The Dual Theory of Choice under Risk

This paper investigates the consequences of the following modification of Expected Utility theory: instead of requiring independence with respect to probability mixtures of risky prospects, require independence with respect to direct mixing of payments o f risky prospects. A new theory of choice under risk- a so-called Dual theory-is obtained. Within this new theory, the following questions are considered: (1) numerical representation of preferences; (2) properties of the utility function; ( 3) the possibility for resolving the "paradoxes" of Expected Utilit y theory; ( 4) the characterization of risk aversion; and (5) comparative statics. The paper ends with a discussion of other non-Expected Utility theories proposed recently.