Robust α-maxmin representations

The class of α-maxmin representations of an agent’s preferences is meant to achieve a separation between the ambiguity he perceives and his attitude toward this perceived ambiguity. Yet the same preferences may admit a multiplicity of α-maxmin representations that contradict each other. We say that an α-maxmin representation is robust when no other α-maxmin representation exists for the same preferences. We obtain a full characterization of robustness for maxmin representation. In the case of general α-maxmin representations, we obtain sufficient conditions for both robustness and non-robustness. This contributes to better identification of the α-maxmin representations that admit a robust interpretation in terms of perceived ambiguity and ambiguity attitudes.