Diversification Preferences in the Theory of Choice

TL;DR

This paper explores the axiomatic foundations of diversification preferences across various choice models, analyzing their relationship with risk aversion and implications for portfolio selection.

Contribution

It provides a comprehensive axiomatization of diversification preferences within multiple choice theories, including expected utility, rank-dependent utility, and Choquet expected utility.

Findings

Diversification preferences relate to convexity in choice models.

Axiomatizations differ across models of risk and uncertainty.

Implications for portfolio choice vary with the underlying preference structure.

Abstract

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.