Quarterly Journal of Political Science > Vol 4 > Issue 3

Two's Company, Three's an Equilibrium: Strategic Voting and Multicandidate Elections

John W. Patty, Department of Political Science, Washington University in St. Louis, jpatty@wustl.edu James M. Snyder Jr., Department of Political Science and Department of Economics, Massachusetts Institute of Technology, millett@mit.edu Michael M. Ting, Department of Political Science and SIPA, Columbia University, mmt2033@columbia.edu
Suggested Citation
John W. Patty, James M. Snyder Jr. 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

Published: 20 Oct 2009
© 2009 J. W. Patty, J. M. Snyder, Jr. and M. M. Ting
Voting theory,  Electoral behavior,  Formal modelling
Multicandidate electionsUndominated equilibriumSpatial competitionMinmax set

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In this article:
Related Literature
The Model
Electoral Equilibrium Existence
Equilibrium Policy Outcomes
The Minmax Set
Conclusion and Future Work
Future Work


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.