23,544 research outputs found
On minimum sum representations for weighted voting games
A proposal in a weighted voting game is accepted if the sum of the
(non-negative) weights of the "yea" voters is at least as large as a given
quota. Several authors have considered representations of weighted voting games
with minimum sum, where the weights and the quota are restricted to be
integers. Freixas and Molinero have classified all weighted voting games
without a unique minimum sum representation for up to 8 voters. Here we
exhaustively classify all weighted voting games consisting of 9 voters which do
not admit a unique minimum sum integer weight representation.Comment: 7 pages, 6 tables; enumerations correcte
On the inverse power index problem
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.Comment: 17 pages, 2 figures, 12 table
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