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On the manipulability of approval voting and related scoring rules

机译：批准投票的可操作性及相关评分规则

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摘要

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable—has the smallest number of manipulable preference profiles—under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.
机译：我们根据偏好对候选人集的三种扩展，对所有可以执行批准（投票）规则的偏好特征进行了描述：通过比较最差的候选人，最佳的候选人，或者根据随机优势进行比较。我们针对k个批准规则执行类似的练习，其中选民批准固定数目k个候选人。这些结果可用于比较（k-）个批准规则的可操作性。对于两个投票者的情况，获得了分析结果，具体来说，确定了在各种偏好扩展下，k批准规则可最小操纵的k值（可操纵偏好分布图的数量最少）。对于趋于无穷大的选民数量，渐近结果是，在所有计分规则中，k数约为候选人总数一半的k批准规则是可操纵的。通过仿真获得了进一步的结果，这些结果表明，就可操纵性而言，k批准规则可能会比批准规则有所改进。

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  • 来源
    《Social Choice and Welfare》 |2012年第3期|399-429|共31页
  • 作者

    Hans Peters; Souvik Roy; Ton Storcken;

  • 作者单位

    Department of Quantitative Economics University of Maastricht PO Box 616 6200 MD Maastricht The Netherlands;

    University of Caen Caen France;

    Department of Quantitative Economics University of Maastricht PO Box 616 6200 MD Maastricht The Netherlands;

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