The most challenging problem confronting decision theorists is that of understanding how we choose in situations involving incommensurable alternatives. In simplest terms the thesis of incommensurable choice can be stated as follows: there are situations in which we must choose between alternative actions, social states, theories, or interpretations, when there is no apparent basis for comparing these alternatives. Beyond its formulation, however, there is little about the problem that is easily dealt with. The widely discussed treatment of incommensurability by Thomas Kuhn in The Structure of Scientific Revolutions, for example, is only one part of a much more extensive literature.1 Incommensurability has not only been assigned a crucial role in the progress of science but has also been seen as a major consideration in politics, economics, law, and ethics. It has been used to challenge our most commonly accepted concepts of science, rationality, and choice as well as the value of utilitarian, formalist, and empiricist modes of thought. At the same time, however, the existence of the problem of incommensurability has been denied, its formulation held to be unclear, and claims for significance disputed.2 This skepticism is warranted, for a great deal remains unclear about incommensurability despite, and in no small part because of, the extensiveness of the discussion.