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Social Welfare Functions for Different Subgroup Utility Scales

Summary: Social Welfare Functions for Different Subgroup
Utility Scales
Anna B. Khmelnitskaya
SPb Institute for Economics and Mathematics Russian Academy of Sciences,
1 Tchaikovsky St., 191187 St.Petersburg, Russia
Abstract. This paper characterizes social welfare functions for different
scales of individual utility measurement in distinct population subgroups.
Different combinations of ordinal, interval, ratio, and translation scales
are studied. We consider situations when utility comparisons among
subgroups of individuals by unit and/or zeropoint can or cannot be made,
that is when subgroup utility scales are dependent or independent. We
show that for combinations of independent subgroup utility scales every
corresponding social welfare function is fully determined by the opinions
of only one subgroup of individuals when there is not more than one
subgroup with ratio or translation scale measurable utilities, otherwise
it also might be determined by the union of subgroups corresponding to
ratio and translation scales, and is in accord with the utility scales of the
decisive coalition. We also investigate social welfare functions admissible
given various combinations of interval scales with a common unit that
combine individual utilities from different subgroups, or with a common


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering