Probabilistic, fuzzy and rough concepts in social choice

We discuss how intrinsic inconsistencies and negative results (concerning opinion aggregation) in social choice may be alleviated by plausible modifications of underlying assumptions and problem formulations, basically by the introduction of some impreciseness of a probabilistic, fuzzy and rough type. First, we discuss briefly probabilistic voting, and the use of fuzzy preference relations and fuzzy majorities. Then, in the main part, we proceed to the use of Pawlak's rough sets theory in the analysis of crucial properties of voting schemes. In this framework we also discuss the concept of a distance between two voting schemes. Finally, we further explore difficult issues of how diverse types of impreciseness can be combined, and we consider in particular the combination of roughness with randomness and fuzziness in the context of spatial voting games.