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, Department of Applied Mathematics
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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