Random sets lotteries and decision theory

• Is it possible to apply the theory of random sets to decision making under?
• The answer (Proposition 1, Theorem 1, Theorem 2) is yes.
• Our model is compatible with Choquet and MaxMin expected utilities.

We apply random sets theory to decision making under risk. This leads to a unifying concept which is compatible with some types of behavior like the Choquet Expected Utility and MaxMin Expected Utility. We show that the “expected utility” of a random set lottery is easy to calculate. Hence a decision making model with random sets is actually very tractable.