ABSTRACT
The Shapley value is a classical method for deriving appropriate payoffs in cooperative games, particularly for simple games. It has very good properties for defining a priori values in cases where the payoffs for each possible coalition are precisely defined. When decisions are made on the basis of a vote to obtain a group decision, often the assumption of determinism is inappropriate. This article considers an adaptation of the Shapley value to situations in which the weights of the individual players in voting games are not deterministic. This means that the number of votes required to pass a decision (the quota) and the set of winning coalitions are not precisely defined. Also, the number of votes cast might be affected by a quorum. The concept of fuzzy sets and a modified version of the characteristic form of a game are utilised to appropriately modify the concept of the Shapley value to such situations. The theory is illustrated by examples including decision making in parliament and the Council of the European Union.
