Relevance and Symmetry

We define a behavioral concept of relevance in the context of decision making under uncertainty. We argue that this concept provides a sensible answer to the question "What probabilistic environments do an individuals' preferences reveal as mattering to her decisions?" under a symmetry assumption. This question has important implications for economic modeling. It is often the case that a modeler desires to restrict the probabilistic environments a decision maker considers. Without a concept of relevant beliefs, it is impossible to check from preferences whether a model is reflecting what the modeler intended. This checking is essential to isolating the effect of changing information while holding tastes fixed. We show that a single concept of relevance delivers this for a wide range of models, including models that allow for ambiguity attitude. We also use symmetry and relevance to provide insight into the foundations of theα-MEU and smooth ambiguity models of decision-making under uncertainty.