Three-Valued Simple Games

M. Musegaas, P.E.M. Borm, M. Quant

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In this paper we introduce three-valued simple games as a natural extension
of simple games. While simple games are used to evaluate single voting systems, three-valued simple games offer the opportunity for a simultaneous analysis of two different voting systems within the same parliamentary body. This paper analyzes the core and the Shapley value of three-valued simple games. Using the concept of vital players, the vital core is constructed and we show that the vital core is a subset of the core. The Shapley value is characterized on the class of all three-valued simple games. The model is applied to evaluate the relative influence of countries within the current EU-28 Council.
Original languageEnglish
Place of PublicationTilburg
Publication statusPublished - 10 Apr 2015

Publication series

NameCentER Discussion Paper


  • simple games
  • three-valued simple games
  • core
  • Shapley value

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