The ordinal Nash social welfare function

A social welfare function entitled 'ordinal Nash' is proposed. It is based on risk preferences and assumes a common, worst social state (origin) for all individuals. The crucial axiom in the characterization of the function is a weak version of independence of irrelevant alternatives. This axiom considers relative risk positions with respect to the origin. Thus, the resulting social preference takes into account non-expected utility risk preference intensity by directly comparing certainty equivalent probabilities. The function provides an interpretation of the Nash-utility-product preference aggregation rule. Necessary and sufficient conditions for the function to produce complete and transitive binary relations are characterized.