Non-manipulable Social Welfare Functions when Preferences are Fuzzy

Abstract

It is well known that many social decision procedures are manipulable through strategic behaviour. Typically, the decision procedures considered in the literature have been social choice correspondences. In this article, we investigate the problem of constructing a social welfare function that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from fuzzy set theory, we introduce a class of fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable social welfare functions are dictatorial, provided that they are not constant. A proof of this theorem first appeared in Perote-Pena and Piggins (2007, J. Math. Econ., 43, 564–580). This article contains a new proof of this theorem which is considerably simpler than the original. Moreover, we also consider a possibility result which this earlier article neglects.