On some oligarchy results when social preference is fuzzy

We consider a model in which individual preferences are orderings of social states, but the social preference relation is fuzzy. We motivate interest in the model by presenting a version of the strong Pareto rule that is suited to the setting of a fuzzy social preference. We prove a general oligarchy theorem under the assumption that this fuzzy relation is quasi-transitive. The framework allows us to make a distinction between a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be undesirable.