A theory of voting in large elections

Abstract

This paper provides a game-theoretic model of probabilistic voting and then examines the incentives faced by candidates in a spatial model of elections. In our model, voters' strategies form a Quantal Response Equilibrium (QRE), which merges strategic voting and probabilistic behavior. We first show that a QRE in the voting game exists for all elections with a finite number of candidates, and then proceed to show that, with enough voters and the addition of a regularity condition on voters' utilities, a Nash equilibrium profile of platforms exists when candidates seek to maximize their expected margin of victory. This equilibrium (1) consists of all candidates converging to the policy that maximizes the expected sum of voters' utilities, (2) exists even when voters can abstain, and (3) is unique when there are only 2 candidates. Journal of Economic Literature Classification Numbers: D71, D72, D50, D60.

Gridlock or Leadership in U.S. Electoral Politics

“…In this model, activists provide crucial resources of time and money to their chosen party, and these resources are dependent on the party position. 12 The party then uses these resources to enhance its image before the electorate, thus affecting its overall 8 Adams and Merrill (2005), Ansolabehere et al (2001), Aragones and Palfrey (2002), Ashworth and Bueno de Mesquita (2009), Banks and Duggan (2005), Groseclose (2001) and McKelvey and Patty (2006). 9 Schofield and Sened (2006), Schofield (2007).…”

“…We develop an electoral model that is an extension of the multiparty stochastic model of McKelvey and Patty (2006), modified by inducing asymmetries in terms of valence. The justification for developing the model in this way is the empirical evidence that valence is a natural way to model the judgements made by voters of party leaders and candidates.…”

Securing the base: electoral competition under variable turnout

“…In the online appendix, I construct two examples to show how variable turnout can lead to divergent equilibria. In addition, it is well known that the presence of third party candidates can lead to divergent equilibria (Adams 2000;Schofield 2003Schofield , 2004McKelvey and Patty 2006). Consequently, the validity of the Securing the Base strategy is theoretically ambiguous, and must be evaluated empirically.…”

Statistical Utilitarianism

“…These equilibria occasionally have surprising social welfare properties. For example, Ledyard (1984), Weibull (1987, 1993), Coughlin (1992;Theorem 3.7 and Corollary 4.4), Banks and Duggan (2004;§4) and McKelvey and Patty (2006) have all shown that, in certain election games, there is a unique Nash equilibrium (sometimes called a "political equilibrium") where all the candidates select the policy which maximizes a utilitarian SWF. But these utilitarian SWFs are based on somewhat peculiar systems of interpersonal utility comparisons.…”