A unified representation of conditioning rules for convex capacities

This paper proposes a unified representation, called the G-updating rule, which includes three conditioning rules as special cases, the naïve Bayes rule, the Dempster-Shafer rule (Shafer(1976)), and the generalized Bayes' updating rule introduced by Dempster(1967) or Fagin and Halpern(1991). It is shown that the G-updating rule constitutes a three-step conditioning, where one of the three rules is applied in each step.

CEU Preferences and Dynamic Consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration.

A General Update Rule for Convex Capacities

A characterization of a general update rule for convex capacities, the G-updating rule, is investigated. We introduce a consistency property which bridges between unconditional and conditional preferences, and deduce an update rule for unconditional capacities. The axiomatic basis for the G-updating rule is established through consistent counterfactual acts, which take the form of trinary acts expressed in terms of G, an ordered tripartition of global states.ambiguous belief, Bayes' rule, update rule, convex capacity, Choquet ex- pected utility, conditional preference

Updating Non-Additive Probabilities -- A Geometric Approach

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non- additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining the notion of independence of non-additive probabilities and Nash equilibrium.updating, non-additive probabilities, conditional expectation

Comparing three ways to update Choquet beliefs

publication-status: Publishedtypes: Article“NOTICE: this is the author’s version of a work that was accepted for publication in Economics Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Economics Letters, 107, 91-94, 2010 doi:10.1016/j.econlet.2009.12.035We analyze three rules for updating neo-additive capacities. Only for Generalized Bayesian Updating is relative optimism the same for both updated and unconditional capacities. For updates of the other two, either the updated capacity is fully optimistic or fully pessimistic. (C) 2010 Elsevier B.V. All rights reserved

Regular updating

We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian updating rule.

Comparison of experts in the non-additive case

We adapt the model of comparisons of experts initiated by Lehrer («Comparison of experts JME 98») to a context of uncertainty which cannot be modelised by expected utility. We examine the robustness of Lehrer in this new context. Unlike expected utility, there exist several ways to define the strategies allowing to compare the experts, we propose some of them which guarantee a positive value of information.Non-additive preferences, experts

Tribute to Jean-Yves Jaffray July 22, 1939 - February 26, 2009

International audienceTribute to Jean-Yves Jaffray by the French Group of Decision TheoryHommage à Jean-Yves Jaffray par le groupe français de Théorie de la Décisio