  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.
