Naive Diversification Preferences and Their Representation

A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides mathematically and economically sound choice theoretic foundations for the naive approach to diversification. We axiomatize naive diversification by defining it as a preference for equality over inequality, derive its relationship to the classical diversification paradigm, and provide a utility representation. In particular, we (i) prove that the notion of permutation invariance lies at the core of naive diversification and that an economic agent is a naive diversifier if and only if his preferences are convex and permutation invariant; (ii) derive necessary and sufficient conditions on the utility functions that give rise to preferences for naive diversification; (iii) show that naive diversification preferences arise when decision makers only consider beliefs that imply some weak form of independence, which is closely related to correlation neglect