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Asymptotic vulnerability of positional voting rules to coalitional manipulation

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  • Moyouwou, Issofa
  • Tchantcho, Hugue

Abstract

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.

Suggested Citation

  • Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
  • Handle: RePEc:eee:matsoc:v:89:y:2017:i:c:p:70-82
    DOI: 10.1016/j.mathsocsci.2017.06.006
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    References listed on IDEAS

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    Cited by:

    1. Mostapha Diss & Boris Tsvelikhovskiy, 2019. "Manipulable outcomes within the class of scoring voting rules," Papers 1911.09173, arXiv.org, revised Sep 2020.
    2. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    3. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2019. "Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention," Working Papers hal-02196387, HAL.
    4. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    5. Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin & Hatem Smaoui, 2021. "Dummy Players and the Quota in Weighted Voting Games," Group Decision and Negotiation, Springer, vol. 30(1), pages 43-61, February.

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