Weighted and restricted Deegan-Packel power indices
Anna Khmelnitskaya, UT-EWI-DMMP
In this paper we introduce weighted and restricted versions of the Deegan-Packel power index and provide their axiomatic characterizations. We show that the classical Deegan-Packel index, its weighted version, and its restricted version in case when restrictions are introduced by means of a communication graph, coincide correspondingly with the Shapley value, weighted Shapley value, and the Myerson value of some particular game determined by the set of minimal winning coalitions. The conditions under which the weighted Deegan-Packel power index is monotonic with respect to the players’ weights are introduced. The computations done for a number of real-life examples from realm of politics clearly demonstrate the coincidence of our theoretical predictions with the reality.
The paper is co-authored with Michela Chessa from the University of Nice