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Correlation, partitioning and the probability of casting a decisive vote under the majority rule

Author

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  • Michel Le Breton

    (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Lepelley

    () (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Hatem Smaoui

    () (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

Abstract

The main purpose of this paper is to estimate the probability of casting a decisive vote under the majority rule for a class of random electorate models encompassing the celebrated Impartial Culture (IC) and Impartial Anonymous Culture (IAC) models. The emphasis is on the impact of correlation across votes on the order of magnitude of this event. Our proof techniques use arguments from probability theory on one hand and combinatorial and algorithmic tools for counting integer points inside convex polytopes on the other hand.

Suggested Citation

  • Michel Le Breton & Dominique Lepelley & Hatem Smaoui, 2016. "Correlation, partitioning and the probability of casting a decisive vote under the majority rule," Post-Print hal-01452554, HAL.
  • Handle: RePEc:hal:journl:hal-01452554
    DOI: 10.1016/j.jmateco.2016.03.001
    Note: View the original document on HAL open archive server: https://hal.univ-reunion.fr/hal-01452554
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    References listed on IDEAS

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    1. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    2. 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.
    3. Michel Le Breton & Dominique Lepelley, 2014. "Une analyse de la loi électorale du 29 juin 1820," Revue économique, Presses de Sciences-Po, vol. 65(3), pages 469-518.
    4. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    5. Berg, Sven, 1990. "The Probability of Casting a Decisive Vote: The Effects of a Caucus," Public Choice, Springer, vol. 64(1), pages 73-92, January.
    6. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    7. Nathaniel Beck, 1975. "A note on the probability of a tied election," Public Choice, Springer, vol. 23(1), pages 75-79, September.
    8. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    9. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
    10. 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.
    11. Peter Fishburn & William Gehrlein, 1976. "Borda's rule, positional voting, and Condorcet's simple majority principle," Public Choice, Springer, vol. 28(1), pages 79-88, December.
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    Citations

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    Cited by:

    1. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    2. Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2017. "Exploring the Effects on the Electoral College of National and Regional Popular Vote Interstate Compact: An Electoral Engineering Perspective," TSE Working Papers 17-861, Toulouse School of Economics (TSE), revised May 2018.
    3. Olivier Mouzon & Thibault Laurent & Michel Le Breton & Dominique Lepelley, 2020. "The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 363-395, March.
    4. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    5. 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.
    6. 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.
    7. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Feb 2021.

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    More about this item

    Keywords

    Economics; Elections; Power measurement; Random electorate; Voting;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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