Binary Diversification Characterizes Exact Capacities

In this paper, we present the first axiomatic characterization of preferences that can be represented by a Choquet integral with respect to an exact capacity. The characterizing axiom, binary diversification, is novel and reflects an inclination for bets on events, thereby capturing a specific type of ambiguity aversion. Furthermore, we demonstrate that the three capacity classes balanced, exact, and convex fully exhaust all levels of our family of k-nary diversification axioms—a unifying framework for the two most popular definitions of ambiguity aversion. We demonstrate that k-nary diversification has a clear interpretation regarding its dual-self expected utility representation. Finally, we illustrate an implication for multiobjective shortest-path problems to demonstrate that our results can be applied in other research fields in which the Choquet integral is utilized.

Funding: L. Hartmann acknowledges financial support from the Swiss National Science Foundation [Grant 200915].