VOTING GAMES AND ACYCLIC COLLECTIVE CHOICE RULES

The subject of this paper is the representation of collective choice r ules by voting games and the acyclicity of these rules. A collective c hoice rule is a function that associates a collective preference with every profile of individual preferences. Such a rule is acyclic if it always yields an acyclic collective preference. A voting game is eithe r a simple game or a non-neutral version of such a game called a binar y game in constitutional form. Both are special forms of cooperative g ames that simply specify the structure of power in a society or an org anization. The power structure conferred by certain collective choice rules takes the form of a voting game. The paper classifies collective choice rules that can or cannot be represented by a voting game. Cond itions for the acyclicity of the collective choice rules that can be r epresented by a voting game are then obtained from the structure of th eir corresponding voting games. These results are applied to a large c lass of voting rules defined by quotas.