An Axiomatic Approach to Decision under Knightian Uncertainty

Based on a set of seven axioms, we develop an original approach to decision making under Knightian uncertainty that circumvents numerous conceptual problems of existing approaches in the literature. We understand and conceptualize Knightian uncertainty as income lotteries with known payoffs in each outcome, but unknown probabilities. This distinguishes our approach from the ambiguity approach where decision makers are assumed to entertain some set of probabilistic beliefs about the likelihoods of outcomes. We provide a proof that there exists a function H from the set of Knightian lotteries to the real numbers such that lottery f is preferred to lottery g if and only if H(f)>H(g) and that H is unique up to cardinal transformations. We propose and illustrate one possible concrete function satisfying our axioms with a static sample decision problem and compare it to other decision rules such as maximin, maximax, the Hurwicz criterion, the minimum regret rule and the principle of insufficient reason. We find that the overall ranking of the lotteries is different from these well-known criteria, but the most preferred option is the same as with the maximin rule and a pessimistic Hurwicz individual.

presentation of research findings at this international conference on risk and insurance economics