Probability and elections: power indices in voting

Document Type : Research Paper

Author

Lorestan University

Abstract

Elections are the most significant political and social events in societies with an electoral system. The lack of awareness about the election outcome can be modeled using probabilistic models to make probable predictions about this result. In this article, we first examine the Probability of tied elections and then introduce the power of voting and the Penrose–Banzhaf Power Index and related probabilistic measures. The investigation of these probabilistic measures is crucial for studying and understanding the phenomenon of elections from a probabilistic perspective and identifying sections of society that have the most significant impact on the election outcome.

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References

[1]D. André, Solution directe du probléme résolu par M. Bertrand, Comptes Rendus de l’Académie des Sciences, Paris, 105 (1887) 436–437.
[2]J. F. Banzhaf, Weighted voting doesn’t work: A mathematical analysis, Rutgers Law Review, 19 (1965) 317–343.
[3]É. Barbier, Généralisation du probléme résolu par M. J. Bertrand, Comptes Rendus de l’Académie des Sciences, Paris, 105 (1887), p. 407.
[4]N. Beck, A Note on the Probability of a Tied Election, Public Choice, 23 (1975) 75–79.
[5]J. Bertrand, Solution d’un problème, Comptes Rendus de l’Académie des Sciences, Paris,105 (1887), p. 369.
[6]K. Pąk, Bertrand’s Ballot Theorem, Formalized Mathematics, 22 (2014) 119–123.
[7]L. S. Penrose, The Elementary Statistics of Majority Voting, Journal of the Royal Statistical Society, 109 (1946) 53–57. [8]M. Renault, Four Proofs of the Ballot Theorem, Mathematics Magazine, 80 (2007) 345–352.
[9]M. A. Cichocki and K. Zyczkowski, Institutional Design and Voting Power in the European Union, Routledge, London, 2016.

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History

  • Receive Date: 30 August 2017
  • Revise Date: 08 July 2018
  • Accept Date: 21 July 2018
  • Publish Date: 20 February 2019

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