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A note on balancedness and nonemptiness of the core in voting games

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Abstract

Consider a society with a finite number,n, of individuals who have to choose an alternative from a setA in them-dimensional Euclidean space IRm. Assuming that the preference relation overA of every individual is convex and continuous, Greenberg (1979) showed some that if the set of winning coalitions (i.e. those that have the veto power) consists of all coalitions with more thanmn/m + 1 individuals the core of the induced game is nonempty. Greenberg and Weber (1984) have strengthened this result by showing that the induced game is in fact balanced. On the other hand Le Breton (1987), Schofield (1984a) and Strnad (1985) have generalized Greenberg's theorem to arbitrary voting games. The purpose of this note is to show that however the induced game is not generally balanced.

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Authors and Affiliations

  1. Cremerc-Leme, Faculté des Sciences Economiques, 7, place Hoche, 35000, Rennes, France

    M. Le Breton

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  1. M. Le Breton
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Additional information

I am grateful to an anonymous referee for a high quality report and insightful observations and suggestions and to an associate editor for helpful classifications. I thank the “Commissariat General du Plan” for financial support.

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Le Breton, M. A note on balancedness and nonemptiness of the core in voting games. Int J Game Theory 18, 111–117 (1989). https://doi.org/10.1007/BF01248498

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  • DOI: https://doi.org/10.1007/BF01248498

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