Variational Bewley preferences

Abstract

This paper characterizes variational Bewley preferences over Anscombe and Aumann acts, a class of binary relations that may fail completeness or transitivity vis à vis independence. The main result gives an axiomatization of preference relations ≿ represented as follows:f≿g⇔∫u(f)dp+η(p)≥∫u(g)dp for all p∈Δ, where u is an affine utility index over a convex set X of consequences, η:Δ→[0,∞] is an ambiguity index, and Δ is the set of priors over the state space S. This representation has a natural interpretation as a weighted unanimity rule, with the function η reflecting the weight given to a prior and higher values of η corresponding to priors given less weight. Bewley's incomplete preferences can be identified precisely with the addition of transitivity or independence, and a prior receives weight either 0 if plausible or ∞ when discarded. Also, by adding only completeness, we recover subjective expected utility, i.e., the lack of transitivity implies incompleteness. Finally, we find a strong connection of our model with the class of variational preferences.