ABSTRACT
When preferences for a set of alternatives are expressed by rank ordering, rankings can be made from best to worst or from worst to best. Intuition suggests that if the same person repeatedly ranks the same alternatives, sometimes in one direction and sometimes the other, rank orders that signify the same preference ordering should occur with the same probability in both cases. However, it is well known that when Luce’s Choice Axiom is extended to ranking behavior in what seems the most natural way, that requirement is only satisfied in the special case of complete indifference. This paper investigates the prevalence of this ‘irreversibility’ property within a family of random utility models that generalizes Case V of Thurstone’s theory of comparative judgment. The analysis focuses on the case of three alternatives. The basic question is whether irreversibility is unique to the Choice Axiom model (i.e., to the generalized Case V random utility model based on the double exponential probability distribution). The answer is no, because the same property characterizes the Case V model based on the exponential distribution. Moreover at least a partial form of irreversibility proves to be common to many models in this family – e.g., all models based on one-sided probability density functions that are square integrable.
