Risk, Probabilities, and a New Theory of Cardinal Utility

Abstract

This paper presents a set of certainty-equivalence (CE) axioms which allow the individual's preferences to be expressed by a cardinal utility index in the case of quantifiable single-good, uncertain (or certain) prospects. This axiom set differs from the von Neumann-Morgenstern (NM) axiom set. The analysis is extended to the multigood case, and its implications for risk taking are derived. Various tests reported in the literature on experimental psychology show the CE theory to outperform the von Neumann-Morgenstern one. Further, the CE theory satisfactory explains the Allais paradox, which contradicts the NM theory, and is thus to be preferred to the latter as a positive theory for decisions under uncertainty.