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To vote or not to vote: The paradox of nonvoting

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  • Guillermo Owen
  • Bernard Grofman

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. Copyright Martinus Nijhoff Publishers 1984

Suggested Citation

  • Guillermo Owen & Bernard Grofman, 1984. "To vote or not to vote: The paradox of nonvoting," Public Choice, Springer, vol. 42(3), pages 311-325, January.
    • Handle: RePEc:kap:pubcho:v:42:y:1984:i:3:p:311-325
    DOI: 10.1007/BF00124949
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    References listed on IDEAS

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    Cited by:

    1. Bernard Grofman & Scott Feld, 2005. "Thinking About the Political Impacts of the Electoral College," Public Choice, Springer, vol. 123(1), pages 1-18, April.
    2. Dan Usher, 2014. "An alternative explanation of the chance of casting a pivotal vote," Rationality and Society, , vol. 26(1), pages 105-138, February.
    3. Serguei Kaniovski & Dennis Mueller, 2006. "Community size, heterogeneity and voter turnouts," Public Choice, Springer, vol. 129(3), pages 399-415, December.
    4. Søberg, Morten & Tangerås, Thomas P., 2003. "Voter Turnout in Direct Democracy: Theory and Evidence," Working Paper Series 596, Research Institute of Industrial Economics.
    5. Montmarquette, Claude, 1988. "Le marché politique : qu’est-ce qui est produit? Qui y participe? Qui en profite?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 64(3), pages 336-360, septembre.
    6. Jan Hansen & Carsten Schmidt & Martin Strobel, 2004. "Manipulation in political stock markets - preconditions and evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 11(7), pages 459-463.
    7. Peter Bönisch & Benny Geys & Claus Michelsen, 2015. "David and Goliath in the Poll Booth: Group Size, Voting Power and Voter Turnout," Discussion Papers of DIW Berlin 1491, DIW Berlin, German Institute for Economic Research.
    8. William H. Kaempfer & Anton D. Lowenberg, 1993. "A Threshold Model of Electoral Policy and Voter Turnout," Rationality and Society, , vol. 5(1), pages 107-126, January.
    9. Claus Michelsen & Peter Boenisch & Benny Geys, 2014. "(De)Centralization and voter turnout: theory and evidence from German municipalities," Public Choice, Springer, vol. 159(3), pages 469-483, June.
    10. Barone, Guglielmo & de Blasio, Guido, 2013. "Electoral rules and voter turnout," International Review of Law and Economics, Elsevier, vol. 36(C), pages 25-35.
    11. Bechtel, Michael M. & Hangartner, Dominik & Schmid, Lukas, 2018. "Compulsory voting, habit formation, and political participation," LSE Research Online Documents on Economics 89714, London School of Economics and Political Science, LSE Library.
    12. Bilal Hafeez & M. Humayun Kabir & Udomsak Wongchoti, 2022. "Are retail investors really passive? Shareholder activism in the digital age," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 49(3-4), pages 423-460, March.
    13. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    14. J. Arias, 2003. "A note on the effect of elections subject to judicial review," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 31(4), pages 376-383, December.
    15. Luis Fernando Medina, 2011. "Is there really a turnout paradox?," Journal of Theoretical Politics, , vol. 23(3), pages 382-399, July.
    16. Robert Grafstein, 2002. "What Rational Political Actors Can Expect," Journal of Theoretical Politics, , vol. 14(2), pages 139-165, April.
    17. Richard Jankowski, 2002. "Buying a Lottery Ticket to Help the Poor," Rationality and Society, , vol. 14(1), pages 55-77, February.
    18. Richard Jankowski, 2007. "Altruism and the Decision to Vote," Rationality and Society, , vol. 19(1), pages 5-34, February.
    19. Tobias Streicher & Sascha L. Schmidt & Dominik Schreyer, 2019. "Referenda on Hosting the Olympics: What Drives Voter Turnout?," Journal of Sports Economics, , vol. 20(5), pages 627-653, June.
    20. Douglas D. Roscoe, 2014. "Yes, Raise My Taxes: Property Tax Cap Override Elections," Social Science Quarterly, Southwestern Social Science Association, vol. 95(1), pages 145-164, March.
    21. Aranson Peter H., 1990. "Rational Ignorance In Politics, Economics And Law," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 1(1), pages 1-18, January.

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