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  1. Itzhak Gilboa, Andrew Postlewaite & David Schmeidler (forthcoming). Rationality of Belief. Synthese.
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  2. Itzhak Gilboa, Andrew Postlewaite & David Schmeidler (2012). Rationality of Belief Or: Why Savage's Axioms Are Neither Necessary nor Sufficient for Rationality. [REVIEW] Synthese 187 (1):11-31.
    Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing (...)
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  3. Itzhak Gilboa, Offer Lieberman & David Schmeidler (2010). On the Definition of Objective Probabilities by Empirical Similarity. Synthese 172 (1):79 - 95.
    We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.
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  4. Itzhak Gilboa, Andrew Postlewaite & David Schmeidler (2009). Is It Always Rational to Satisfy Savage's Axioms? Economics and Philosophy 25 (3):285-296.
    This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between (...)
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  5. Itzhak Gilboa & David Schmeidler (2004). Subjective Distributions. Theory and Decision 56 (4):345-357.
    A decision maker has to choose one of several random variables whose distributions are not known. As a Bayesian, she behaves as if she knew the distributions. In this paper we suggest an axiomatic derivation of these (subjective) distributions, which is more economical than the derivations by de Finetti or Savage. Whereas the latter derive the whole joint distribution of all the available random variables, our approach derives only the marginal distributions. Correspondingly, the preference questionnaire needed in our case is (...)
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  6. David Schmeidler (1989). Subjective Probability and Expected Utility Without Additivity. Econometrica 57:571-589.
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