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Voting Rules, Manipulability and Social Homogeneity

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  • Lepelley, Dominique
  • Valognes, Fabrice

Abstract

To what extent are some voting rules more vulnerable to strategic manipulation than others? In order to answer this question, representations are developed for the coalitional manipulability of eight voting rules under various assumptions concerning the likelihood that given voters' preference profiles are observed on three alternatives. Of particular interest is the impact that social homogeneity (defined as the tendency of voters' preference to be similar) has on the manipulability of voting rules. The results we obtain show that the hierarchy of the voting rules that results from our computations can crucially depend on the degree of social homogeneity. However, it turns out that, whatever the degree of homogeneity, the Hare method (or two-stage plurality) minimizes susceptibility to strategic manipulation by coalitions of voters in three-candidate elections. Copyright 2003 by Kluwer Academic Publishers

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  • Lepelley, Dominique & Valognes, Fabrice, 2003. "Voting Rules, Manipulability and Social Homogeneity," Public Choice, Springer, vol. 116(1-2), pages 165-184, July.
    • Handle: RePEc:kap:pubcho:v:116:y:2003:i:1-2:p:165-84
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    Cited by:

    1. James Green-Armytage, 2014. "Strategic voting and nomination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 111-138, January.
    2. James Green-Armytage, 2023. "A Dodgson-Hare synthesis," Constitutional Political Economy, Springer, vol. 34(3), pages 458-470, September.
    3. Lirong Xia, 2022. "The Impact of a Coalition: Assessing the Likelihood of Voter Influence in Large Elections," Papers 2202.06411, arXiv.org, revised Jun 2023.
    4. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    5. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    6. Mostapha Diss, 2015. "Strategic manipulability of self-selective social choice rules," Annals of Operations Research, Springer, vol. 229(1), pages 347-376, June.
    7. Burak Can & Ali Ihsan Ozkes & Ton Storcken, 2017. "Generalized Measures of Polarization in Preferences," AMSE Working Papers 1734, Aix-Marseille School of Economics, France.
    8. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    9. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    10. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    11. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    12. Yuliya A. Veselova, 2020. "Does Incomplete Information Reduce Manipulability?," Group Decision and Negotiation, Springer, vol. 29(3), pages 523-548, June.
    13. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    14. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 485-509, June.
    15. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    16. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    17. Eyal Baharad & Zvika Neeman, 2007. "Robustness against inefficient manipulation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 55-67, July.
    18. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.
    19. Geoffrey Pritchard & Arkadii Slinko, 2006. "On the Average Minimum Size of a Manipulating Coalition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 263-277, October.
    20. James Green-Armytage & T. Nicolaus Tideman, 2020. "Selecting the runoff pair," Public Choice, Springer, vol. 182(1), pages 119-137, January.
    21. Yuliya A. Veselova, 2016. "Does Incomplete Information Reduce Manipulability?," HSE Working papers WP BRP 152/EC/2016, National Research University Higher School of Economics.
    22. Karthik H. Shankar, 2022. "Normed Negative Voting to Depolarize Politics," Group Decision and Negotiation, Springer, vol. 31(6), pages 1097-1120, December.
    23. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.

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