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Relative Maximum Likelihood Updating of Ambiguous Beliefs

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Document pages: 58 pages

Abstract: This paper proposes and axiomatizes a new updating rule: Relative MaximumLikelihood (RML) for ambiguous beliefs represented by a set of priors (C). Thisrule takes the form of applying Bayes rule to a subset of the set C. Thissubset is a linear contraction of C towards its subset ascribing a maximalprobability to the observed event. The degree of contraction captures theextent of willingness to discard priors based on likelihood when updating. Twowell-known updating rules of multiple priors, Full Bayesian (FB) and MaximumLikelihood (ML), are included as special cases of RML.An axiomatic characterization of conditional preferences generated by RMLupdating is provided when the preferences admit Maxmin Expected Utilityrepresentations. The axiomatization relies on weakening the axiomscharacterizing FB and ML. The axiom characterizing ML is identified for thefirst time in this paper, addressing a long-standing open question in theliterature.

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