Explaining Midterm Election Outcomes: A New Theory and an Overview of Existing Explanations John Wiggs Patty Department of Social and Decision Sciences Carnegie Mellon University October 6, 2004 Abstract This paper describes a theory of political participation based on loss aversion and de- rives its predictions for midterm Congressional elections. In addition, the paper discusses the five most prominent explanations for the midterm effect, an empirical regularity of US Congressional elections in which the president’s party tends to perform poorly. Note: Incomplete Version. 1 The Loss Aversion Theory Let X denote a one-dimensional policy space, representing the liberal-conservative ideological dimension of American politics.1 There are two political parties, d and r, each associated with a policy position in X, xd and xr, respectively. We assume that these positions are not equal (xr = xd) and treat them as exogenously fixed. Public policy is chosen by a unicameral leg- islature (referred to simply as “Congress”) and a unitary president. For simplicity, we assume that the legislature is strictly majoritarian, with the party that controls a majority of the seats in the legislature determining the revealed preferences of that body. The final policy outcome is a convex combination of the positions of the party holding the presidency and the party control- ling Congress. In particular, denoting the final policy outcome by y ∈ X, the platform of the president’s party by xP , and the platform of the party controlling Congress by xC , y = αxC +(1− α)xP 1Aside from the intuitive appeal of this construct, its usefulness as a prediction tool with regard to legislative behavior in the United States is examined in great detail in Poole and Rosenthal [1997]. 1 for some exogenously fixed value α ∈ (0, 1). Thus, in this model, the most extreme pol- icy outcomes result from unified control – i.e., when one party controls both the presidency and Congress – whereas divided control of the two branches leads to more moderate policies. The parameter α measures the importance of Congress in the determination of public policy (in other words, it is analogous to the legislative branch’s bargaining strength). Equivalently, this parameter also measures the practical importance (in terms of public policy) of midterm elections relative to presidential ones. 1.1 Voters The finite set of potential voters is denoted by N. Each citizen i possesses an ideal public policy, pi ∈ X, and the following policy utility function u : X × X → R: u(y,pi)=−|y − pi|. In other words, citizens are assumed to have preferences over policy that are linearly decreas- ing in terms of the distance between the implemented policy outcome and their ideal policy.2 If individual i chooses to turnout and vote, he or she pays a net cost of ci, which is expressed in the same units as the policy utility function. The final utility received by voter i, conditional upon turning out to vote, is then u(y,pi) − ci. The final utility received by the voter conditional upon abstaining is simply u(y,pi). We do not assume that ci is positive. A negative value of ci implies that voter i enjoys a net “consumption” benefit from the act of voting itself. We assume that ci is privately observed and distributed according to a continuously differentiable cumula- tive distribution function F , with probability density function f. Furthermore, we assume for simplicity that the distribution of ci possesses positive support everywhere. In other words, ci might take any value.3 Each voter i is characterized by a reference-level of public policy utility, ri. Essentially, this represents the minimally acceptable public policy – it is useful to think of any public policy x for which u(x, pi) <ri as being viewed as “unacceptable” by voter i, whereas any public 4 policy x for which u(x, pi) ≥ ri is at least satisfactory. 2Little, if any, of the analysis conducted in the paper relies upon the assumption of linearity. It is made only to simplify the exposition of the theory. 3This assumption is made only to make the presentation of the results clearer. Otherwise, the results would depend in uninteresting ways upon the distribution of the (unobservable) private costs of participation. The only binding requirement for our model is that, with positive probability, some individuals will possess “sufficiently small” costs of voting (e.g., zero). 4As the term “satisfactory” suggests, an alternative interpretation of the theory might involve the “satisficing” 2 Given a reference-level ri, the payoff from voting for a policy outcome x is denoted by 2 v(u(x, p),u(ri)). The function v : R → R is assumed to be a continuous function that is twice continuously differentiable in both of its arguments except possibly at u(x)=u(ri). Furthermore, v is also assumed to satisfy the following conditions: 1. Normalized. Without loss of generality, v(z, z)=0for all z ∈ R. 2. Monotonicity. The payoff of voting for a policy outcome is an increasing function of z ∈ R ∂v(k,z) > 0 k = z the utility received from that outcome. Formally, for all , ∂k for all . 3. Loss Aversion. Policy gains are less valuable than similarly-sized policy losses. For- mally, for all z ∈ R and δ>0, v(z + δ, z) <v(z − δ, z). 4. Diminishing Effect of Losses and Gains. The marginal effect of increasing gains and the marginal effect of increasing losses are both decreasing functions. Formally, for all z ∈ R ∂2v(k,z) < 0 k>z ∂2v(k,z) > 0 k<z , ∂k2 for and ∂k2 for . This payoff function is consistent with the characteristics of the “S-shaped” payoff func- tion formalized in prospect theory by Kahneman and Tversky [1979].5 In addition, it shares similarities (especially with regard to predicted behavior) to the theory of satisficing, as devel- oped by Simon [1957]. The mapping of utility into payoffs is pictured in Figure 1. The payoff v(u(x, pi),ri) is the subjective reward received by voter i from casting a ballot that would re- 6 sult in a policy outcome of x. Voter i’s cost of voting is denoted by ci. In our theory, voters are assumed to ignore the behavior of other voters. They are assumed to believe (irrationally) that abstention will result in the least preferred feasible public policy being implemented fol- lowing the election. Accordingly, we assume that voters are behaving in a very conservative fashion – in game theory terms, they are “maxminners” with respect to the choice to turnout or abstain, basing their behavior on a belief that the worst will occur if they abstain. Even with such beliefs, voter i will still abstain if the cost of voting, ci, is large enough. We assume that voters are naive in two relatively intuitive ways. First, they assume that they are pivotal and calculate the utility difference between ballots accordingly. In addition, each voter believes that if he or she abstains, the worst feasible public policy outcome will result. (In this setting, the worst feasible outcome results from unified control by the voter’s model of decision making (Simon [1957]). 5For an important (and, as far as we are aware, the seminal) application of prospect theory to political science, see Quattrone and Tversky [1988]. 6This cost might be negative, representing a nonpolicy-based benefit from voting. 3 least preferred party.) The assumptions that voters are naive and sincere jointly imply that voter i’s subjective payoff of voting from for policy outcome x is equal to w(x, pi,ri,ci)=v(u(x, pi),ri) − ci, (1) while, denoting the set of feasible public policy outcomes by Y , the subjective payoff from abstaining is assumed to be equal to w(0,pi,ri,ci)=v(min[u(y,pi)],ri). (2) y∈Y The theory of voter behavior is based on maximization of the perceived payoff, w, rather than the traditional policy utility function, u. This assumption is key to the theory precisely because the individual’s policy payoff function, v, is assumed to distort the utility function – in particular, perceived payoffs are subject to loss aversion – voters are assumed to be more strongly compelled to avoid losses than achieve similarly-sized gains, relative to the voter’s reference-level, ri. Thus, as elucidated in Propositions 1 and 2 below, the theory predicts that individuals will turn out to cast a ballot if their most preferred ballot, when evaluated through Equation 1, leads to a payoff that exceeds the evaluation of Equation 2. Formally, the theory predicts that voter i will turn out and vote if W (pi,ri,ci,Y)=v(max[u(y,pi)],ri) − v(min[u(y,pi)],ri) − ci (3) y∈Y y∈Y is nonnegative.7 Equation 3 makes clear that the individual turnout decision depends on the set of feasible public policy outcomes that can follow an election (Y ), the voter’s reference level (ri), his or her ideal policy (pi), and the cost of voting (ci). Electoral Setting: Elections. There are two types of elections, presidential and midterm. In presidential elections, voters cast a ballot for both Congress and the presidency, whereas in midterm elections, voters choose only which party to vote for in Congress. Accordingly, the set of feasible policy outcomes, Y , in a midterm election consists of two elements, whereas it consists of four elements in a presidential election. 7It suffices for our purposes to presume that individuals who are indifferent about turning out to vote do so. This is only a technical consideration, given our assumption that the cumulative distribution function of c i is continuously differentiable; in such an environment, individual indifference about turning out “almost never” occurs (i.e., the event is assigned zero Lebesgue measure.