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On the Probablistic Relationship between the Public Good Index and the Normalized Bannzhaf Index

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  • Mika WidgrÚn

    (Turku School of Economics and Business Administration, Yrj÷ Jahnsson Foundation and CEPR, Turku, Finnland)

Abstract

In this paper we develop a probablistic interpretation for the normalized Banzhaf index and the public good index. We then derive a way to decompose the normalized Banzhaf index into two parts. The first of them relates the Banzhaf index with the public good index and the other one on a special type of luck. Similarities and differences of the two indices are then discussed.

Suggested Citation

  • 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.
  • Handle: RePEc:hom:homoec:v:19:y:2002:p:373-386
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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. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    3. Manfred J. Holler, 1998. "Two Stories, One Power Index," Journal of Theoretical Politics, , vol. 10(2), pages 179-190, April.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    6. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    7. 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.
    8. Leech, Dennis, 1990. "Power Indices and Probabilistic Voting Assumptions," Public Choice, Springer, vol. 66(3), pages 293-299, September.
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