Characterizations of the Deegan–Packel and Johnston power indices

Computing power indices: Multilinear extensions and new characterizations

“…It refers to a specific property of monotonicity that is similar to the monotonicity property proposed to characterize the Deegan-Packel index in Lorenzo-Freire et al (2007). The differences between the two properties reflect the differences of the alternative axioms of mergeability which the two indices satisfy.…”

“…In this paper, some of these properties will be mentioned, as well as some characterizations of the main power indices according to them. In Lorenzo-Freire et al (2007), new characterizations of Deegan-Packel and Johnston indices are obtained with monotonicity properties. In this paper, a new characterization of the Public Good…”

Power, Voting, and Voting Power: 30 Years After

“…The last two properties were presented in Alonso-Meijide et al (2008) and Lorenzo-Freire et al (2007). In this case, exactly two games are used in the definitions of the properties.…”

“…(Lorenzo-Freire et al 2007) The unique power index f that satisfies DPminimal monotonicity, null player, symmetry, and efficiency is the Deegan-Packel index. The unique power index f that satisfies transfer, null player, symmetry, and efficiency is the Shapley-Shubik index.…”

Power Indices and Minimal Winning Coalitions in Simple Games with Externalities

“…As we will see, the basic properties of efficiency, null player, and symmetry (Felsenthal and Machover, 1998) are easily generalized to our class of games. Then, in order to single out each of the proposed indices we can use either a merging property (Deegan and Packel, 1978;Holler and Packel, 1983) or a monotonicity property (Lorenzo-Freire et al, 2007;Alonso-Meijide et al, 2008).…”