Voting games and acyclic collective choice rules

Abstract The subject of this paper is the representation of collective choice rules by voting games and the acyclicity of these rules. A collective choice 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 either a simple game or a non-neutral version of such a game called a binary game in constitutional form. Both are special forms of cooperative games that simply specify the structure of power in a society or an organization. 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. Conditions for the acyclicity of the collective choice rules that can be represented by a voting game are then obtained from the structure of their corresponding voting games. These results are applied to a large class of voting rules defined by quotas.