A simple and general axiomatization of average utility maximization for infinite streams

Abstract

This paper provides the most general preference axiomatization of average utility (AU) maximization over infinite sequences presently available, reaching almost complete generality. The only restriction is that all periodic sequences should be contained in the domain. Infinite sequences may designate intertemporal outcomes streams where AU models patience, welfare allocations where AU models fairness, or decisions under ambiguity where AU models complete ignorance. As a methodological contribution, this paper shows that infinite-dimensional representations can be simpler, rather than more complex, than finite-dimensional ones. Infinite dimensions provide a richness that may be convenient rather than cumbersome. In particular, (empirically problematic) continuity assumptions are not needed in our axiomatization. Continuity is optional.