Theory of Generalized Risk Attitudes

Abstract

This paper develops a theory of risk attitudes that can be applied in a broad array of settings, including those in which the decision maker (DM) abides by a preference model other than the expected utility model and in which decisions are being made over multiattribute alternatives. The theory is based on (i) a set of plausible axioms in which the DM’s preferences over consequences and lotteries are defined separately and (ii) the premise that a risk neutral DM is indifferent between a lottery and the average (in terms of preference) of the outcomes obtained from infinite repetition of the lottery. We show that, under these assumptions, a risk neutral DM seeks to maximize the expectation of classic cardinal utility (i.e., measurable value). This means, in particular, that the DM’s risk attitude in expected utility theory is related to the transformation function between the classic cardinal utility function and the von Neumann-Morgenstern utility function. The results also suggest that the applicability of the conventional definitions of risk attitudes may be limited to settings in which the DM’s classic cardinal utility function is linear and that a more generalized treatment of risk attitudes is required for settings in which this is not the case.