Dynamic choice without the completeness axiom

Abstract Robert 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. These assertions may conflict, however, even in mundane decision problems lacking any form of preference change. I characterise the most permissive preference-based choice rule which allows an agent with incomplete but transitive preferences to satisfy a strong form of dynamic consistency. The resulting behaviour is not generally rationalisable by a completed preference relation. I thereby present a challenge to—and conditions for—the simultaneous satisfaction of strong dynamic consistency and preservation of preferential gaps.