Revised version. Original dated to February 1999. Proposed Running Head: Voting in Large Elections A previous version of this paper was entitled "Quantal Response Voting". The financial support of NSF grants #SBR-9631627 and #SES-0079301 to the California Institute of Technology are gratefully acknowledged. In addition, Patty acknowledges the financial assistance of the Alfred P. Sloan Foundation. This paper benefited from helpful comments from seminar participants at CERGY-Pontoise (Oct 1998), CORE (Oct 1998), Tilburg (Oct 1998), Caltech Theory Workshop (May, 1999), Public Choice Society (New Orleans, March 1999), the Stan and Cal Show (Pismo Beach, May, 1999), the APSA annual meetings (Atlanta, 1999), and the Wallis Conference on Political Economy (Rochester, NY, October, 1999). We especially thank John Duggan, Tom Palfrey, Norman Schofield, Bob Sherman, two anonymous referees, and an Associate Editor for helpful input. Richard passed away on April 22, 2002. He is, and will be, terribly missed as both a friend and a scholar. Published as McKelvey, R.D., & Patty, J.W. (2006). A theory of voting in large elections. Games and Economic Behavior, 57(1), 155-180.

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.

Submitted - sswp1056.pdf