We apply Pires’s coherence property between unconditional and conditional preferences that admit a CEU representation. In conjunction with consequentialism (only those outcomes on states which are still possible can matter for conditional preference) this implies that the conditional preference may be obtained from the unconditional preference by taking the Full Bayesian Update of the capacity....

The left Hermite-Hadamard inequality of several variables for convex functions on certain convex compact sets is proved via elementary approach, independently of Choquet theory.

It is well known that the main tool for finding dependencies among data is the linear regression model, which expresses one or several variables in term of a linear combination of the others. Linear regression is based on the least square principle, and has been studied at length, its statistical performance are well known. In real situations however, the linear assumption happens to be often r...

This paper characterizes the core of a differentiable convex distortion of a probability measure on a non atomic space by identifying it with the set of densities which dominate the derivative of the distortion, for second order stochastic dominance. Furthermore the densities that have the same distribution as the derivative of the distortion are the extreme points of the core. These results ar...

s: Plenary Speakers Spiros Argyros (National Technical University of Athens, Greece) [email protected] HI extensions of L∞ spaces and spaces with very few operators Tuesday, July 30, HA4, 9:00–9:50 We will present a general method of embedding Banach spaces with separable dual into L∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i...

In decision under uncertainty, the Choquet integral yields the expectation of a random variable with respect to a fuzzy measure (or non-additive probability or capacity). In general, for the discrete setting, this technique allows to integrate functions taking values on a finite n-set with respect to a (fuzzy) measure taking values on subsets of such a set. Yet, the integrand may well be treate...

We show that small-bound isomorphisms of spaces affine continuous functions on Choquet simplices with Lindel?f boundaries induce Baire measurable bijections their sets extreme points.