Robust α-maxmin representations

The class of $\alpha$-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 $\alpha$-maxmin representations that contradict each other. We say that an $\alpha$-maxmin representation is robust when no other $\alpha$-maxmin representation exists for the same preferences. We obtain a full characterization of robustness for maxmin representation. In the case of general $\alpha$-maxmin representations, we obtain sufficient conditions for both robustness and non-robustness. This contributes to better identification of the $\alpha$-maxmin representations that admit a robust interpretation in terms of perceived ambiguity and ambiguity attitudes.