Publication detail

Power Indices: Shapley-Shubik or Penrose-Banzhaf?

Author(s): prof. RNDr. Ing. František Turnovec CSc., Jacek W. Mercik, Mariusz Mazurkiewicz
Type: IES Working Papers
Year: 2004
Number: 48
Published in: IES WP 2004/48
Publishing place: Prague
Keywords: Absolute power, cooperative games, I-power, pivot, power indices, relative power, P-power, swing
JEL codes: D710, D740
Suggested Citation:
Abstract: Power indices methodology is widely used to measure an a priori voting power of members of a committee. In this paper we analyse Shapley-Shubik and Penrose-Banzhaf concepts of power measure and classification of so called I power (voter's potential influence over the outcome of voting) and P power (expected relative share in a fixed prize available to the winning group of committee members) introduced by Felsenthal, Machover and Zwiker (1998). We show that objections against Shapley-Shubik power index, based on its interpretation as a P-power concept, are not sufficiently justified. Both Shapley-Shubik and Penrose-Banzhaf measure could be successfully derived as cooperative game values, and at the same time both of them can be interpreted as probabilities of some decisive position (pivot, swing) without using cooperative game theory at all.
Downloadable: WP 48


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