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On the inverse power index problem

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arxiv 1211.6353 v1 pith:3T36VPIP submitted 2012-11-27 math.OC cs.GT

classification math.OCcs.GT
keywords powerindexinfluencegiveninverseproblemvotervoters
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Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring the influence of a voter. We treat the inverse problem: Given an influence vector and a power index, determine a weighted voting game such that the distribution of influence among the voters is as close as possible to the given target value. We present exact algorithms and computational results for the Shapley-Shubik and the (normalized) Banzhaf power index.

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