Electoral rules, strategic entry and polarization☆
Introduction
The rules of the electoral game matter a great deal. Electoral institutions have been shown to affect a constellation of economic and political outcomes such as, to name a few: redistribution, public spending and public good provision (e.g. Lizzeri and Persico, 2001, Milesi-Ferretti et al., 2002, Persson et al., 2007, Persson et al., 2003), turnout (e.g. Blais and Dobrzynska, 1998, Herrera et al., 2016), and campaign spending (Iaryczower and Mattozzi, 2013). Importantly, since Duverger (1954) we know that electoral rule disproportionality (understood broadly as the size of the electoral advantage assigned to the winner of the election) affects the structure of the party system (i.e. the number and policy platforms of the competing parties). Indeed, it is a stylized fact that the number of competing parties is higher in proportional representation (henceforth PR) systems compared to more disproportional ones, and that proportional systems provide parties with stronger centrifugal incentives than disproportional ones such as the plurality rule or first-past-the-post (e.g. Calvo and Hellwig, 2011, Cox, 1990, Matakos et al., 2016).1
Yet, despite electoral institutions altering parties' incentives to enter the electoral race but also to propose moderate or extreme platforms, our understanding – both theoretically and empirically – about the exact mechanisms via which electoral rules operate is rather incomplete. That is, are the effects of electoral rules on party entry and platform choice independent, or are they intertwined, thus making it more difficult to establish clear causal links? For instance, could it be that electoral rule disproportionality has direct effects only on the number of parties that decide to enter, and that platform decisions are only indirectly affected by the number of competing parties? Is it likely that the opposite holds (i.e. that electoral rules affect only platform selection, and this indirectly determines entry decisions)? Or, even, could it be that electoral rules affect both entry and platform selection incentives in a more convoluted manner?
The current literature has not revealed the exact mechanism via which electoral rules jointly affect entry and platform decisions. Typically, existing approaches instead analyze the effects of the electoral rule on electoral competition by focusing either on entry decisions, or on platform selection independently.2 The literature that focuses on entry decisions often builds on the citizen-candidate approach (à la Osborne and Slivinski, 1996, Besley and Coate, 1997). Yet candidates' platforms are exogenously fixed – once they enter the election, they do so in a predetermined position – and, hence, cannot answer the posited questions.3 Similarly, the literature which assumes an exogenous number of parties and endogenous platform selection cannot provide the necessary answers since it effectively shuts down the entry channel.4 In other words, there is no formal analysis examining the simultaneous effects of electoral rule disproportionality on party entry and platform choice and, at the same time: a) focuses on parties' strategic decisions,5 b) considers endogenous entry, and c) allows for the choice of platform to be endogenously determined. Indeed, the last two points are essential if one is to account for a potentially intertwined relationship between platform and entry decisions. In this paper we undertake the task of formulating such an argument and fill the described gap in the literature.
We consider a formal model in which parties compete under a continuum of alternative electoral rules that differ only in terms of disproportionality, and where both entry and platform decisions are endogenous. The parties are mainly policy motivated, in the sense that they want the implemented policy to be as close as possible to their ideal policies, but also care about their office rents reflected in their parliamentary power. In specific, a party in our framework is willing to participate in the election if by doing so it can influence the implemented policy to its benefit, or if it can secure substantial parliamentary power. If neither of these conditions are met, then it prefers to save the cost of entering the election. Under these assumptions, we show that both the number of parties that decide to enter and platform polarization (throughout the paper defined as the distance between the two most distant platforms) are decreasing in electoral rule disproportionality. That is, our theoretical results are in line with existing stylized facts confirming the original Duvergerian predictions and linking PR systems with higher polarization than disproportional ones.
But more importantly, we identify a three-step mechanism that may lie behind these stylized facts, and which uncovers that electoral rules do not exhibit only direct effects on entry and polarization incentives. A more intricate logic seems to be in operation. As more disproportional rules generate centripetal forces (see e.g. Cox, 1990) and extreme parties move towards the center (first-order effect), centrist parties are squeezed by competition and might eventually drop out (second-order effect). Thus, the electoral rule influence on entry decisions operates mainly via polarization. Interestingly, this generates an additional feedback effect: as the number of parties decreases, polarization becomes even lower in reaction to the smaller number of competing parties (third-order effect).6 That is, an increasing electoral rule disproportionality exhibits both a direct (first-order effect) and an indirect (third-order effect) negative force on polarization, and a negative force on the number of competing parties (second-order effect).
This bi-directional relationship between platform positions (polarization) and the number of competing parties (entry decision) implies that, despite widespread empirical support for the aggregate prediction, conclusive causal evidence is still wanting and, arguably, hard to obtain by the means of real elections' results. For this reason we turn to the laboratory and design an experiment in line with the main assumptions of our theoretical model. In this way we can test not only for the aggregate effect of electoral rule disproportionality on the number and the platforms of parties, but also for the relevance of the described two-way relationship between platform and entry choices and the resulting feedback effect.
In our experiment we limit attention to the two most asymmetric rules in terms of disproportionality (the plurality rule and the PR) and we find strong support for our theoretical predictions. In aggregate terms, the number of parties and polarization are found to be significantly higher under PR than under plurality; however, we do find excessive entry under PR compared to the theoretical benchmark. Moreover, the described three-step mechanism seems to be in full operation: a) for a fixed number of parties, polarization decreases when we move from a PR rule to plurality (first-order effect), b) entry (by the centrist party) is smaller under plurality compared to a PR rule in anticipation of lower polarization (second-order effect), and c) for a given electoral rule, polarization is decreasing in the number of parties (third-order effect).
There is a long literature in which researchers have tested in the laboratory the effect of electoral rules on various aspects of electoral competition.7 There are two sets of experimental studies that more specifically study the strategic entry of candidates in an electoral context: those that follow variations of the classic Hotelling-Downs model, and which typically assume an exogenous number of candidates and pure office motives (among a large literature see for e.g., Huck et al., 2002, Aragones and Palfrey, 2004, Bol et al., 2018), and those that follow the citizen-candidate model (Cadigan, 2005, Elbittar and Gomberg, 2009, Grosser and Palfrey, 2019, Kamm, 2017).8 The latter are closer to ours because they study the choice of candidates to enter or not, and assume that these candidates have policy motives in the sense that their payoff is, at least in part, a function of the distance between their ideal policy position and the policy position ultimately implemented after the election. However, these studies differ from ours in several important aspects. First, in Cadigan, 2005, Elbittar and Gomberg, 2009, Kamm, 2017, and Grosser and Palfrey (2019), the candidates only choose whether to enter or not. They cannot choose their policy platform strategically, as they can only compete under their ideal policy position. Second, our experiment tests the model predictions for two electoral rules: plurality and proportional representation. Only Kamm (2017) compares these two electoral rules and also finds that entry is larger under proportional representation, while others restrict themselves to plurality rule (Cadigan, 2005, Grosser and Palfrey, 2019), sometimes in combination with majority runoff (Elbittar and Gomberg, 2009). Finally, unlike Grosser and Palfrey (2019), but similar to other studies, the candidates in our experiment have complete information about the ideal policy positions of other participants, and so do voters. By contrast, Grosser and Palfrey (2019) study an environment with incomplete information, in which voters can only infer candidates' position from equilibrium outcomes. Our experiment is thus unique, as it allows the candidates to enter or not the election, and to compete under the policy platform of their choice, which might or might not be the same than their ideal position.
Overall, our work makes a dual contribution. On the theory side, existing approaches that allow for both endogenous entry and platform selection – even solely in the context of plurality rule – do not consider that candidates have substantial policy concerns, and hence cannot pin down the identified relationship between entry and polarization (see Bol et al., 2016). Moreover, this is the first study that formally documents the simultaneous existence of three intertwined channels through which electoral rules affect parties' entry and platform decisions. On the experimental side, our study is the first to propose a comprehensive test of a political competition model under plurality and proportional rules, in which both the platform choices and entry decisions are made endogenously by the participants. As a result, our research design allows us to account for the two-way relationship between polarization and candidate entry that our theory predicts and fully characterizes the effects of the electoral rule (dis)proportionality on the party-system structure.
In what follows, we first present our theoretical arguments (Section 2), then we describe our experimental design and results (Section 3), and, finally, we conclude (Section 4). In the Appendix we prove our main theoretical result and provide additional empirical analysis.
Section snippets
The model
In order to incorporate parties' entry decision we consider the following “standard” two stage entry game: In the first stage, parties decide whether to enter the (costly) electoral race or not. In the second stage, each competing party observes which other parties entered the race and strategically selects its political platform. Parties' strategic behavior then determines the electoral outcome and implemented policy (as later detailed), and hence the subsequently realized payoffs. We focus on
The experiment
We conducted 14 experimental sessions between January 2018 and March 2019 at the LExEL Lab of the University of Lancaster with 190 unique subjects participating in the experiment. The pool of participants is composed of undergraduate and postgraduate university students from various degrees. Participants were recruited using standard procedures via ORSEE (Greiner, 2015) and the experiment was executed on z-Tree (Fischbacher, 2007).
Each session involved 10 or 15 participants (depending on the
Conclusions
Our paper develops a formal model where both candidates' entry and location decisions are endogenously determined under different electoral rules. This allows us to account for the bi-directional effect between party platform positions (polarization) and entry decisions in addition to the first-order effect of electoral rule (dis)proportionality on polarization. Thus our model provides a formal result in line with Duverger (1954) hypotheses that stipulate that more candidates advancing distinct
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The paper benefited significantly from the constructive comments of two anonymous referees and the co-editor, Erik Snowberg. We are also grateful to Laurent Bouton, Thomas Bräuninger, Wioletta Dziuda, Konstantinos Georgalos, Emma Manifold, Konstantinos Protopappas, and Stephane Wolton. For valuable feedback we thank the participants in the following events: EPSA, ECPR, and MPSA conferences, Barcelona GSE Summer Forum, KCL workshop on game theory, Mannheim workshop on spatial models of party competition, PSE Brownbag Seminar of the Behaviour Group.