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

Author

Listed:
  • Frits Hof

    (University of Twente)

  • Walter Kern

    (University of Twente)

  • Sascha Kurz

    (University of Bayreuth)

  • Kanstantsin Pashkovich

    (University of Ottawa)

  • Daniël Paulusma

    (Durham University)

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.

Suggested Citation

  • Frits Hof & Walter Kern & Sascha Kurz & Kanstantsin Pashkovich & Daniël Paulusma, 2020. "Simple games versus weighted voting games: bounding the critical threshold value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 609-621, April.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:4:d:10.1007_s00355-019-01221-6
    DOI: 10.1007/s00355-019-01221-6
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    References listed on IDEAS

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