Simple games versus weighted voting games: bounding the critical threshold value

Frits Hof (), Walter Kern (), Sascha Kurz (), Kanstantsin Pashkovich () and Daniël Paulusma ()
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Frits Hof: University of Twente
Walter Kern: University of Twente
Sascha Kurz: University of Bayreuth
Kanstantsin Pashkovich: University of Ottawa
Daniël Paulusma: Durham University

Social Choice and Welfare, 2020, vol. 54, issue 4, No 5, 609-621

Abstract: Abstract A simple game (N, v) is given by a set N of n players and a partition of $$2^N$$2N into a set $$\mathcal {L}$$L of losing coalitions L with value $$v(L)=0$$v(L)=0 that is closed under taking subsets and a set $$\mathcal {W}$$W of winning coalitions W with value $$v(W)=1$$v(W)=1. We let $$\alpha = \min _{p\geqslant {\varvec{0}}, p\ne {\varvec{0}}}\max _{W\in \mathcal{W}, L\in \mathcal{L}} \frac{p(L)}{p(W)}$$α=minp⩾0,p≠0maxW∈W,L∈Lp(L)p(W). It is known that the subclass of simple games with $$\alpha 0$$α0>0.

Date: 2020
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DOI: 10.1007/s00355-019-01221-6

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