PROBABILISTIC, FATTY AND ROUGH CONCEPTS IN SOCIAL CHOICE

We discuss how intrinsic inconsistencies and negative results (concern ing opinion aggregation) in social choice may be alleviated by plausib le modifications of underlying assumptions and problem formulations, b asically by the introduction of some impreciseness af 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 fram ework we also discuss the concept of a distance between two voting sch emes. Finally, we further explore difficult issues of how diverse type s 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.