THE IRRATIONALITY OF INTRANSITIVITY

A RECENT discussion of welfare economics 'summarizes the question of transitivity as follows. There is not now conclusive reason to believe that the assumption of transitivity of preference in individual choice is deeply suspect. There are, however, grounds for being willing to make deep empirical investigations into the validity of the assumption'.' At another point the same author says: 'My conclusions indicate that we currently possess no strong evidence to warrant dropping (the assumption of transitivity). '2 Given the role that transitivity plays in much of the modern literature, and in Rothenberg's book, his attitude towards it seems very defensive. We do not have strong evidence against it; there is no conclusive reason to suspect deeply the assumption. In sum, the evidence against transitivity is not sufficient to condemn it, but Rothenberg is clearly doubtful. In this he is more or less in accord with the bulk of current opinion on the matter. It is the purpose of this article to present a contrary view. It will be argued that the assumption of transitivity is not particularly doubtful or dubious. In view of the apparent suspicion of the assumption by the bulk of modern welfare economists this might seem to be a revolutionary position, but the practice of the same economists has indicated relatively little real doubt of the transitive nature of preference orderings. Article after article has appeared in which this assumption is made, something which would seem to indicate that the writers have at least some confidence in its reliability. Further, the chains of reasoning based upon this assumption do not appear to have led to demonstrably false conclusions about the real world. This fact, in itself, is powerful although not conclusive evidence for the truth of the transitivity assumption. The debate about the assumption of transitivity turns upon the interpretation of certain real world experiences. If an individual is asked to take his choice among a large number of pairs of alternatives, with each alternative appearing as one member of quite a number of the pairs,3 or a large number of people are asked to judge between three alternatives