Weighted and Restricted Deegan-Packel Power Indices
24 Pages Posted: 21 Oct 2020
Date Written: October 17, 2020
In the paper we introduce weighted and restricted versions of the Deegan-Packel power index. We show that the classical Deegan-Packel index, which was proposed as an alternative to the Shapley-Shubik index, in fact coincides with the Shapley value of some specific game determined by the set of minimal winning coalitions, and therefore, it has close affinities with the Shapley-Shubik index. We investigate monotonicity properties of the weighted Deegan-Packel index and introduce easy to check conditions under which it is monotonic with respect to the players' weights. An axiomatic characterization of the weighted Deegan-Packel index is provided. The computations done for three real-life examples from realm of politics demonstrate clearly the coincidence of our theoretical predictions with the reality.
Keywords: simple games, Deegan-Packel power index, party's weight, communication graph
JEL Classification: C71
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