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Measures of Powerlessness in Simple Games

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  • Thomas Quint

Abstract

Consider a simple game with n players. Let ψ i be the Shapley–Shubik power index for player i. Then 1-ψ i measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q i (which measures how much of a `quixote' i is), and a `follower index' F i (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Thomas Quint, 2001. "Measures of Powerlessness in Simple Games," Theory and Decision, Springer, vol. 50(4), pages 367-382, June.
    • Handle: RePEc:kap:theord:v:50:y:2001:i:4:p:367-382
    DOI: 10.1023/A:1010315526150
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    References listed on IDEAS

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    1. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
    2. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    3. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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