Arrow Impossibility Theorem

One of the astonishing findings of modern economics (and from a student's PhD thesis at that) is that a set of quite reasonable sounding requirements about social choice orderings necessarily implies that there is no method for constructing social preferences from ordinal individual preferences. In other words, there is no rule, such as majority voting (nor any other), for deriving social preferences from arbitrary individual preferences of the kind commonly assumed by economists. The reasonable requirements are completeness: in a choice between alternatives A and B either A is socially preferred to B, or B is preferred to A, or there is a social indifference between A and B; transitivity: if A is socially preferred to B and B is preferred to C then A is also preferred to C; if every individual prefers A to B then socially A should be preferred to B; non-dictatorship: social preferences should not depend upon the preferences of only one individual; social preferences should be independent of irrelevant alternatives: that is, the social preference of A compared to B should be independent of preferences for C. Health economists seem to be less reluctant to use cardinal and interpersonally comparable ' utilities' than economists working in many other areas of application. See Kenneth J. Arrow (1951), Social Choice and Individual Values, New York: Wiley.

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