A note on decisive symmetric games

  • Authors:
  • Francesc Carreras;Josep Freixas;María Albina Puente

  • Affiliations:
  • Department of Applied Mathematics II and Industrial and Aeronautical Engineering School of Terrassa, Universitat Politècnica de Catalunya, Spain;Department of Applied Mathematics III and Engineering School of Manresa, Universitat Politècnica de Catalunya, Spain;Department of Applied Mathematics III and Engineering School of Manresa, Universitat Politècnica de Catalunya, Spain

  • Venue:
  • Decision Support Systems
  • Year:
  • 2011

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Abstract

Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the ''decisiveness index'' of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricted to decisive symmetric games and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negative, in p when p=1/2 takes the decisiveness to quickly approach, respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.