Rational Preferences With A Discontinuity Structure

10/24/2000 Abstract. We present an Axiom System and a Representation Theorem for a class of preferences on lotteries which we call Rational Preference Orderings with a Discontinuity Structure, and which implies Expected Utility Theory as a continuous special case. Rational Preference Orderings with a Discontinuity Structure are based on so-called Security Level E¤ects, independently introduced by I.Gilboa and Y.-J.Ja¤ray, and Potential Level E¤ects, introduced by M.Cohen, which formalize particular psychological attitudes towards the evaluation of uncertain outcomes. In this paper we present two main extensions of these models: 1. We introduce the concept of a Discontinuity Structures which determines unambiguously the occurence of Security Level E¤ects and of a Potential Level E¤ects for a given preference ordering. As a consequence our Representation Theorem provides an exact speci...caton of the discontinuities in the Utility function. 2. We introduce a more general partition into ”Security Level/Potential Level”-subsets, whereas we allow for small ”threshold”-probabilities which do not necessarily in‡uence the Securityor Potential Level of a lottery. Final ly, we discuss how the concepts of Marginal Utility for Monetary Wealth and of RiskAttitudes may be separated by Rational Preferences with a Discontinuity Structure. As an economical application we describe a game of founding an egalitarian Insurance Club where we obtain quite di¤erent results as under Expected Utility Theory.