Independence of irrelevant interpersonal comparisons
The author studies an aspect of the Arrow problem under the condition that the voters' ordering profile and, accordingly, the collective ordering are explicitly depending from a parameter belonging to some fixed set, which can be interpreted as reflecting ``ethics''. The case is studied when the parameter can change within the bounds of the fixed set. The Arrow condition of independence of irrelevant alternatives is reformulated for this case and this gives rise to a strengthened analogy of the Arrow theorem. In the last paragraphs it is assumed that the individual and the collective ordering is specified by an expected utility representation, which means the possibility of risk is accounted for. The connection between the obtained results and previous results obtained by \textit{A. Sen} and \textit{D. K. Osborne} [Econometrica 44, 1001- 1015 (1976; Zbl 0338.90010)] is investigated in detail.
scientific article; zbMATH DE number 4213697