Abstract
One paradox of voting states that, in a general election, in which many citizens vote, the probability that a single voter can affect the outcome is so small that in general citizens have no rational reason for voting. However, if all citizens accept this reasoning, then none will vote, and so each vote has a large probability of affecting the outcome. Hence all should vote after all. The adoption of mixed strategies resolves this paradox: if each citizen adopts a certain (small) probability of voting, then the actual number of citizens voting will be just enough to make it worth those citizens' while to vote. A Nash equilibrium point thus occurs. Here we compute Nash equilibria for the simple case of majority voting; for the more complicated case of composite voting (for example, as in a presidential election), we draw certain qualitative inferences.
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This research was supported by NSF Grant # SES 80-07915, Program in Political Science. We thank the members of the staff of the Word Processing Center, School of Social Sciences, University of California, Irvine, for their invaluable assistance in typing repeated drafts of this manuscript; we also thank Linton Freeman, Dean of the School of Social Sciences, and Charles Lave, Chair of the Program in Economics and Public Choice, for facilitating a visiting appointment for Professor Owen at the University of California, Irvine, to permit the authors to pursue their collaborative research. The junior author also thanks the students in his course ‘Introduction to Decision Analysis, ’whose questions about rational choice models of citizen turnout prompted the writing of this essay.
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Owen, G., Grofman, B. To vote or not to vote: The paradox of nonvoting. Public Choice 42, 311–325 (1984). https://doi.org/10.1007/BF00124949
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DOI: https://doi.org/10.1007/BF00124949