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Information and capacities

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  • Jean-Christophe Vergnaud

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.
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Suggested Citation

  • Jean-Christophe Vergnaud, 2002. "Information and capacities," Statistical Papers, Springer, vol. 43(1), pages 111-125, January.
    • Handle: RePEc:spr:stpapr:v:43:y:2002:i:1:p:111-125
    DOI: 10.1007/s00362-001-0089-0
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    References listed on IDEAS

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    1. Jaffray, Jean-Yves & Wakker, Peter, 1993. "Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 255-271, December.
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    Cited by:

    1. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Post-Print halshs-00130451, HAL.
    2. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130451, HAL.
    3. Pascal Toquebeuf, 2013. "The value of information with neo-additive beliefs," Economics Bulletin, AccessEcon, vol. 33(3), pages 2402-2406.

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