We provide a simple characterization of updating rules that can be rationalized as Bayesian. Namely, we consider a general setting in which an agent observes finite sequences of signals and reports probabilistic predictions on the underlying state of the world. We study when such predictions are consistent with Bayesian updating, i.e., when does there exist some theory about the signal generation process that would be consistent with the agent behaving as a Bayesian updater. We show that the following condition is necessary and sucient for the agent to appear Bayesian: the probability distribution that represents the agent's belief after observing any finite sequence of signals is a convex combination of the probability distributions that represent her beliefs conditional on observing sequences of signals that are the possible continuations of the original sequence. This condition cannot be derived from the ones the literature has identied when confounding the problem with maximization of expected utility. Additional restrictions are identied for all histories of signals to be given positive probability under the identied information generation process, and for the agent's theory to entail conditional independence or exchangeability of signals. Talk by Leeat Yariv Associate Professor, Division of Humanities and Social Sciences, Caltech.
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