Traditional models of rational choice assume that preferences are complete, but the completeness axiom is neither normatively compelling nor psychologically plausible. Building on recent work in economics, we develop a rational analysis of decision making with incomplete preferences. The analysis sheds surprising light on a range of well-known behavioral "anomalies," including the endowment effect, status quo maintenance, the sunk cost effect, and coherent arbitrariness. We propose a two-part division of rational choice theory-into preference theory and "implementation theory"-and show how conservative and coherently arbitrary policies can effectively implement incomplete preferences. The two-part normative framework motivates a psychological distinction between evaluation and implementation phases in decision making. We argue that the endowment effect and related phenomena, which have usually been attributed to loss aversion in the evaluation phase, are better explained by conservatism in the implementation phase. The rational analysis challenges the normative adequacy of expected utility theory and raises questions about the explanatory scope of prospect theory. It illustrates the rich interplay between psychological models of value structure and normative models of rational choice. (PsycInfo Database Record (c) 2025 APA, all rights reserved).