A method for evaluating the behavior of power indices in weighted plurality games |
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| Authors: | Vincent C H Chua C H Ueng H C Huang |
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| Institution: | (1) School of Economics and Social Sciences, Singapore Management University, 469 Bukit Timah Road, Singapore 259756 (e-mail: vincentchua@smu.edu.sg), SG;(2) Department of Industrial and Systems Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, SG |
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| Abstract: | In this paper, a systematic method to facilitate the comparison of a priori measures of power in an n-player r-candidate (n, r) weighted plurality game is proposed. This method, which exploits the notion of a structure of embedded winning coalitions
(SEWC), enables the listing of all power profiles relevant to an (n, r) game under a given index and permits the computation of the probability of occurrence of each of these profiles. The vulnerability
of an index to different paradoxes of power can also be systematically studied. For the purpose of illustration, we apply
this method to the analysis of four well-known 2-candidate power indices namely the Shapley-Shubik index, the Banzhaf index,
the Johnston index and the Deegan-Packel index. In each case, the set of power profiles and the likelihood of occurrence of
each of these profiles are enumerated. The superadditivity property of these indices is also studied.
Received: 20 October 1999/Accepted: 25 April 2001 |
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