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The Shapley-Shubik index, the donation paradox and ternary games

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  • Vincent C. H. Chua
  • H. C. Huang

Abstract

In this paper, we show that although the Shapley-Shubik index is immune to the donation paradox in weighted binary games, extension of the index to ternary games along the direction suggested in Felsenthal and Machover (1996, 1997) will cause it to be vulnerable to the paradox and this is the case as long as the number of players in the game exceeds three. This undermines the attractiveness of the Shapley-Shubik index as a measure of a priori voting power. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Vincent C. H. Chua & H. C. Huang, 2003. "The Shapley-Shubik index, the donation paradox and ternary games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 387-403, June.
    • Handle: RePEc:spr:sochwe:v:20:y:2003:i:3:p:387-403
    DOI: 10.1007/s003550200186
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    Cited by:

    1. J. Bilbao & J. Fernández & N. Jiménez & J. López, 2007. "The core and the Weber set for bicooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 209-222, October.
    2. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.

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