Wulf Gaertner provides a comprehensive account of an important and
complex issue within social choice theory: how to establish a
social welfare function while restricting the spectrum of
individual preferences in a sensible way. Gaertner's starting point
is K. J. Arrow's famous 'Impossibility Theorem', which showed that
no welfare function could exist if an unrestricted domain of
preferences is to be satisfied together with some other appealing
conditions. A number of leading economists have tried to provide
avenues out of this 'impossibility' by restricting the variety of
preferences: here, Gaertner provides a clear and detailed account,
using standardized mathematical notation, of well over forty
theorems associated with domain conditions. Domain Conditions in
Social Choice Theory will be an essential addition to the library
of social choice theory for scholars and their advanced graduate
students.
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