Weighted and Restricted Deegan-Packel Power Indices

24 Pages Posted: 21 Oct 2020

See all articles by Anna Khmelnitskaya

Anna Khmelnitskaya

St.-Petersburg State University, Faculty of Applied Mathematics & Control Processes; Trapeznikov Institute of Control Sciences RAS

Michela Chessa

Université de Nice Sophia Antipolis

Date Written: October 17, 2020

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.

Keywords: simple games, Deegan-Packel power index, party's weight, communication graph

JEL Classification: C71

Suggested Citation

Khmelnitskaya, Anna and Chessa, Michela, Weighted and Restricted Deegan-Packel Power Indices (October 17, 2020). Available at SSRN: https://ssrn.com/abstract=3713983 or http://dx.doi.org/10.2139/ssrn.3713983

Anna Khmelnitskaya (Contact Author)

St.-Petersburg State University, Faculty of Applied Mathematics & Control Processes ( email )

Universitetskii prospekt 35, Petergof
Saint-Petersburg, 198504
Russia

HOME PAGE: http://https://wwwhome.ewi.utwente.nl/~khmelnitskayaab/

Trapeznikov Institute of Control Sciences RAS ( email )

65 Profsoyuznaya street
Moscow, 117997
Russia

Michela Chessa

Université de Nice Sophia Antipolis ( email )

250, rue Albert Einstein
B.P. 70
Sophia Antipolis, 06560
France

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