Three-Valued Simple Games

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.