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Forming Voting Blocs and Coalitions as a Prisoner's Dilemma: A Possible Theoretical Explanation for Political Instability

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  • Gelman Andrew

    (Department of Statistics, Columbia University)

Abstract

Individuals in a committee or election can increase their voting power by forming coalitions. This behavior is shown here to yield a prisoner's dilemma, in which a subset of voters can increase their power, while reducing average voting power for the electorate as a whole. This is an unusual form of the prisoner's dilemma in that cooperation is the selfish act that hurts the larger group. Under a simple model, the privately optimal coalition size is approximately 1.4 times the square root of the number of voters. When voters' preferences are allowed to differ, coalitions form only if voters are approximately politically balanced. We propose a dynamic view of coalitions, in which groups of voters choose of their own free will to form and disband coalitions, in a continuing struggle to maintain their voting power. This is potentially an endogenous mechanism for political instability, even in a world where individuals' (probabilistic) preferences are fixed and known.

Suggested Citation

  • Gelman Andrew, 2003. "Forming Voting Blocs and Coalitions as a Prisoner's Dilemma: A Possible Theoretical Explanation for Political Instability," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-16, October.
    • Handle: RePEc:bpj:bejeap:v:contributions.2:y:2003:i:1:n:13
    DOI: 10.2202/1538-0645.1185
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    References listed on IDEAS

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    1. R. H. Coase, 2013. "The Problem of Social Cost," Journal of Law and Economics, University of Chicago Press, vol. 56(4), pages 837-877.
    2. Van Kolpin, 2003. "Voting Power Under Uniform Representation," Economics Bulletin, AccessEcon, vol. 4(2), pages 1-5.
    3. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    4. Peter Bernholz, 1982. "Externalities as a Necessary Condition for Cyclical Social Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(4), pages 699-705.
    5. Donal G. Saari & Katri K. Sieberg, 1999. "Some Surprising Properties of Power Indices," Discussion Papers 1271, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. repec:ebl:ecbull:v:4:y:2003:i:2:p:1-5 is not listed on IDEAS
    7. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Kazuya Kikuchi & Yukio Koriyama, 2019. "The Winner-Take-All Dilemma," ISER Discussion Paper 1059, Institute of Social and Economic Research, Osaka University.
    2. Jon X. Eguia, 2007. "United We Vote," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 607-639, August.
    3. repec:cup:judgdm:v:10:y:2015:i:6:p:511-537 is not listed on IDEAS
    4. Jon X. Eguia, 2006. "United We Vote," Working Papers 2006.9, Fondazione Eni Enrico Mattei.
    5. Kazuya Kikuchi & Yukio Koriyama, 2019. "The Winner-Take-All Dilemma," ISER Discussion Paper 1059r, Institute of Social and Economic Research, Osaka University, revised Dec 2019.
    6. Daniel A. DeCaro & Marco A. Janssen & Allen Lee, 2015. "Synergistic effects of voting and enforcement on internalized motivation to cooperate in a resource dilemma," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 10(6), pages 511-537, November.
    7. Kikuchi, Kazuya & Koriyama, Yukio, 2023. "The winner-take-all dilemma," Theoretical Economics, Econometric Society, vol. 18(3), July.
    8. Eguia, Jon X., 2011. "Voting blocs, party discipline and party formation," Games and Economic Behavior, Elsevier, vol. 73(1), pages 111-135, September.

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