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The blocker postulates for measures of voting power

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  • Arash Abizadeh

    (McGill University)

  • Adrian Vetta

    (McGill University)

Abstract

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose–Banzhaf measure, the classic Shapley–Shubik index, and the newly proposed recursive measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the recursive measure as a reasonable measure of voting power.

Suggested Citation

  • Arash Abizadeh & Adrian Vetta, 2023. "The blocker postulates for measures of voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 595-623, May.
    • Handle: RePEc:spr:sochwe:v:60:y:2023:i:4:d:10.1007_s00355-022-01428-0
    DOI: 10.1007/s00355-022-01428-0
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
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    3. Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
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    6. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
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