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Aumann influentially claimed that the completeness axiom in utility theory is neither descriptively accurate nor normatively compelling. Separately, it’s commonly accepted that dynamic consistency in individual decision-making is a demand of rationality. I prove the following three results. First, even when incomplete preferences are acyclic, standard Maximal choice and backward induction are insufficient to guarantee dynamic consistency. Second, there exists a rationalising (dynamic) choice rule that does guarantee dynamic consistency, including under uncertainty, without imposing transitivity. Finally, it’s possible to bound above the extent to which this rule can lead the behaviour of such agents to be rationalisable by a complete preference relation.
