Three aspects of multicandidate competition in plurality rule elections

Citation

Fey, Mark (1995) Three aspects of multicandidate competition in plurality rule elections. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1j5k-pc62. https://resolver.caltech.edu/CaltechETD:etd-10022007-130421

Abstract

This thesis considers three issues relevant to multicandidate competition in plurality rule elections--entry decisions by candidates, strategic voting, and informational concerns.

In the first chapter, we consider a model of spatial competition with entry introduced by Palfrey (1984). In the model, there are two dominant candidates and a potential entrant. The established candidates choose positions first, anticipating the entry decision of the third candidate. In the resulting equilibrium, this threat of entry forces the established parties to adopt spatially separated "moderate" positions. We develop a general model that applies to the complex institutional features of modern elections. Specifically, we introduce the winner-take-all aspects of the Electoral College and show how these characteristics make a difference in the equilibrium predictions of the model. We find that, in one case at least, increasing diversity in the electorate causes the established candidates to initially shift toward more moderate positions and then back toward more extreme positions.

The second chapter examines strategic voting and Duverger's Law. A voter whose favorite candidate has no hope of victory may choose to avoid a "wasted vote" by settling for a less preferred candidate with a higher chance of winning. This behavior erodes the electoral support of minor candidates and results in Duverger's Law: "plurality rule elections favor two party competition." Palfrey (1989) constructs an incomplete information game among voters and shows that as the size of the electorate gets large, the support for the least popular candidate vanishes. We show that there exist equilibria in this model in which all three candidates receive votes under plurality rule, in violation of Duverger's Law, as suggested by Myerson and Weber (1993). However, we proceed to demonstrate that these equilibria are unstable and any uncertainty by voters leads voters back toward Duvergerian equilibria. In addition, we develop a dynamic model of pre-election polls that describes how voters react to changing information about the viability of the candidates and show that this process leads voters to coordinate on a Duvergerian outcome. Thus, we not only reestablish Duverger's Law, we also describe how voters can use pre-election polls to coordinate on a particular pair of competitive candidates.

In the third chapter we analyze the relationship between voter information and election outcomes in a multicandidate setting. We extend a model originally developed by McKelvey and Ordeshook for two candidate elections to the multicandidate case. In the model, voters are either informed or uninformed about the exact positions of the candidates. The uninformed voters, however, are able to make plausible inferences about these positions based on the vote share each candidate receives. In equilibrium, voters vote optimally, given their beliefs, and beliefs are self-fulfilling in the sense that they are not contradicted by observable information. Our first result is that in the unique voter equilibrium of our model, all voters, informed and uninformed alike, vote as if they had perfect information. We then define a dynamic process involving a sequence of polls that illustrates that this equilibrium is always reached. In addition, we obtain results about candidate positioning equilibria when candidates are also uncertain about the characteristics of the voters. Finally, we show that if a small minority of voters are fully informed and use this information to vote strategically, in equilibrium all voters, including uninformed sincere voters, act as if they were voting strategically based on full information. The uninformed voters view the lack of support for trailing candidates by informed voters as evidence that these candidates are undesirable and react by voting for a more prominent candidate.

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