When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to...

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We...

Peleg (1978) presents a necessary and sufficient condition for the non-emptiness of the core, by considering quota games. The purpose of this paper is to present a similar result for the non-emptiness of another solution concept introduced by Rubinstein (1980) and called the stability set. <!--ID="" Acknowledgments. I am grateful to Maurice Salles, Vincent Merlin and Ashley Piggins for many helpful comments. I have a particular debt to Michel Le Breton for suggesting improvements in the proof of theorem 2. Of course, all errors remain the author's responsibility.-->