Hierarchy of players in swap robust voting games

Date
2009-10-22
Authors
Bishnu, Monisankar
Roy, Sonali
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Economics
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Abstract

Ordinarily, the process of decision making by a committee through voting is modelled by a monotonic game the range of whose characteristic function is restricted to {0,1}. The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori influence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a number-based power index (e.g., the Shapley-Shubik index, the Banzhaf-Coleman index) for each player or conduct a pairwise comparison between players in order to find out whether there exists a coalition in which player i is desirable over another player j as a coalition partner. In this paper we outline a much simpler and more elegant mechanism to determine the ranking of players in terms of their a-priori power using only minimal winning coalitions, rather than the entire set of winning coalitions.

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simple game, swap robust game, desirability, weak desirability, lexicographic ordering
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