Uncertainty aversion and preference for randomisation

In this paper we show that while individuals with non-additive beliefs may display a strict preference for randomisation in an Anscombe-Aumann framework, they will not do so in a Savage style decision theory. Moreover they will be indifferent to randomisation, unless they have strict preferences between two randomising devices with the same probabilities. We argue that this is related to the distinction between one- and two-stage Choquet integrals. We believe our result will have implications for determining a solution concept for games with uncertainty-averse players. (C) 1996 Academic Press, Inc.