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The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System

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  • Laurent, Thibault
  • Le Breton, Michel
  • Lepelley, Dominique
  • de Mouzon, Olivier

Abstract

In this article, we evaluate asymptotically the probability ϕ(n) of an election inversion in a toy symmetric version of the US presidential electoral system. The novelty of this paper, in contrast to all the existing theoretical literature, is to assume that votes are drawn from an IAC (Impartial Anonymous Culture)/Shapley–Shubik probability model. Through the use of numerical methods, it is conjectured, that n−−√ϕ(n) converges to 0.1309 when n (the size of the electorate in one district) tends to infinity. It is also demonstrated that ϕ(n)=o(ln(n)3n−−−−√) and ϕ(n)=Ω(1n√).
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  • Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2016. "The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System," TSE Working Papers 16-671, Toulouse School of Economics (TSE), revised Feb 2018.
  • Handle: RePEc:tse:wpaper:30551
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    References listed on IDEAS

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    1. Owen, Guillermo, 1975. "Evaluation of a Presidential Election Game," American Political Science Review, Cambridge University Press, vol. 69(3), pages 947-953, September.
    2. Nicholas Miller, 2012. "Why the Electoral College is good for political science (and public choice)," Public Choice, Springer, vol. 150(1), pages 1-25, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    8. 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.
    9. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    10. Lepelley, Dominique & Merlin, Vincent & Rouet, Jean-Louis, 2011. "Three ways to compute accurately the probability of the referendum paradox," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 28-33, July.
    11. Tufte, Edward R., 1973. "The Relationship between Seats and Votes in Two-Party Systems," American Political Science Review, Cambridge University Press, vol. 67(2), pages 540-554, June.
    12. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, July.
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    Cited by:

    1. 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.
    2. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel & Moyouwou, Issofa, 2020. "“One Man, One Vote” Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May," TSE Working Papers 20-1074, Toulouse School of Economics (TSE).
    3. 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.
    4. Michael Geruso & Dean Spears & Ishaana Talesara, 2019. "Inversions in US Presidential Elections: 1836-2016," NBER Working Papers 26247, National Bureau of Economic Research, Inc.
    5. Kazuya Kikuchi, 2022. "Welfare ordering of voting weight allocations," Papers 2208.05316, arXiv.org, revised Mar 2024.
    6. Serguei Kaniovski & Alexander Zaigraev, 2018. "The probability of majority inversion in a two-stage voting system with three states," Theory and Decision, Springer, vol. 84(4), pages 525-546, June.

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    More about this item

    Keywords

    Electoral system; Election Inversions; Impartial Anonymous Culture;
    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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