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Revising non-additive priors

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The authors consider the updating of a convex non-additive prior over 'types' upon the receipt of a signal. Conditioned on each type, the distribution for the signal is additive and known. This updating requires the construction of beliefs on the product space of all possible pairs of the type and the signal. Lam and Sarafidis propose 2 rules. Th first uses the idea of Choquet integration over identity functions and produces a non-additive measure over the product space. The second converts the initial non-additive prior to a set of additive priors, and then applies Bayes's rule to this set. The two rules are closely related but not eqivalent. This non-equivalence arises because non-additive measures are unable to capture certain restrictions on the relative likelihood of events. While this does not matter for the representation of uncertainty-averse beliefs, it results in a loss of information when beliefs have to be revised. Related to this, the authors argue that the differences between choice over Anscombe-Aumann 'horse-lotterires' and choice over Savage acts when the decision maker has non-additive beliefs does not arise from inherent differences between one and two-stage lotteries. Rather, it arises from the inability of non-additive priors to model uncertainty as precisely as multiple priors.

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en

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application/pdf

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http://flora.insead.edu/fichiersti_wp/inseadwp2002/2002-25.pdf

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