TY - UNPB

T1 - Weighted and Restricted Deegan-Packel Power Indices

AU - Khmelnitskaya, Anna

AU - Chessa, Michela

PY - 2020/10/22

Y1 - 2020/10/22

N2 - 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.

AB - 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.

KW - simple games

KW - Deegan-Packel power index

KW - party's weight

KW - communication graph

KW - simple games

KW - Deegan-Packel power index

KW - power index, party's weight

KW - Communication graph

UR - https://www.mendeley.com/catalogue/ae547082-4c2e-301f-92e2-3ac4c97563b2/

U2 - 10.2139/ssrn.3713983

DO - 10.2139/ssrn.3713983

M3 - Preprint

T3 - SSRN electronic journal

BT - Weighted and Restricted Deegan-Packel Power Indices

ER -