Weighted and restricted Deegan-Packel power indices

Anna Borisovna Khmelnitskaya*, Michela Chessa

*Corresponding author for this work

Research output: Book/ReportReportProfessional

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Abstract

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.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages24
Publication statusPublished - 1 Oct 2020

Publication series

NameTW-Memoranda
PublisherUniversity of Twente, Department of Applied Mathematics
No.2070
ISSN (Print)1874-4850

Keywords

  • simple games
  • Deegan-Packel power index
  • party's weight
  • communication graph

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