Domain conditions in social choice theory - Gaertner, Wulf (Cambridge University Press, 2001)
"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 40 theorems associated with domain conditions."