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The $$q$$ q -majority efficiency of positional rules

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  • Sébastien Courtin
  • Mathieu Martin
  • Issofa Moyouwou

Abstract

According to a given quota $$q$$ q , a candidate $$a$$ a is beaten by another candidate $$b$$ b if at least a proportion of $$q$$ q individuals prefer $$b$$ b to $$a$$ a . The $$q$$ q -majority efficiency of a voting rule is the probability that the rule selects a candidate who is never beaten under the $$q$$ q -majority, given that such a candidate exits. Closed form representations are obtained for the $$q$$ q -majority efficiency of positional rules (simple and sequential) in three-candidate elections. It turns out that the $$q$$ q -majority efficiency is: (i) significantly greater for sequential rules than for simple positional rules; and (ii) very close to the $$q$$ q -Condorcet efficiency, the conditional probability that a positional rule will elect the candidate who beats all others under the $$q$$ q -majority, when one exists. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The $$q$$ q -majority efficiency of positional rules," Theory and Decision, Springer, vol. 79(1), pages 31-49, July.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:1:p:31-49
    DOI: 10.1007/s11238-014-9451-2
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    References listed on IDEAS

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    Cited by:

    1. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    2. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    3. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers hal-01757761, HAL.
    4. 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.
    5. Erik Friese & William V. Gehrlein & Dominique Lepelley & Achill Schürmann, 2017. "The impact of dependence among voters’ preferences with partial indifference," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(6), pages 2793-2812, November.
    6. 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.
    7. Muhammad Mahajne & Oscar Volij, 2019. "Condorcet winners and social acceptability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 641-653, December.
    8. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2018. "An Evaluation of the Benefit of Using Two-Stage Election Procedures," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(1), pages 53-79, June.
    9. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2016. "Further Support for Ranking Candidates in Elections," Group Decision and Negotiation, Springer, vol. 25(5), pages 941-966, September.

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