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The Winner-Take-All Dilemma

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  • Kazuya Kikuchi
  • Yukio Koriyama

Abstract

This paper considers collective decision-making when individuals are partitioned into groups (e.g., states or parties) endowed with voting weights. We study a game in which each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members' preferences. We show that under quite general conditions, the game is a Prisoner's Dilemma: while the winner-take-all rule is a dominant strategy, the equilibrium is Pareto dominated. We also show asymptotic Pareto dominance of the proportional rule. Our numerical computation for the US Electoral College verifies the sensibility of the asymptotic results.

Suggested Citation

  • 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.
    • Handle: RePEc:dpr:wpaper:1059r
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    References listed on IDEAS

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    1. Claus Beisbart & Stephan Hartmann, 2010. "Welfarist evaluations of decision rules under interstate utility dependencies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 315-344, February.
    2. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    3. Assar Lindbeck & Jörgen Weibull, 1987. "Balanced-budget redistribution as the outcome of political competition," Public Choice, Springer, vol. 52(3), pages 273-297, January.
    4. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2004. "The probability of conflicts in a U.S. presidential type election," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 227-257, January.
    5. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    6. Héloïse Cloléry & Yukio Koriyama, 2020. "Trapped by the Prisoner’s Dilemma, the United States Presidential Election Needs a Coordination Device," Institut des Politiques Publiques halshs-03019446, HAL.
    7. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    8. Olivier Mouzon & Thibault Laurent & Michel Breton & Dominique Lepelley, 2019. "Exploring the effects of national and regional popular vote Interstate compact on a toy symmetric version of the Electoral College: an electoral engineering perspective," Public Choice, Springer, vol. 179(1), pages 51-95, April.
    9. Le Breton, Michel & Lepelley, Dominique & Smaoui, Hatem, 2016. "Correlation, partitioning and the probability of casting a decisive vote under the majority rule," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 11-22.
    10. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    11. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    12. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    14. Melis Kartal, 2015. "A Comparative Welfare Analysis of Electoral Systems with Endogenous Turnout," Economic Journal, Royal Economic Society, vol. 125(587), pages 1369-1392, September.
    15. Claus Beisbart & Luc Bovens & Stephan Hartmann, 2005. "A Utilitarian Assessment of Alternative Decision Rules in the Council of Ministers," European Union Politics, , vol. 6(4), pages 395-418, December.
    16. Moyes Patrick, 1994. "Inequality Reducing and Inequality Preserving Transformations of Incomes: Symmetric and Individualistic Transformations," Journal of Economic Theory, Elsevier, vol. 63(2), pages 271-298, August.
    17. 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.
    18. Patrick Hummel, 2011. "Proportional versus winner-take-all electoral vote allocations," Public Choice, Springer, vol. 148(3), pages 381-393, September.
    19. 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.
    20. David Stromberg, 2008. "How the Electoral College Influences Campaigns and Policy: The Probability of Being Florida," American Economic Review, American Economic Association, vol. 98(3), pages 769-807, June.
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    Cited by:

    1. Kazuya Kikuchi & Yukio Koriyama, 2023. "A General Impossibility Theorem on Pareto Efficiency and Bayesian Incentive Compatibility," Papers 2303.05968, arXiv.org, revised Mar 2024.
    2. Héloïse Cloléry & Yukio Koriyama, 2020. "Trapped by the Prisoner’s Dilemma, the United States Presidential Election Needs a Coordination Device," Institut des Politiques Publiques halshs-03019446, HAL.
    3. Héloïse Cloléry & Yukio Koriyama, 2020. "Elections présidentielles américaines : comment sortir du dilemme du prisonnier ?," Post-Print halshs-03019443, HAL.

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