Jonathan Woon Existing theoretical models of two-stage elections fice motivations.Parties are completely homogeneous also typically maintain the assumption that all politi- as candidates and voters belonging to the same party cal actors,candidates as well as voters,are strategic and both care about policy and have the same ideal point. forward-looking (e.g..Owen and Grofman 2006).Sev- Thus,there are three ideal points in the model:0,for eral models consider the issue of raiding and crossover members of Party L,Og for members of Party R,and voting in open primaries (Cho and Kang 2014;Chen eM for the electorate's median voter,where <M< and Yang 2002:Oak 2006).which requires a fairly high R.I assume that preferences are symmetric and single- degree of strategic sophistication,but this kind of be- peaked.Specifically,in the experimental implementa- havior is outside the scope of my analysis.My results tion,all actors have linear loss utility functions,ui(w) also differ from Adams and Merrill (2014).who find =K-w -6il,for i[L,M,R)and some constant that strategic versus expressive voting both generate K>0.Preferences are also common knowledge,so the divergence,but in their model candidates are office- election takes place under conditions of complete in- motivated and vary in their campaign skills.In contrast formation. to the preponderance of existing formal models,I take There are two types of elections.In one-stage elec- a behavioral (i.e.,bounded rationality)approach advo- tions(1S),each party has one candidate and their posi- cated by Simon (1955).Ostrom(1998).Bendor (2010). tions are cL and cR.respectively,and there is one round and others.I do so by explicitly allowing for sincere of majority rule voting to select the winning candidate (myopic)voting as well as subjective beliefs that are In two-stage elections (2S),each party has two candi- inconsistent with observed behavior. dates (denoted cLi and cL2 for Party L,cRI and cR2 This paper is also related to two distinct literatures for Party R)who first compete in intraparty elections in experimental political science.The experimental lit- (the primaries).The candidates who win their respec- erature on candidate positioning in two-party elections tive party primaries then compete in a second-round finds a strong tendency for candidates and election out- election (the general election)to select the winning comes to converge to the median voter's position and, policy w.In other words,the parties hold simultaneous more generally,to the Condorcet winner under a va- "closed"primaries in which the voter with ideal point riety of conditions,including incomplete information eL chooses cL E [CLI,CL2)for Party L while the voter (Collier et al.1987:McKelvey and Ordeshook 1982 with ideal point OR chooses cR E[CR1,cR2 for Party R.In 1985).An exception is Morton (1993),in which can- the general election,the median voter with ideal point didates are ideological and voting is probabilistic.The ey chooses the election outcome from the two candi- other related literature,on strategic voting,generally dates selected by the parties'respective median voters finds little (at best,mixed)evidence for voter sophisti- w∈{CL,CR}. cation in the early stages of a multistage voting agenda To generate predictions about candidate positioning or election contest (Cherry and Kroll 2003;Eckel and and to identify the effects of the election format,I con- Holt 1989;Herzberg and Wilson 1988;McCuen and sider a variety of alternative behavioral assumptions.I Morton 2010:Plott and Levine 1978:Van der Straeten begin with standard game theoretic analysis,applying et al.2010).5 Taken together,these previous studies Nash equilibrium as the solution concept.Since I am raise doubts that voters will be highly strategic (even interested in making behavioral predictions,the inter- if candidates are),calling into question theories predi- pretation of Nash equilibrium is worth a brief discus- cated on voter rationality and strategic sophistication. sion.One way to interpret Nash equilibrium is to think of it as an idealized set of assumptions such that actors THEORETICAL FRAMEWORK AND are not only fully rational but also that their rationality ANALYSIS is common knowledge(Aumann and Brandenburger 1995).In this interpretation,we can think of political I consider an environment with two parties,Party L and actors as forming beliefs about others'current and fu- Party R,competing to win a single office.Candidates ture behavior (as well as beliefs about beliefs and ra- choose positions in a one-dimensional policy space, tionality,and so on)that are fully consistent with play- and the winning candidate's position is implemented ers'actual strategies and behavior.Alternatively,Nash as the policy outcome.In the electorate,there are an equilibrium can be interpreted as merely representing equal number of voters in each party and a set of inde- a stable outcome in which strategies are mutual best pendent,nonpartisan "swing"voters.Candidates and responses,without necessarily invoking an epistemic or voters alike are entirely policy-motivated,caring only belief-based justification of how individuals make deci- about the location of the policy outcome we R.The in- sions in games.The latter approach,however,does not centive to win office is therefore purely instrumental in make clear cut predictions about how games are played this model,which departs from the usual Downsian of- before an equilibrium state is reached.Nevertheless under a wide variety of learning models,experience can lead play to converge to Nash equilibrium(Fudenberg Smirnov (2009),who studies endogenous agendas and finds behav- and Levine 1998).and the role of experience can be ior consistent with sophisticated expected utility maximization,is an investigated experimentally. exception.There is stronger experimental evidence for other kinds Relaxing the Nash assumption of the mutual con- strategic voting.however,such as coordinating on a less-preferred candidate in multicandidate contests (Rietz 2008),and in incom sistency of beliefs and actions generates an interest- plete information pivotal voter settings(e.g.,Battaglini,Morton,and ing variety of behavioral possibilities.In my analysis Palfrey 2010). I first explore the implications of voter sophistication 828Jonathan Woon Existing theoretical models of two-stage elections also typically maintain the assumption that all politi￾cal actors, candidates as well as voters, are strategic and forward-looking (e.g., Owen and Grofman 2006). Sev￾eral models consider the issue of raiding and crossover voting in open primaries (Cho and Kang 2014; Chen and Yang 2002; Oak 2006), which requires a fairly high degree of strategic sophistication, but this kind of be￾havior is outside the scope of my analysis. My results also differ from Adams and Merrill (2014), who find that strategic versus expressive voting both generate divergence, but in their model candidates are office￾motivated and vary in their campaign skills. In contrast to the preponderance of existing formal models, I take a behavioral (i.e., bounded rationality) approach advo￾cated by Simon (1955), Ostrom (1998), Bendor (2010), and others. I do so by explicitly allowing for sincere (myopic) voting as well as subjective beliefs that are inconsistent with observed behavior. This paper is also related to two distinct literatures in experimental political science. The experimental lit￾erature on candidate positioning in two-party elections finds a strong tendency for candidates and election out￾comes to converge to the median voter’s position and, more generally, to the Condorcet winner under a va￾riety of conditions, including incomplete information (Collier et al. 1987; McKelvey and Ordeshook 1982, 1985). An exception is Morton (1993), in which can￾didates are ideological and voting is probabilistic. The other related literature, on strategic voting, generally finds little (at best, mixed) evidence for voter sophisti￾cation in the early stages of a multistage voting agenda or election contest (Cherry and Kroll 2003; Eckel and Holt 1989; Herzberg and Wilson 1988; McCuen and Morton 2010; Plott and Levine 1978; Van der Straeten et al. 2010).5 Taken together, these previous studies raise doubts that voters will be highly strategic (even if candidates are), calling into question theories predi￾cated on voter rationality and strategic sophistication. THEORETICAL FRAMEWORK AND ANALYSIS I consider an environment with two parties,Party L and Party R, competing to win a single office. Candidates choose positions in a one-dimensional policy space, and the winning candidate’s position is implemented as the policy outcome. In the electorate, there are an equal number of voters in each party and a set of inde￾pendent, nonpartisan “swing” voters. Candidates and voters alike are entirely policy-motivated, caring only about the location of the policy outcome w ∈ R. The in￾centive to win office is therefore purely instrumental in this model, which departs from the usual Downsian of- 5 Smirnov (2009), who studies endogenous agendas and finds behav￾ior consistent with sophisticated expected utility maximization, is an exception. There is stronger experimental evidence for other kinds strategic voting, however, such as coordinating on a less-preferred candidate in multicandidate contests (Rietz 2008), and in incom￾plete information pivotal voter settings (e.g., Battaglini, Morton, and Palfrey 2010). fice motivations. Parties are completely homogeneous, as candidates and voters belonging to the same party both care about policy and have the same ideal point. Thus, there are three ideal points in the model: θL for members of Party L, θR for members of Party R, and θM for the electorate’s median voter, where θL < θM < θR. I assume that preferences are symmetric and single￾peaked. Specifically, in the experimental implementa￾tion, all actors have linear loss utility functions, ui(w) = K − |w − θi|, for i ∈ {L, M, R} and some constant K > 0. Preferences are also common knowledge, so the election takes place under conditions of complete in￾formation. There are two types of elections. In one-stage elec￾tions (1S), each party has one candidate and their posi￾tions are cL and cR, respectively, and there is one round of majority rule voting to select the winning candidate. In two-stage elections (2S), each party has two candi￾dates (denoted cL1 and cL2 for Party L, cR1 and cR2 for Party R) who first compete in intraparty elections (the primaries). The candidates who win their respec￾tive party primaries then compete in a second-round election (the general election) to select the winning policy w. In other words, the parties hold simultaneous “closed” primaries in which the voter with ideal point θL chooses cL ∈ {cL1, cL2} for Party L while the voter with ideal point θR chooses cR ∈ {cR1, cR2} for Party R. In the general election, the median voter with ideal point θM chooses the election outcome from the two candi￾dates selected by the parties’ respective median voters, w ∈ {cL, cR}. To generate predictions about candidate positioning and to identify the effects of the election format, I con￾sider a variety of alternative behavioral assumptions. I begin with standard game theoretic analysis, applying Nash equilibrium as the solution concept. Since I am interested in making behavioral predictions, the inter￾pretation of Nash equilibrium is worth a brief discus￾sion. One way to interpret Nash equilibrium is to think of it as an idealized set of assumptions such that actors are not only fully rational but also that their rationality is common knowledge (Aumann and Brandenburger 1995). In this interpretation, we can think of political actors as forming beliefs about others’ current and fu￾ture behavior (as well as beliefs about beliefs and ra￾tionality, and so on) that are fully consistent with play￾ers’ actual strategies and behavior. Alternatively, Nash equilibrium can be interpreted as merely representing a stable outcome in which strategies are mutual best responses, without necessarily invoking an epistemic or belief-based justification of how individuals make deci￾sions in games. The latter approach, however, does not make clear cut predictions about how games are played before an equilibrium state is reached. Nevertheless, under a wide variety of learning models, experience can lead play to converge to Nash equilibrium (Fudenberg and Levine 1998), and the role of experience can be investigated experimentally. Relaxing the Nash assumption of the mutual con￾sistency of beliefs and actions generates an interest￾ing variety of behavioral possibilities. In my analysis, I first explore the implications of voter sophistication 828 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515