The Impossibility of a Just Liberal

Abstract

In literature that tries to find a way around difficulties suggested by Arrow's (1963) Impossibility Theorem, one strand has taken issue with nature of domain of social welfare function (and often, at same time, with independence of irrelevant alternatives). Arrow assumed that a social preference ordering was to be obtained by examining only individuals' (ordinal) preferences over social states. But several authors have suggested that, in doing so, he has excluded possibility of making use of certain kinds of information that might aid us in making good social choices. A common remark is that, in this restricted format, Arrow ignores issues of intensity of preference. This is raised, for example, by Phelps (1973, p. 19), who relates this issue to the matter of whether preferences are to be supposed representable by an ordinal utility function or instead by a cardinal utility function. However, simply seeing a difficulty in one of Arrow's conditions does not solve problem, as those conditions were sufficient, not necessary, for revealing difficulties in social choice. Phelps continues: It appears to have been proven by Sen [1970b], however, that representability of individual preferences in terms of cardinal utility does not suffice to dispel Arrow's impossibility result. Another variant of this theme suggests that Arrow's framework ignores information available from extended sympathy. Arrow himself (1963, p. 114; 1967) raises this issue in talking about English tombstone carving: