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Manipulable outcomes within the class of scoring voting rules

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  • Diss, Mostapha
  • Tsvelikhovskiy, Boris

Abstract

Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their votes in order to secure an outcome they all prefer to the outcome of the election when they vote honestly. The present paper is devoted to studying coalitional manipulability within the class of scoring voting rules. For any such rule and any number of alternatives, we introduce a new approach allowing us to characterize all the outcomes that are manipulable by a coalition of voters. This then opens the possibility of determining the probability of manipulable outcomes for some well-studied scoring voting rules in the case of small number of alternatives and large electorates, under a well-known assumption on individual preference profiles.

Suggested Citation

  • Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    • Handle: RePEc:eee:matsoc:v:111:y:2021:i:c:p:11-18
    DOI: 10.1016/j.mathsocsci.2021.02.002
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    References listed on IDEAS

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    1. Mostapha Diss, 2015. "Strategic manipulability of self-selective social choice rules," Annals of Operations Research, Springer, vol. 229(1), pages 347-376, June.
    2. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
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    4. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    5. Eric Kamwa & Issofa Moyouwou, 2021. "Susceptibility to Manipulation by Sincere Truncation: The Case of Scoring Rules and Scoring Runoff Systems," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 275-295, Springer.
    6. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, December.
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    16. Lepelley, Dominique & Mbih, Boniface, 1987. "The proportion of coalitionally unstable situations under the plurality rule," Economics Letters, Elsevier, vol. 24(4), pages 311-315.
    17. Geoffrey Pritchard & Mark Wilson, 2007. "Exact results on manipulability of positional voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 487-513, October.
    18. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "Borda rule, Copeland method and strategic manipulation," Post-Print halshs-00069522, HAL.
    19. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
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    21. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Voting; Scoring rules; Coalition; Strategic manipulation; Probability;
    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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