We study political in ‡uence in institutions where members choose from among several options their levels of support to a collective goal, these individual choices determining the degree to which the goal is reached. In ‡uence is assessed by newly de…ned binary relations, each of which compares any two individuals on the basis of their relative performance at a corresponding level of participation. For institutions with three levels of support (e.g., voting games in which each voter may vote "yes", "abstain", or vote "no"), we obtain three in ‡uence relations, and show that the strict component of each of them may be cyclical. The cyclicity of these relations contrasts with the transitivity of the unique in ‡uence relation of binary voting games. Weak conditions of anonymity are su¢ cient for each of them to be transitive. We also obtain a necessary and su¢ cient condition for each of them to be complete. Further, we characterize institutions for which the rankings induced by these relations, and the Banzhaf-Coleman and Shapley-Shubik power indices coincide. We argue that the extension of these relations to …rms would be useful in e¢ ciently allocating workers to di¤erent units of production.Applications to various forms of political and economic organizations are provided.
The Isbell desirability relation (I), the Shapley-Shubik index (SS) and the Banzhaf-Coleman index (BC) are power theories that grasp the notion of individual influence in a yes-no voting rule. Also, a yes-no voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes-no voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.