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...

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.-->

The Condorcet winner in an election is a candidate that could defeat each other candidate in a series of pairwise majority rule elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that such a winner...