaty,butthenresignthemselvestoalliance tor leader performance (see Lohmann 1998). Journalistic obligationsatthemomentof war.Publicopiniondatasug- accounts often emphasize the role of special interest gests instead that war decisions are far more salient than groups in policy formation. Wheatcroft, for example, ar- alliance decisions. A September 1997 poll by the Pew Re- gues that NATO expansion “was inspired ...by [Clinton] search Center for the People and the Press, for example, re- ingratiating himself with ethnic lobbies. Historians will portedthatonly20%of U.S.respondentsfolloweddebates date NATO expansion to Clinton’s grovelling to a Polish- on NATO expansion and only 10% could identify a single American audience in Chicago” (2000, 15). In a more prospective member. Although respondents were largely academic vein, Kaempfer and Lowenberg (1988) outline supportive of maintaining NATO after the Cold War, only how interest groups shape economic sanctions. a narrow plurality wanted expansion, and supportive re- Issue salience determines the degree to which foreign spondents tended to cite broadly inclusive reasons such as policy in democracies can depart from public opinion “the larger the better.” In a crisis, such vague conceptions and be influenced by interest groups. If the preferences of seem destined to be recast in terms of the perfidy and high-value constituents diverge from that of the majority, back room wrangling of malevolent politicians. A realis- then the policies a state adopts will depend on the relative tic view of democracy must involve a recognition of the political weight of special interests and the salience of autonomy of citizens. Chanting “hell no, we won’tgo” is issues. High-value constituents will tend to have a greater at least as consistent with democracy as honoring foreign role in policy making when issues are abstruse, or when contracts.13 In some cases, breaking commitments may salience among the larger population is low. Policies will enjoy widespread popular support, and emerging leaders then fluctuate as consequences become more immediate sometimes campaign on promises to overturn decisions or obvious. of their predecessors.14 Explanations for the democratic peace emphasize In sum, if the decision to ally is less salient to the how liberal institutions constrain dispute involvement. public than war involvement, domestic support for an Leaders intent on war must rally public support by jus- alliance and for mobilization may differ dramatically. tifying the recourse to violence. Yet, Gaubatz (1996) and Alliance decisions that involve complex assessments of others suggest that democracies are unresponsive to pop- contingent events are more likely to reflect special inter- ular preferences when it comes to honoring alliance agree- ests, while domestic audiences will remain pivotal in the ments. It seems peculiar to argue that the use of force in choice to intervene. By contrast, autocratic commitment democracies is contingent upon public approval, but that follows from the more-or-less consistent preferences of domestic politics cannot influence the decision to inter- political elites. vene. Even if status quo policies are easier to maintain in democracies, mobilization for war is hardly politics as usual. The institutional features that make it easy to con- punish Iraq for obstructing UNSCOM had been delayed given the tinue existing policies make it difficult for democracies to need to first “properly educate the public.” act decisively in a crisis.12 As Reiter and Stam put it, “auto- 13Opposition to the U.S. defense pact with Vietnam was initially modest, but grew steadily as the cost of honoring the agreement became clear (e.g., Gartner and Segura 1998). 12Democracies often mobilize slowly: The U.S. Congress resisted 14“What you’re going to see under a Bush-Cheney administration military action against Iraq over the invasion of Kuwait even after is the narrowing of commitments ....” (Rep. John Kasich on NBC Bush secured UN and popular support. Similarly, in December News’ Meet the Press, 27 August 2000). Once in office, Bush moved 1998, U.K. Prime Minister Blair argued that the air campaign to quickly to reverse many of the previous administration’s policies. REGIME TYPE AND ALLIANCE COMMITMENT 783

FIGURE 1 The Alliance Game

N

A l~ l C C

f~~ f f f

A A 34

UA = - xA - k UA = - xA

UC = - xC UC = - xC t ~ t t ~ t

12 56

UA = pABC(2xA - xC) - xA - k - wA UA = pBC(2xA - xC) - xA - k - r UA = pABC(2xA - xC) - xA - wA UA = pBC(2xA - xC) - xA

UC = (pABC - 1)xC - wC UC = (pBC - 1)xC - wC UC = (pABC - 1)xC - wC UC = (pBC - 1)xC - wC

Modeling Regime Effects or not (∼t)ifB is attacked; B, the potential target, is a on Alliance Reliability nonstrategic actor; C, the potential attacker, uses force ( f ) or not (∼f ); N, “nature,” assigns A and C’s ideal points. Given players’ ideal points, no equilibrium exists where In this section, we provide three versions of a formal A seeks to ally and B does not. For this reason, and to model of alliance reliability. We first present a baseline simplify exposition, we therefore treat B as nonstrategic. (autocratic) model and then derive results for the cycling Assume states compete over outcomes on a unit do- andinterestgrouparguments.Allmodelsinvolvesimplifi- main (x, where [0 ≤ x ≤ 1]) representing issues, territory, cations and generalizations. One can assume that democ- etc. Players’ ideal points are as follows: A : x ∼ U[0,1/ ]; racies pay a higher price for abandoning allies and find A 3 B : x = 0, C : x ∼ U[2/ ,1]. The status quo ante, x , can that democracies less often abandon allies. Conversely, B C 3 SQ be anywhere in the domain, but with no loss of generality, one can assume that democracies experience higher war we assume x = 0. Figure 1 details the game (payoffs costs or that democracies discount reputation and show SQ are listed at terminal nodes). First, Nature (N) randomly that democracies are unreliable. Our approach is to pa- assigns A and C ideal points. We initially assume that rameterize costs and instead show how differences in ideal points are public information, but we later relax this structure affect outcomes. We model commitment us- assumption. Second, A decides to ally with B (l)ornot ing both full and asymmetric information. States ally to (∼l). Third, C decides to fight ( f ) or not (∼f ). Finally, A counter incentives not to intervene, enhancing deterrence intervenes (t) or not (∼t). C wins with probability p or providing bargaining leverage.15 ABC if A intervenes and with probability pBC if A does not in- ≤ < ≤ The Baseline (Autocratic) Model tervene (where, 0 pABC pBC 1). If A intervenes, B obtains its ideal point (0) with probability (1 − pABC). If The baseline (autocratic) model includes four actors: A, A does not intervene, B wins with probability (1 − pBC). the potential ally, allies (l) or not (∼l), and intervenes (t) Alliances may involve initial costs k (where k ≥ 0), as does fighting wi (where wi > 0, and where i ∈ [A, B, C]). Fi- 15Alliances can also signal resolve. Sunk cost aspects of alliances nally, A pays r (where r > 0), equal to A’s reputation loss have little effect on reliability since, by definition, sunk costs do not for failing to intervene. Players’ utility functions are: weigh on subsequent decision making, but instead affect observers’ beliefs about the credibility of commitments. UA ={(−|x − xA|) − twA − l[k + (1 − t)r ]} (1) 784 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH

= − − − w × [p (2x − x ) − x − k − r ] UB [( x) lk f B ] (2) BC A C A − − w > 3[xC (pBC pABC) A] = − − w UC [(x xC ) f C ] (3) 2 (pBC − pABC) × [p (2x − x ) − x − w ] Payoffs are obtained by substituting one (1) for each af- ABC A C A A firmative decision in the decision variables and zero (0) − − w + 1 − 3 [xC (pBC pABC) A] for negative decisions. For example, if player A allies (l) 3 2 (pBC − pABC) but does not intervene (∼t) while player C does not fight, × [pBC (2xA − xC ) − xA] (5) (∼ f ), then (l = 1, t = 0, f = 0) or U A = [(−|x − xA|) − k], U = [(−x) − k], U = [(x − x )]. The formal Simplifying terms and solving for xA produces: B C C + − w statement of players’ optimal strategies and the subgame < − (r k) + r 2 A xA xC − (6) perfect Nash equilibria appear in the appendix. 9r 2 (pBC pABC) wC wC If ≥ xC > , then C only fights if A˜ will not inter- pABC pBC The (Democratic) Cycling Model vene. A allies if (7) and (8) hold: We can modify the baseline model to represent the peri- ˜ | l∼f + ˜ ∼ | lf ∼t Pr(A : t l) UA Pr(A : t l) UA odic election of leaders. Governments differ in their in- > ˜ |∼ ∼l∼f + ˜ ∼ |∼ ∼lf ∼t terests. To model this variation, assume that A is replaced Pr(A : t l) UA Pr(A : t l) UA by A˜,asecondrandomdrawbyNature(N). As in the (7) baseline, Nature first identifies ideal points for A and C. Substituting, simplifying terms and solving for xA yields: A next decides whether to ally with B. Nature then ran- + + − 16 (r k) pABC [2k r (2 9xC )] domly reassigns A’s ideal point as A˜. In stage four, C xA < xC − + (8) 9r 18r (p ) chooses whether to attack B. Finally, if A allied with B, A˜ BC decides whether to honor the commitment. A’s alliance The inequalities are similar to the alliance decision in the choice occurs before Nature’s revelation of A˜. If allied, baseline model but without a lower bound. All players A − w + − A˜ intervenes with probability { r A xC (pBC pABC ) / 1 = for which Equations 6 or 8 hold (subject to C’s war costs) 2(pBC − pABC ) 3 − w + − ally.If alliancecostsaresmallrelativetotheincentive A˜has 3[r A xC (pBC pABC )] } ˜ − , the portion of types A that will 2(pBC pABC ) to intervene, the region over which A allies is large, but this r − wA + xC (pBC − pABC ) intervene (where x ˜ < intervene and A 2(pBC − pABC ) region is always (weakly) larger than in the baseline model. ≤ 1 ˜ xA˜ 3 is the typespace). The probability that A inter- Players’strategiesandsubgameperfectNashequilibriaare − − w venes with no alliance is 3[xC (pBC pABC ) A] . listed in the appendix. 2(pBC − pABC ) A’s alliance decision (imposing an alliance on A˜) also To summarize, additional equilibria appear at nodes w C 1 and 2. Because A and A˜ often differ in their preferences depends on the actions of C.IfxC ≤ , C never fights pBC w C and because A decides whether to ally without knowing and there is no point in allying. If xC > , C fights pABC ˜ regardless of A’s alliance choice. Yet, A can still prefer A, A more often has incentives to make commitments, but ˜ to ally if this forces A˜ to intervene when it would not thesecommitmentsinturnareonesthat Awilloftenfailto w C keep. Periodic replacement of leaders can make alliances otherwise. A allies if xC > and if the inequality in pABC Equations 4–6 hold: less reliable. Future leaders may be less enthusiastic about protecting proteg´ es,´ creating added incentives for incum- ˜ | lft + ˜ ∼ | lf ∼t Pr(A : t l) UA Pr(A : t l) UA bent administrations to form alliances to institutionalize ∼ ∼ ∼ > Pr(A˜ : t |∼l) U lft + Pr(A˜ : ∼t |∼l) U lf t foreign policy to increase the chance of intervention even A A as this increases the risk of abandonment. (4) Which equates to: The (Democratic) Interest Group Model 3 [r − w + x (p − p )] A C BC ABC ⊆ ∼ − Assume S members of A’s selectorate (S N, S U[0, 2 (pBC pABC) 1 /3]). Let s i denote a member of the selectorate, where × [pABC (2xA − xC ) − xA − k − wA] ∈ ... i [1, , S], and where xAi is s i ’s ideal point. Define 1 3 [r − w + x (p − p )] ⊆ , (V + 1) ∈ + − A C BC ABC V j S 2 N, as a subset of the selectorate willing ∈ 3 2 (pBC − pABC) to pay (e) for nonstochastic policy influence (where j = 1 [a, t]). Assume s i are placed at intervals d 3(S − 1) , with − x = 0 and x = 1/ , so that x = (i 1) . The median 16A more general approach could introduce a trend, but results A1 AS 3 Ai 3(S − 1) v = V + 1 would be similar. voter, ¯ j 2 , determines policy. REGIME TYPE AND ALLIANCE COMMITMENT 785

Modeling the interest group argument necessitates the product of the probability that C only fights if A¯ does that alliance policy occur while members of A are uncer- not intervene and the odds that A¯ will intervene if C fights w w w − tain about factors influencing first the alliance decision ( 3 C − 3 C )(2 − 3[ A (l)r ] ). Members of A calculate the pABC pBC (pBC − pABC ) and then the intervention decision. The cost of NATO ex- expected utility of participating in alliance policy as pansion was a key focus of the ratification debate in the follows: United States, and pundits offered widely divergent fig- ¯ | lft 17 Pr(A : t; C : f l) UA ures in attempts to influence decision making. Assume alliance costs (k) are uncertain k ∼ U[0, k ], where + ¯ ∼ | lf ∼t max Pr(A : t; C : f l) UA k is some arbitrary value. Assume as well that C’s ideal max + ¯ ∼ | l∼f point is initially private information, but that A knows x Pr(C : f l) UA C before the intervention decision. − ¯ |∼ ∼lft Pr(A : t; C : f l) UA There are a number of strategic factors in collective + ¯ ∼ |∼ ∼lf∼t decision making. For example, if attempting to influence Pr(A : t; C : f l) UA ∼ ∼ policy involves costs, then actors that fail to obtain pre- + Pr(C¯ : ∼ f |∼l) U l f ferred outcomes would generally rather not participate A (regret violates conditions of a Nash equilibrium). Of − + 1 − e 3(S 1) xALOW xAHIGH (10) course, losing factions do participate. We assume sincere 3 (simultaneous) decision making. Voters decide whether { − + 1 − } V l is replaced by 3(S 1)[xALOW ( 3 xAHIGH )] . to seek to influence outcomes while ignorant of others’ Define x ≡ x s.t. E (U l ) − V e = E (U ∼l ) and ALOW A xA l xA preferences. Voters determine whether to vote by weight- x ≡ x s.t. E (U l ) + V e = E (U ∼l ). Participation AHIGH A xA l xA ing outcomes by the probability that their vote is pivotal, costs (e) and the number of voters influencing policy subtracting participation costs. form a band of size 2V le, whose center we define as ˜ − l ∼l 1 j j Vj 1 x ≡ x s.t. E (U ) = E (U ). Members s between E U − E U + (0) > e (9) AINDIFF A xA xA i Vj A A Vj x ALOW and x AHIGH find it too costly to influence pol- With no loss of generality, we assume that the decision icy. Those between x A1 and x ALOW and between x AHIGH v = to intervene imposes no participation cost (et = 0). ¯t and xAS absorb the costs involved in affecting alliance 1 ¯ ⇒ v = ¯ S x A¯t 6 ,isA’s intervention preference (labeled A). policy. V l thus equals the portion of the selectorate in The fight and intervention decisions are similar to these two regions. The structure of the game also implies 1 (v¯ −1) (V −1) those in the previous games. The alliance decision is con- > , v = l = l that if xAINDIFF 6 x¯l 3(S−1) 6(S−1) .Conversely,if − siderably different, however. Members of A must estimate ≤ 1 = 1 − (V l 1) xA , it follows that xv¯l − . We then de- C’s decision and A¯’s intervention response. The proba- INDIFF 6 3 6(S 1) rive solutions for x ALOW and x AHIGH using simultaneous bility that C fights is equal to the portion of C’s types- equations. pace that exceeds critical values of C’s objective functions w w C 2 3 C = − − − with [i.e., (1 − )/(1 − ) = (3 − )] or without xALOW e(S 1) 2k(pABC pBC) pABC 3 pABC 3wC [i.e., (3 − )] A¯’s intervening. Members of A(s i ) es- × − w + w pBC (pABC(pBC 3 C ) 3pBC C ) ˆ timate the probability of intervention using A’s objec- − 3r p2 (3p − 2w ) r − w + x (p − p ) ABC BC C tive functions, which are x ¯ < A C BC ABC with A 2(pBC − pABC ) − − w − 3pBCwC (2wA + wC ) < xC (pBC pABC ) A an alliance and xAˆ 2(p − p ) without. Since s i BC ABC + p (3w (2r + w − 2w ) do not know xC , they must estimate the portion of C’s ABC C C A typespace over which the appropriate inequality holds. + 2p 6w + w − 3r ) − 3p2 BC A C BC Large values of xC make acquiescing to a contest be- − 3r 2k(pABC − pBC) tween B and C less appealing. Define xCCRIT,l ≡ xC s.t., − w + − = (l)r A xC (pBC pABC ) = × − w + w xA¯ − ,wherel 1 if the median (pABC(pBC 3 C ) 3pBC C ) 2(pBC pABC ) 1 voter (v¯) allies, else 0. Given x v = , A¯ intervenes with − 2 − w A¯t 6 3r pABC(5pBC 2 C ) − w − (1 xCCRIT,l ) = − 3[ A (l)r ] probability 2 2 − . The probability (1 − ) (pBC pABC ) − 3p w (2w + w ) 3 BC C A C that the status quo obtains (nodes 3 and 4) equals the + w − w + w wC 3wC pABC 3 C (2r 2 A C ) odds that C will not fight [xC ≤ ⇒ ( − 2)] plus pBC pABC + 2p (6w + w − 3r ) − p2 BC A C BC 17 Estimates of the cost of NATO expansion vary from $1.5 to $125 {36pABC pBCr (pABC − pBC) billions (Ek 1998). Informational asymmetries are another way to model our claims (Gilligan and Krehbiel 1990). × [3r + e(S − 1)]} (11) 786 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH = − − − ¯ ∼ ¯ | xAHIGH e(S 1) 2k(pABC pBC) ment, Pr(A : t; C : f l). Large selectorates lead to more × (p (p − 3w ) + 3p w ) alliance failures. ABC BC C BC C − 2 − w 3r pABC(7pBC 2 C ) − 3p w (2w + w ) Testing Alliance Reliability: BC C A C Research Design + p 3w (2r + w − 2w ) ABC C C A + 2p (6w + w − 3r ) − 7p2 BC A C BC We offer two arguments about how democracy limits al- − 3r 2k(pABC − pBC) liance reliability. We believe that our claims about cycling and coalitions are uncontroversial, but the role we accord × (p (p − 3w ) + 3p w ) ABC BC C BC C domestic politics hinges on the distribution of preferences − 2 − w 3r pABC(5pBC 2 C ) and is not easily demonstrated deductively. If democratic leaders face different incentives in deciding whether to en- − 3pBCwC (2wA + wC ) ter or honor alliances, then we should observe systematic +p 3w (2r + w − 2w ) ABC C C A differences in alliance behavior across different regimes. + w + w − − 2 2pBC(6 A C 3r ) 5pBC Both explanations suggest that democracies should ap- pear less likely to intervene on the side of their allies than {36p p r (p − p ) ABC BC ABC BC other states. × [3r + e(S − 1)]} (12)

∂x − ∂x ALOW = er < AHIGH = A Quantitative Test of Alliance Note that ∂ S 2[3r + e(S − 1)]2 0 and that ∂ S er > Reliability in Wars 2[3r + e(S − 1)]2 0. A nonzero cost for participation tends to drive out “moderates” as the selectorate gets large. Panel To assess whether democracies are less likely than other (a) in Figure 2 offers an illustration of the effect of S on regimes to assist allies in wars, we prepare a data set of ob- = . , = . ,w = w = x ALOW and xAHIGH (pABC 0 25 pBC 0 5 A C served alliance behavior under the conditions stipulated 5 0.1, r = 0.1, k¯ = 0.1, e = 0.1 × 10 ). Recall that voters by the alliance. We focus on situations where some state vote above and below the critical values of xA. Even with B becomes involved in a war with another state C, and minute costs, large selectorates tend to result in policy- its alliance partner A must choose whether to fulfill its making at the extremes. alliance commitment. We consider an alliance partner A Partisanship alone does not explain why selectorate to have fulfilled its commitment if A intervenes on the size can influence alliance behavior. Recall that members same side as its ally B in a dispute. We conceive of initial . = ¯ of A are uncertain about k s i use E [k] k to decide combatants in a dispute as state Bs and examine whether whether to participate in alliance policy. The median voter or not any of a states’ allies (As) become involved in the v (¯l ) confronts the actual k in determining whether to ally. dispute. Since implications of alliances for disputes below This allows a continuum of interest. As the median voter the level of war are less clear, we consider only interven- departs from the selectorate median, A is more likely to tion in disputes with at least 1,000 total battle deaths, accept an expensive alliance. as measured by the Correlates of War (COW) project’s Panel (b) in Figure 2 describes the effect of selec- Militarized Interstate Dispute data (MID v. 2.1). We ex- torate size on the value of k needed to make the median clude 96 incidents where dispute originators were not in- voter just indifferent between alliance alternatives. The volved in formal alliances. > 1 graph assumes that xAINDIFF 6 , that the median selec- Formal alliances differ in their level of commitment. torate member at least weakly favors allying at the mean In particular, nonaggression pacts entail no commitment alliance cost (here, k¯ = 0.1). The area under the curve to assist alliance partners, only a promise to refrain from represents the portion of values of k for which the me- attacking a partner in the event of war (Levy 1981). Our dian voter is willing to ally. The probability of alliance main data on formal alliances are taken from the Cor- increases with selectorate size. relates of War project. Since our interest is in the ability How does willingness to ally affect alliance reliabil- to commit to intervention in support of alliances, we ex- ity? Recall that A’s alliance choice is based on estimates amine only formal defense pacts.18 Our data contain 64 of probabilistic outcomes. The value of allying for v¯l de- pends on comparing preferred outcomes to commitment 18 costs. Large selectorates exhibit greater partisanship, and Since the key interest is the ability to make commitments that are costly to carry out, we believe that tests of alliance reliability should thus more willingness to gamble on less reliable alliances. focus on whether states fulfill defense commitments rather than Panel (c) in Figure 2 plots the probability of abandon- less costly formal obligations such as undertaking consultations. REGIME TYPE AND ALLIANCE COMMITMENT 787

FIGURE 2 Illustrations of the Interest Group Model 788 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH cases where the originators of a war were involved in de- to supply assistance. We include an indicator of whether fense pacts at the onset of the dispute. We then create state A and B in an alliance are contiguous by land or river dyads paring the allied country B involved in war with borders, as indicated by the COW contiguity data, to con- its ally (A). These data give raise to 480 A-B defense pact trol for the effects of proximity.23 As wealth or capability dyads between 1816 and 1992.19 may influence intervention, we control for the overall ca- The COW alliance data have often been criticized for pabilities of states A and B as measured by the Composite failing to identify the specific details of commitments, and Indicator of Capabilities (CINC) scores from the COW it could be argued that many defense pacts in the COW National Material Capabilities data. data do not entail an actual obligation to intervene in de- Although we expect to find systematic differences in fense of an ally. The ATOP data offer an advancement behaviorbyregimetype,wedonotanticipatethattheseef- on the COW alliance data by the more specific coding fects will be large. If a state’s primary concern in seeking to of commitments. Unfortunately, the ATOP data cur- ally remains security, then it will generally avoid partners rently in the public domain cover only the period 1816– that do not favorably alter the state’s security situation. 1944. Given the limited number of democracies prior to The fact that we identify the hypothesized relationship World War II, this period seems poorly suited for testing in spite of rational expectations (democratic unreliability differences between democracies and autocracies in al- should discourage alliance formation with the most unre- liances.20 Although we have been unable to obtain a copy liable democratic states, attenuating the observed effects) of the ATOP data for the period 1816–1991, Brett Ashley give us additional confidence in the validity of our results. Leeds of the ATOP project has generously reestimated our model on these data for us. States may be more reluctant to honor a commitment Quantitative Analysis and Results if intervention means fighting against allies on the oppos- ing side. Weuse a dichotomous indicator scored 1 if a state In the COW data, autocracies honor alliance commit- A has an alliance with some state C on the opposing side ments by intervening on the side of allies in about 16.3% of a dispute.21 of all cases where allies are at war, while democracies in- We operationalize regime type using the Polity 98d tervene only in about 6% of the cases.24 This supports our data.22 We code states as democracies if they score at least claim that democracies are less reliable, but other factors 6 on the Polity institutionalized democracy scale ranging may also affect intervention. Table 1 displays a multivari- from−10 to 10 (Jaggers and Gurr 1995). Regime type may ate logistic regression of the probability of a state A hon- change from the outbreak of a dispute to the time when oring an alliance with a partner B facing war as a function a state actually intervenes. To facilitate comparisons with of regime type A and other characteristics. As can be seen alliance parties A that do not become involved in disputes, from Table 1, the negative coefficient estimate for whether we consider the regime type characteristics at the outbreak state A is a democracy indicates that democracies are less of the dispute. likely to intervene to assist allies than are other states. The Many factors other than regime type conceivably af- coefficient estimate is significant at the 0.05 level in a one- fect intervention. Some of these factors, such as wealth tailed test. The odds of nondemocratic intervention are or capability, also correlate with democracy. We include almost twice as high as for democratic allies A. several control variables to ensure that results do not stem The other variables display effects on the likelihood from democracy serving as a proxy. Proximity to an al- that states will assist allies that are largely consistent with liance partner may influence a state’s willingness or ability our expectations. Intervention is more likely when states A and B are contiguous. Capable states A are more likely 19In cases where states A switch sides during a war, we use only to intervene to defend allies. The coefficient estimate for the first intervention to assess reliability. There are no cases where state B’s capabilities is negative, suggesting that a strong originators B switch sides during a war.

20 Many studies of regime type and alliance behavior report differ- 23 ences before and after World War II (see Farber and Gowa 1995; We have also examined the distance between capital cities as a Lai and Reiter 2000). measure of proximity, and the results are substantively equivalent irrespective of the measure used. 21 Leeds did not include this variable in the ATOP replication as she 24 lacks precise dates for the duration of some of the alliances not Sabrosky (1980, 176–78) measures the reliability for the alliance involving defense commitments tested in wars. as a whole, based on whether at least one ally intervenes, with no allies intervening on the other side. Sabrosky’s measure yields a 22Using the Polity 98d data, which provide the actual dates of regime higher intervention rate than our dyadic measure. Interestingly, change within years, helps ensure that we do not code regime type the proportion of democratic allies is lower in Sabrosky’s “reliable” based on changes following dispute onset. alliances than in the “unreliable” alliances. REGIME TYPE AND ALLIANCE COMMITMENT 789

TABLE 1 Logistic Regression of Democracy and TABLE 2 Logistic Regression of Democracy Other Variables on Intervention and Other Variables on Violation (COW) (ATOP)

Coefficient Standard Coefficient Standard Covariate Estimate Error t-value p-value† Covariate Estimate Error t-value p-value† Intercept −2.727 0.326 −8.374 >0.001 Intercept 0.976 0.228 4.280 >0.001 A is a −0.509 0.281 −1.810 0.035 A is a 0.917 0.441 2.080 0.019 democracy democracy A allied to −0.085 0.313 −0.272 0.393 A and B −0.101 0.329 −0.310 0.380 other side contiguous A and B 0.886 0.305 2.907 0.002 CINC A −23.168 3.377 −6.860 >0.001 contiguous CINC B −6.111 2.694 −2.270 0.012 CINC A 8.108 2.720 2.981 0.002 N = 273, LR- 2 (df = 4) 103.80 CINC B −3.273 2.348 −1.394 0.082 †p-values for one-tailed tests, expect for the intercept. = 2 = N 469, LR- (df 5) 27.6 Note that the dependent variable is scored as 1 for violation, i.e., the reverse of Table 1, following Leeds (2003). †p-values for one-tailed tests, expect for the intercept.

alliance partner is less likely to receive assistance, but the in Table 2 is scored as 1 for violation, or not honoring an result is not statistically significant. Finally, the coefficient alliance, following Leeds (2003). In these results, contigu- estimate for whether a defender has an alliance with a state ous partners are no longer significantly less likely to vio- on the opposing side (state C) has the correct sign, but is late commitments, and stronger states B are no longer less not statistically significant. This provides only weak evi- likely to receive support. This suggests that the COW data dence that states with conflicting alliance commitments may include some defense pacts between large and small are less likely to intervene. In sum, although other factors states where commitment is asymmetric, and the smaller influence the likelihood of intervention, these factors do state may not be obliged to defend the larger state. How- not account for the observed differences between democ- ever, the positive coefficient estimate for whether state racies and nondemocracies. A is a democracy indicates that democracies are about Other studies of regime type and alliance have fo- 2.5 times more likely to violate alliance obligations than cused on jointly democratic alliance partners. It may be autocracies. These results reinforce our conclusion that argued that a democracy’s willingness to intervene de- democracies are less likely to intervene in defense of al- pends on the regime type of its proteg´ e.´ Adding a variable lies, even using a more restrictive identification of alliance for whether state B is a democracy yields an insignificant commitments.25 negative coefficient estimate, suggesting that democracies are no more likely to receive assistance from allies. The co- 25Leeds and Gigliotti-Labay (2003) similarly report a logit coeffi- efficient estimate for state A’s regime type remains nega- cient for democracy on the likelihood of alliance violation of 0.516 tive and statistically significant. Replacing the democracy in their multivariate analysis, but argue that there are no differ- terms for the individual states by a single indicator of ences between democracies and autocracies since the estimate is not statistically significant. Whether individual variables reach sig- whether both allies (A and B) are democracies also yields nificance will depend on model specification. Leeds (2003) and her a negative coefficient estimate. This estimate is just below coauthors control for changes between the time of entering an al- the usual thresholds for statistical significance. These re- liance and the time at which a state must decide whether to keep an alliance commitment. Their results suggest that observable changes sults yield no support for the hypothesis that democratic significantly increase the probability of an alliance violation (no- allies are more likely to assist democratic partners, but tably, democracies are particularly likely to violate treaties signed strengthen our claim that democracies are generally less before transitions to democracy). Leeds suggests that even when reliable. a“new leadership does not officially abrogate past treaties, when it comes time to fulfill a particular international commitment, ...a Table 2 reports the results for our model estimated new leadership may have a different decision calculus than a prede- on the ATOP data, allowing us to see whether our previ- cessor” (2003, 816). Whereas Leeds assumes that democracies op- ous findings stem from measurement error in the COW erate under stability, we see change as an essential feature of democ- racy: governments that are responsive to evolving public opinion alliance data that in some way is systematically associ- and external conditions face additional challenges in making for- ated with regime type. Note that the dependent variable eign policy commitments. 790 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH

Inmanycasesitmaybedifficulttoseparatetheobliga- after the disappearance of the threats that initially gave tions of an alliance treaty from the implicit expectations of rise to them. Establishing who initiates disputes is also members. Alliance commitments may not be interpreted wrought with difficulties in the existing MID data. equally by all participants in a crisis, especially since con- Sample selection can be addressed by two-stage equa- tingencies will often pose different incentives, and expose tion estimation approaches (Greene 1997). Such models the different interests, of alliance members. Expectations are appropriate when the situation of interest is observed of what alliances are meant to achieve in terms of de- if and only if another factor z exceeds some threshold terrence or coercive diplomacy may go beyond the de- value. The selection equation stipulates the sample se- tails specified in treaties. The controversy between NATO lection process (the likelihood of observing the situation members in February 2003 over assistance to Turkey il- of interest in the main equation). The outcome and the lustratesthetensiongeneratedbydifferentinterpretations selection equations are estimated jointly, allowing for cor- of alliance obligations and plausible threats.26 Conversely, relation between the error terms in the two equations. Leeds and Gigliotti-Labay (2003, 14–15) hold that states We are skeptical as to whether one can predict which sometimes may be satisfied when parties in defense pacts alliances will be targeted on the basis of structural or ob- provide assistance short of intervening, even if they do not servable factors alone (see Signorino 2002). Nonetheless, carry out the exact commitment stipulated by the alliance. we can test whether augmenting the Model in Table1 with Future research may examine more closely the implica- a selection equation for war involvement as a function of tions of subjective evaluation of alliance obligations by democracy and attributes of alliances yields different re- members and other interested states. sults.27 We construct a sample of nonwar cases from all Selection effects are a potential confounding factor the years where neither member of an alliance dyad is in using wartime behavior to measure alliance reliability. involved in a war. We randomly select the assignment of One of the principal aims of an alliance is to deter war. Ac- defender state A and proteg´ e´ state B in nonwar cases. The tually reaching war implies that alliance effectiveness may selection equation stipulates the risk of an alliance dyad have been in doubt (Smith 1995). The sample of wartime being targeted by third parties (i.e., one party becomes in- intervention decisions on behalf of allies may thus over- volved in war) as a function of whether at least one of the represent unsuccessful alliances. Selection bias can pose a two parties to alliance A and B are democracies, their ca- problem if factors that influence observed behavior in a pabilities, and whether the states are contiguous. Results situation also affect the likelihood that cases are selected of the model appear in Table 3.28 into the situation. The large positive estimated ˆ in Table 3 suggests that In the absence of a precise theory of how alliances get there exists significant correlation between the error terms targeted it is difficult to establish whether selection bias of the two equations. Nonmeasured factors in the model poses a major problem for our analysis or not. If democ- that increase the likelihood that an alliance dyad will be racies are less reliable allies, then they should more often involved in a war also increase the likelihood that states be challenged, and democratic alliances that are attacked will assist their allies. The coefficient estimate for democ- should make up a larger portion of challenged alliances racy in the selection or war equation is negative, indicating than the ratio of democratic alliances to all alliances. How- that alliance dyads involving a democracy are less likely to ever, we can only observe whether states are involved in experience war onsets. However, allowing the error terms war, and our model cannot assess whether alliances make in the two equations to be correlated does not change a difference to whether a state is targeted or not. Some in- our inferences about the effect of democracy on the like- stitutional theories suggest that alliances may persist even lihood that a state will intervene in support of an ally. The coefficient estimate for democracy in the assistance 26For example, NATO chose to treat the retaliation against equation remains negative, indicating that democracies Afghanistan and Al-Qaeda in the wake of 11 September as pertinent are less likely to come to the aid of defense pact partners to the alliance since the attack on the World Trade Center and the Pentagon involved a member state. However, Afghanistan itself was in a war. not accused of having attacked the United States, but targeted for not cooperating in the counterattack against Osama Bin Laden and Al-Qaeda. The United States and many European allies differed in 27Leeds is at the present not able to replicate our selection model their assessment on whether Iraq was a legitimate target in the war with the ATOP data as she lacks precise dates for the duration of on terrorism and a plausible threat against member countries. De- some of the alliances not involving wars in the post 1944 period. cisions to invoke alliances will be shaped by perceptions about what actions or initiatives might achieve consensus. Ferguson (2001) re- 28Bivariate probit is generally more efficient than Heckman pro- minds us that “not even the most extreme Unionists were prepared bit (see Reed 2000). Heckman probit estimation yields a similar to bomb Boston in retaliation ...” against Americans who provided negative coefficient estimate for democracy (results available on “the lion’s share of the money that financed the IRA” (2001, A31). request). REGIME TYPE AND ALLIANCE COMMITMENT 791

TABLE 3 Bivariate Probit of Democracy democracies are less likely to intervene in wars on behalf of and Other Variables on War allies than nondemocracies. For democracies to make reli- and Intervention able allies, they must overcome the structural weaknesses thathavepreviouslybeeninterpretedasstrengths.Wesug- Coefficient Standard † gest that democracies do not overcome these weaknesses. Covariate Estimate Error z-value p-value The utility of alliances is that they reinforce partnerships. Selection: Alliance challenges Democratic alliances are both a sign of democratic un- Intercept −2.362 0.028 −84.18 >0.001 reliability and of the potency of alliances in mitigating At least one −0.370 0.041 −9.10 >0.001 democratic weakness. democracy A and B 0.083 0.043 1.93 0.027 Appendix contiguous CINC A 0.961 0.443 2.17 0.015 Solutions for the Alliance Reliability Game CINC B 5.668 0.293 19.32 >0.001 The appendix lists optimal strategies and equilibria for Outcome: Intervention each of the three variants of the alliance reliability game − − > Intercept 3.141 0.073 42.93 0.001 discussed in the main text. A is a −0.509 0.151 −3.37 >0.001 democracy Optimal Strategies in the Baseline (Autocratic) Model. CINC A 2.278 0.782 2.91 0.002 x (p − p ) − w CINC B 2.866 0.735 3.90 >0.001 = C BC ABC A ≤ A: l 1if − xA A and B 0.366 0.091 4.01 >0.001 2 (pBC pABC) − w + − contiguous < r A xC (pBC pABC) − N = 42,131 (outcome N = 433) 2 (pBC pABC) w w ˆ = 0.99 (SE = 0.005) C C and ≥ xC > LR- 2 (df = 8) 497.60 pABC pBC − † xC (pBC) k p-values for one-tailed tests, expect for the intercept. and xA ≤ 2pBC = . We are hesitant to infer too much from the results 0 if else in Table 2, given the problems with the model and the t = 1ifl = 1, f = 1, lack of a strong theory on selection into wars. However, r − wA + xC (pBC − pABC) these results lend no support to the idea that selection into and xA < 2 (p − p ) war undercuts the findings in Table1 and thus strengthens BC ABC = , = , ourconclusionthatdemocraciesfaceproblemsincredibly or if l 0 f 1 − − w committing. xC (pBC pABC) A and xA < 2 (pBC − pABC) = 0 if else. Conclusion w C: f = 1ift = 1, and x > C C p Regimes differ in their foreign policy behavior, but not ABC wC necessarily in the ways that many have come to expect. or if t = 0, and x > C p Distributive domestic politics and informational asym- BC = . metries enhance the political leverage of high value mi- 0 if else nority coalitions on many issues, rendering explanations that emphasize constraining domestic audiences suspect Equilibria in the Baseline (Autocratic) Model. in some areas of foreign policy. Pacifying domestic con- wC wC [Node 3]if ≥ xC > , straints may induce differences in conflict involvement pABC pBC between political systems, but public opinion is unlikely and k < pBC (xC − 2xA) , to influence decisions to enter formal alliances as much as x (p − p ) − w whether to honor treaty conditions. Consistent with our C BC ABC A ≤ and − xA argument, leaders in democracies appear to face different 2 (pBC pABC) − w + − incentives when choosing to form alliances and when de- < r A xC (pBC pABC) ciding whether to intervene to assist an ally. We show that 2 (pBC − pABC) 792 ERIK GARTZKE AND KRISTIAN SKREDE GLEDITSCH

wC wC [Node 4]if xC ≤ C: f = 1ift = 1, and xC > pBC pABC wC wC wC or if ≥ xC > , or if t = 0, and xC > pABC pBC pBC

xC (pBC − pABC) − wA = 0 if else. and xA < 2 (pBC − pABC) wC [Node 5]if xC > , pABC Equilibria for the (Democratic) Cycling Model. − − w w xC (pBC pABC) A > C and xA < [Node 1]if xC 2 (pBC − pABC) pABC w − − w > C , < xC (pBC pABC) A [Node 6]if xC and xA˜ pABC 2 (pBC − pABC) − − w xC (pBC pABC) A r + k and x ≥ < − ( ) A − and xA xC 2 (pBC pABC) 9r w w C C r − 2wA or if ≥ xC > , + pABC pBC 2 (pBC − pABC) − w + − w r A xC (pBC pABC) > C and xA ≥ [Node 2]if xC 2 (pBC − pABC) pABC w w − − w C ≥ > C , ≥ xC (pBC pABC) A or if xC and xA˜ pABC pBC 2 (pBC − pABC) and k ≥ p (x − 2x ) , + − w BC C A < − (r k) + r 2 A − − w and xA xC xC (pBC pABC) A 9r 2 (pBC − pABC) and ≤ xA 2 (p − p ) wC wC BC ABC or if ≥ x > − w + − p C p < r A xC (pBC pABC) ABC BC − − w + − 2 (pBC pABC) ≥ r A xC (pBC pABC) and xA˜ 2 (pBC − pABC) Optimal Strategies in the (Democratic) Cycling Model. (r + k) and x < x − w A C 9r A: l = 1ifx > C C pABC [2k + r (2 − 9xC )] pABC + + 18r (pBC) < − (r k) and xA xC wC wC 9r [Node 3]if ≥ xC > − w pABC pBC + r 2 A r − wA + xC (pBC − pABC) 2 (pBC − pABC) < and xA˜ − + 2 (pBC pABC) < − (r k) or if xA xC (r + k) 9r and x < x − + − A C 9r + pABC (2k r (2 9xC )) pABC [2k + r (2 − 9xC )] 18r (pBC) + wC wC 18r (pBC) and ≥ xC > w p p C ABC BC [Node 4]if xC ≤ = 0 if else. pBC w w C ≥ > C A˜: t = 1ifl = 1, f = 1, or if xC pABC pBC − w + − < r A xC (pBC pABC) x (p − p ) − w and xA˜ < C BC ABC A 2 (pBC − pABC) and xA˜ 2 (pBC − pABC) = , = , or if l 0 f 1 (r + k) and x ≥ x − xC (pBC − pABC) − wA A C and x ˜ < 9r A 2 (p − p ) + − BC ABC + pABC [2k r (2 9xC )] = . 0 if else 18r (pBC) REGIME TYPE AND ALLIANCE COMMITMENT 793 w ∼ C x ≡ x s.t. E U l = E U l [Node 5]if x > AINDIFF A xA xA C p ABC = . − − w 0 if else < xC (pBC pABC) A and xA˜ A¯: t = 1ifl = 1, f = 1, 2 (pBC − pABC) − w + − (r + k) < r A xC (pBC pABC) and x ≥ x − and xA¯ − A C 9r 2 (pBC pABC) − w or if l = 0, f = 1, + r 2 A − − − w 2 (pBC pABC) < xC (pBC pABC) A w and xA¯ C 2 (pBC − pABC) [Node 6]if xC > pABC = 0 if else. − − w wC ≥ xC (pBC pABC) A C: f = 1ift = 1, and x > and xA˜ C 2 (p − p ) pABC BC ABC w r + k r − 2w = , > C ≥ − ( ) + A or if t 0 and xC and xA xC p 9r 2 (p − p ) BC BC ABC = . wC wC 0 if else or if ≥ xC > pABC pBC − − w ≥ xC (pBC pABC) A and xA˜ Equilibria for the (Democratic) Interest Group Model. 2 (pBC − pABC) w (r + k) > C and x ≥ x − [Node 1]if xC A C 9r pABC − w + − pABC [2k + r (2 − 9xC )] r A xC (pBC pABC) + and x ¯ < A 2 (p − p ) 18r (pBC) BC ABC ∼ [Node 2]if E U l > E U l v¯l v¯l r − w + x (p − p ) Optimal Strategies in the (Democratic) Interest Group ≥ A C BC ABC and xA¯ − Model. 2 (pBC pABC) w > C and xC = l > ∼l pBC A: l 1ifE Uv¯ E Uv¯ l l l > ∼l [Node 3]if E Uv¯ E Uv¯ > 1 l l and xAINDIFF : − w + − 6 r A xC (pBC pABC) and x ¯ ≥ A 2 (p − p ) v = 1 + BC ABC it follows that ¯l (V l 1) w w 2 C C and < xC > (V l − 1) pABC pBC ⇒ xv¯l = − ∼ wC 6 (S 1) or if E U l > E U l and x ≤ v¯l v¯l C l > ∼l pBC if E Uv¯ E Uv¯ l l l ≤ ∼l [Node 4]if E Uv¯ E Uv¯ ≤ 1 l l and xAINDIFF : − w + − 6 r A xC (pBC pABC) and x ¯ < A 2 (p − p ) v = 1 + BC ABC it follows that ¯l (V l 1) w w 2 C C and ≥ xC > 1 (V l − 1) pABC pBC ⇒ xv¯l = − − ∼ w 3 6 (S 1) or if E U l ≤ E U l and x ≤ C v¯l v¯l C pBC where l ∼l 1 [Node 5]if E Uv ≤ E Uv = − + − , ¯l ¯l Vl 3 (S 1) xALOW xAHIGH 3 xC (pBC − pABC) − wA and x ¯ < l ∼l A − xA ≡ xA s.t. 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