Ambiguity under growing awareness

Abstract

In this paper, we study choice under growing awareness in the wake of new discoveries. The decision maker's behavior is described by two preference relations, one before and one after new discoveries are made. The original preference admits a subjective expected utility representation. As awareness grows, the original decision problem expands and so does the state space. Therefore, the decision maker's original preference has to be extended to a larger domain, and consequently the new preference might exhibit ambiguity aversion. We propose two consistency notions that connect the original and new preferences. Unambiguity Consistency requires that the original states remain unambiguous while new states might be ambiguous. This provides a novel interpretation of ambiguity aversion as a systematic preference to bet on old states than on newly discovered states. Likelihood Consistency requires that the relative likelihoods of the original states are preserved. Our main results axiomatically characterize a maxmin expected utility (MEU) representation of the new preference that satisfies the two consistency notions. We also extend our model by allowing the initial preference to be MEU, and characterize reverse full-Bayesianism, which is an extension of the reverse Bayesianism of Karni and Vierø (2013) to MEU preferences.