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That an individual's preference or indifference relations may fail to be transitive is familiar. Such intransitivities are harmless, per se, and probably an inevitable part of the human condition. When such relations must function as principles of selection, however, intransitivity can lead to irrational choices. The task of devising rational methods for eliminating intransitivity would thus appear to be an important problem of decision theory. While there are usually many ways to eliminate intransitivity, our contention is that, in general, no one of these methods is rationally superior to any other. We argue for this position with respect to the well known problem, first considered by Luce [1956], of extending a semi-order to a weak order. In particular, we show that problems of sequential choice, which require a weak order, are equally well solved by any weak order extension of the original semi-order. We thus establish the …