I am honored to have been asked to deliver this lecture in memory of Nancy Schwartz. We who knew her as friend and colleague share a sadness that these lectures should take place in her memory rather than in her presence. Because Nancy Schwartz was professor of decision sciences at this University, it was felt that a memorial lecture devoted to the foundations of decision science - the theory of choice under risk - would be appropriate. My task is to be both general and specific at the same time. Generality alone (attempting to survey the field as a whole) would not have been feasible, and specificity alone (attempting to analyze a specific research problem) would not have been proper. My approach will consist, therefore, of trying to be general in scope but specific in point of view.