Existence of a dictatorial subgroup in social choice with independent subgroup utility scales, an alternative proof

Social welfare orderings for different scales of individual utility measurement in distinct population subgroups are studied. In Khmelnitskaya and Weymark (2000), employing the continuous version of Arrow’s impossibility theorem, it was shown that for combinations of independent subgroups scales every corresponding social welfare ordering depends on the utilities of only one of the subgroups and is determined in accordance with the scale type proper to this dictatorial subgroup. In this article we introduce an alternative completely self-contained proof based on the study of the structure of level surfaces of a social welfare function which provides a real-valued representation of the social welfare ordering.