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Two Stories, One Power Index

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  • Manfred J. Holler

Abstract

This paper demonstrates that the mathematical properties of the member bargaining power measure (MBP) are identical with those of the public good index (PGI). However, the underlying theoretical concepts of the two measures are different. The MBP refers to bargaining over shares of the coalition value, and thus has a private good perspective, whereas the PGI considers power with respect to providing a public good as coalition value. The identity of the mathematical properties is used to study the properties of the two measures. For weighted voting games, both measures violate monotonicity with respect to voting weights, and the paradox of weighted voting applies.

Suggested Citation

  • Manfred J. Holler, 1998. "Two Stories, One Power Index," Journal of Theoretical Politics, , vol. 10(2), pages 179-190, April.
    • Handle: RePEc:sae:jothpo:v:10:y:1998:i:2:p:179-190
    DOI: 10.1177/0951692898010002002
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    References listed on IDEAS

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    1. Steven J. Brams & Peter C. Fishburn, 1996. "Minimal winning coalitions in weighted-majority voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 397-417.
    2. Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    3. Dietrich Fischer & Andrew Schotter, 1978. "The inevitability of the “paradox of redistribution” in the allocation of voting weights," Public Choice, Springer, vol. 33(2), pages 49-67, September.
    4. 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.
    5. Turnovec, Frantisek, 1997. "Monotonicity of Power Indices," East European Series 41, Institute for Advanced Studies.
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    Cited by:

    1. Mika WidgrÚn, 2002. "On the Probablistic Relationship between the Public Good Index and the Normalized Bannzhaf Index," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 373-386.
    2. Fabi'an Riquelme & Pablo Gonz'alez-Cantergiani & Gabriel Godoy, 2018. "Voting power of political parties in the Senate of Chile during the whole binomial system period: 1990-2017," Papers 1808.07854, arXiv.org, revised Sep 2019.

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