To require the transitivity of the indifference relation is tantamount to requiring that human beings be capable of discriminating infinitesimal differences, which is obviously unreasonable. Suzumura (1976) introduced a novel concept of consistency, which lies in between full transitivity and acyclicity, and showed that it plays central roles in the theory of preference and rational choice. Capitalizing on recent explorations, this paper expounds the role of consistency in the theory of extending a binary relation into an ordering, on the one hand, and in the theory of rationalizing a choice function in terms of an underlying preference relation, on the other.
