VOLUME 4, ISSUE 3, 2009 <Previous Two’s Company, Three’s an Equilibrium: Strategic Voting and Multicandidate Elections John W. Patty James M. Snyder Michael M. Ting SUGGESTED CITATION: John W. Patty, James M. Snyder and Michael M. Ting (2009) "Two’s Company, Three’s an Equilibrium: Strategic Voting and Multicandidate Elections", Quarterly Journal of Political Science: Vol. 4:No 3, pp 251-278. http:/dx.doi.org/10.1561/100.00008056 Download this article Tell a Colleague Get Acrobat Reader Printing Tip: Select the option to 'print as image' in the Acrobat print dialog to ensure the article prints as it appears on screen. Learn more... In this paper, we characterize equilibria in games of electoral competition between three or more office-seeking candidates. Recognizing that electoral equilibrium involves both candidates’ and voters’ strategies, we first prove existence of pure strategy electoral equilibria when candidates seek to maximize their vote share. Accordingly, the main difficulty with electoral equilibria is multiplicity. We prove that, even after restricting attention to subgame perfect Nash equilibria in weakly undominated strategies, the set of electoral equilibria is very large. We provide several characterizations of candidates’ equilibrium platforms, including a set of conditions under which equilibrium platforms are located in the minmax set. We also examine welfare implications of the results as well as connections between the noncooperative equilibria and the uncovered set.

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