Simplifying the Choice between Uncertain Prospects Where Preference is Nonlinear

Abstract

This work makes analytical progress in reducing or avoiding two practical difficulties in using preference or utility theory in the analysis of decisions involving uncertainty: (1) assessing the preference curve, and (2) doing calculations with the resultant curve, which may not have an analytically-convenient functional form. The paper identifies circumstances under which simplifications can be found which overcome these difficulties, while at the same time properly reflecting attitude towards risk in the analysis. It is assumed that a decision-maker must choose between risks w̃1 and w̃2. He wishes to make decisions consistent with a preference curve u(·) which exists, but has not necessarily been assessed, so he can choose i to maximize expected preference, Eu(w̃i). Most results require that the cumulative probability distribution of w̃1 and w̃2 cross at most once. The results are widely but not universally applicable. Situations are identified where an easy-to-assess, easy-to-analyze preference curve will serve as a proxy for the decision-maker's own preference curve. These situations permit use of any preferences curve from a class having a specified relationship with the decision-maker's curve. For example, in some instances a negative exponential (constant risk aversion) preference function can be used in place of the decision-maker's curve, and in others an expected value analysis will suffice.