An Axiomatic Approach to Failures in Contingent Reasoning

The aim of this paper is to characterize incomplete preferences with optimism and pessimism (IPOP) over Anscombe-Aumann acts, a class of preference orders that may fail axioms that require the decision-maker to think contingency. The main result axiomatizes preferences that compare any pair of distinct acts in such a way that an act is ranked higher than another act if and only if the minimal expected utility from the former is still greater than the maximal expected utility from the latter. This representation has a natural interpretation as cautious attitudes of the decision-maker under contingencies. The class reduces to the standard SEU preferences when belief sets are minimal, while it encapsulates obvious dominance, the decision criterion proposed by Li (2017), as the polar case of when belief sets are maximal