The vulnerability of majority rule to Anscombe's and Ostrogorkski's paradoxes : A comparative analysis

Authors

  • Boniface Mbih CREM UMR CNRS 6211, Université de Caen Normandie, 14032 Caen, France
  • Aristide Valeu Enseignant vacataire à l’université de Nanterre Paris X

Keywords:

Anscombe’s paradox, Ostrogorski’s paradox, culture impartiale, culture impartiale anonyme, simulations

Abstract

The aim of this paper is to study the circumstances at which the Anscombe and Ostrogorski paradoxes are susceptible to arise when individual votes are dichotomous, that is, in the context of yes-no voting. Our main results provide an answer to the question of the likelihood of those paradoxes under two classical probabilistic models: the impartial culture (IC) and the impartial anonymous culture (IAC) assumptions. More precisely, we determine the exact frequencies of occurrence of these phenomena in the three-issue case, under simple majority rule; we also provide estimates - obtained by means of the Monte Carlo technique - for more than three issues.

References

Anscombe GEM, (1976), On Frustration of the Majority by Fulfillment of the Majority’s Will, Analysis, vol. 36, no. 4, pp. 161–168.
View in Google Scholar

Bezembinder, T., Van Acker, P., (1985), The Ostrogorski Paradox and its Relation to Nontran- sitive Choice, Journal of Mathematical Sociology vol. 11, pp. 131–158.
View in Google Scholar

Dummett, M., (1984), Voting procedures, Clarendon Press, Oxford. Gehrlein, W.V., (2006), Condorcet’s Paradox, Springer, Berlin.
View in Google Scholar

Gehrlein, W.V., (1976), Condorcet’s Paradox and Anonymous Preference Profiles, Public Choice, vol. 26, pp. 1–18.
View in Google Scholar

Gehrlein, W.V., Lepelley, D., (2012), The Value of Research Based on Simple Assumptions on Voters’ Preferences, dans: Felsenthal, D., Machover, M. (eds), Electoral Systems, Springer, Berlin.
View in Google Scholar

Kelly, J.S., (1989), The Ostrogorski paradox, Social Choice and Welfare, vol. 6, pp. 71–76.
View in Google Scholar

Laffond, G., Lainé, J., (2009), Condorcet Choice and the Ostrogorski Paradox, Social Choice and Welfare, vol. 32, pp. 317–333.
View in Google Scholar

Laffond, G., Lainé, J., (2011), Unanimity and the Anscombe’s paradox, TOP.
View in Google Scholar

Lepelley, D., Louichi, A., Smaoui, H., (2008), On Ehrhart Polynomials and Probability Calculations in Voting Theory, Social Choice and Welfare, vol. 30, pp. 363–383.
View in Google Scholar

Mbih, B., Moyouwou, I., Picot, J., (2008), Pareto Violations of Parliamentary Voting Systems, Economic Theory, vol. 34, pp. 331–358.
View in Google Scholar

Mbih, B., Courtin, S., Moyouwou, I., (2010), Susceptibility to Coalitional Strategic Sponsoring: the Case of Parliamentary Agendas, Public Choice, vol. 144, pp. 133–151.
View in Google Scholar

Nurmi, H., (1999), Voting Paradoxes and How to Deal with Them, Springer, Berlin.
View in Google Scholar

Nurmi, H., Meskanen, T., (1997), Voting Paradoxes and MCDM, Social Choice and Welfare, vol. 15, pp. 333–350.
View in Google Scholar

Nurmi, H., Saari, DG., (2010), Connections and Implications of the Ostrogorski Paradox for Spatial Voting Models, dans: van Deemen, A., Rusinowska, A. (eds.), Collective Decision Making: Views from Social Choice and Game Theory, Springer, Berlin.
View in Google Scholar

Ostrogorski, M., (1902), La démocratie et l’organisation des partis politiques, Calmann-Levy, Paris.
View in Google Scholar

Regenwetter, M., Grofman, B., Marley, A.A.J., Tsetlin, I.M., (2006), Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications, Cambridge University Press, Cambridge.
View in Google Scholar

Downloads

Published

2016-06-30

Issue

Vol. 1 No. 1 (2016)

Section

Articles

License

Copyright (c) 2016 Poznań University of Economics and Business

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.