 
Summary: Existence of a dictatorial subgroup in social
choice with independent subgroup utility scales,
an alternative proof
Anna B. Khmelnitskaya
Abstract Social welfare orderings for different scales of individual utility measure
ment 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 selfcontained proof based on the
study of the structure of level surfaces of a social welfare function which provides a
realvalued representation of the social welfare ordering.
1 Introduction
In Arrow's famous impossibility theorem [1], individual preferences are ordinally
measurable and interpersonally noncomparable. Building on the seminal work of
Sen [14], there is now an extensive literature that investigates the implications for
social decisionmaking of alternative assumptions concerning the measurability and
interpersonal comparability of individual preferences. See, for example, Roberts
[12], [13], d'Aspremont [3], Yanovskaya [16], [17], Tsui and Weymark [15], Bossert
