It is a commonplace that in making decisions agents often have to juggle competing values, and that no choice will maximize satisfaction of them all. However, the prevailing account of these cases assumes that there is always a single ranking of the agent's values, and therefore no unresolvable conflict among them. Isaac Levi denies this assumption, arguing that agents often must choose without having balanced their different values and that to be rational, an act does not have to be optimal, only what Levi terms "admissible." This book explores the consequences of denying the assumption and develops a general approach to decision-making under unresolved conflict. Professor Levi argues not only against the "strict Bayesian" position, but also against all the recent attempts to develop alternative models to Bayesianism. The book, which continues from his earlier The Enterprise of Knowledge, is certain to make an original and controversial contribution to the debates over choice theory.