The Core of Voting Games: A Partition Approach

The purpose of this article is to analyze a class of voting games in a partition approach. We consider a society in which coalitions can be formed and where a finite number of voters have to choose among a set of alternatives. A coalition is winning if it can veto any proposed alternative. In our model, the veto power of a coalition is dependent on the coalition formation of the outsiders. We show that whether or not the core is non-empty depends crucially on the expectations of each coalition regarding outsiders’ behavior when it wishes to veto an alternative. On the one hand, if each coalition has pessimistic expectations, then the core is non-empty if and only if the dimension of the set of alternatives is equal to one. On the other hand, if each coalition has optimistic expectations, the non-emptiness of the core is not ensured.