Information and capacities |
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Authors: | Jean-Christophe Vergnaud |
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Institution: | 1. EUREQUA-CNRS, University Paris 1, Maison des Sciences Economiques, 106-112 Bid de l’H?pital, 75647, Paris, Cedex 13, France
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Abstract: | Most economists consider that the cases of negative information value that non-Bayesian decision makers seem to exhibit,
clearly show that these models are not models representing rational behaviour. We consider this issue for Choquet Expected
Utility maximizers in a simple framework, that is the problem of choosing on which event to bet. First, we find a necessary
condition to prevent negative information vlaue that we call Separative Monotonicity. This is a weaker condition than Savage
Sure thing Principle and it appears that necessity and possibility measures satisfy it and that we cand find conditioning
rules such that the information value is always positive. In a second part, we question the way information value is usually
measured and suggest that negative information values are merely resulting from an inadequate formula. Yet, we suggest to
impose what appears as a weaker requirement, that is, the betting strategy should not be Statistically Dominated. We show
for classical updating rules applied to belief functions that this requirement is violated. We consider a class of conditioning
rules and exhibit a necessary and sufficient condition in order to satisfy the Statistical Dominance criterion in the case
of belief functions.
Received: November 2000; revised version: July 2001 |
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Keywords: | : information value non additive measure update rule statistical dominance |
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