Ordinal Nash Social Welfare Function

A social welfare function entitled ‘ordinal Nash’ is proposed based on risk preferences and assuming a common, worst social state for all individuals. The crucial axiom in the characterisation of the solution is a weak version of IIA, in which only the relative risk position with respect to the worst state is considered. Thus the resulting social preference takes into account non (necessarily) EU risk preference intensity by directly comparing certainty equivalent probabilities. The solution provides an interesting interpretation of the Nash-like utility product principle in the realm of social choice. However, necessary and sufficient conditions over the solution domain state that all individuals should have the same probability distortion functions in their preference representations (clearly satisfied in the EU case). ∗This paper is based on part of the author’s Ph.D. thesis, whose advisor was Professor Zvi Safra, Faculty of Management, Tel Aviv University. I thank Uzi Segal for helpful comments on an earlier version of this paper.