Related papers: Exchangeable choice functions
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take…
We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…
We study reductions well suited to compare structures and classes of structures with respect to properties based on enumeration reducibility. We introduce the notion of a positive enumerable functor and study the relationship with…
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical…
Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…
The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
Inspired by Lehner's results on exchangeability systems we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
Aggregated phenomena in social sciences and economics are highly dependent on the way individuals interact. To help understanding the interplay between socio-economic activities and underlying social networks, this paper studies a…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…
Based on the observation that many existing discrete choice models admit a welfare function of utilities whose gradient gives the choice probability vector, we propose a new representation of discrete choice model which we call the…
Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing…
Any exchangeable Markov processes on $[k]^{\mathbb{N}}$ with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type…
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…
I introduce a favor exchange model where favors are substitutable and study bilateral enforcement of cooperation. Without substitutability, the value of a relationship does not depend on the rest of the network, and in equilibrium there is…