Explaining the Paradox of Allais: A Hyper-Bayesian Account

Abstract

In this paper we show that decision makers who maximize expected utility on a two-dimensional set of the real numbers (i.e., who maximize expected utility on R×R) rather than on the real numbers alone, can act in ways predicted by the Allais paradox. In particular, we show that the ‘common consequence effect’ and the ‘common ratio effect’ as described by Allais in his original 1953 paper can be explained by the extended expected utility model that is described in this paper. The main part of the argument is presented in cognitive-functional terms, whilst a behavioural-axiomatic foundation is provided in an appendix.

Keywords: Allais paradox, commutative ring, direct sum

JEL Classification: D80, D81