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The probability of majority inversion in a two-stage voting system with three states

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  • Serguei Kaniovski

    (Austrian Institute of Economic Research (WIFO))

  • Alexander Zaigraev

    (Nicolaus Copernicus University)

Abstract

Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of the election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-018-9660-1
    DOI: 10.1007/s11238-018-9660-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Dominique Lepelley & Vincent R Merlin & Jean-louis Rouet & Laurent Vidu, 2014. "Referendum paradox in a federal union with unequal populations: the three state case," Economics Bulletin, AccessEcon, vol. 34(4), pages 2201-2207.
    4. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    5. 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.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
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    Cited by:

    1. Michael Geruso & Dean Spears & Ishaana Talesara, 2022. "Inversions in US Presidential Elections: 1836–2016," American Economic Journal: Applied Economics, American Economic Association, vol. 14(1), pages 327-357, January.
    2. Kazuya Kikuchi, 2022. "Welfare ordering of voting weight allocations," Papers 2208.05316, arXiv.org, revised Mar 2024.

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