Related papers: Axiomatization of the Choquet integral for 2-dimen…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the…
We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention that each alternative receives decreases as the choice problem becomes larger. Using this…
We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We demonstrate that in a model of public goods provision, multidimensional…
We study here preference revision, considering both the monotonic case where the original preferences are preserved and the nonmonotonic case where the new preferences may override the original ones. We use a relational framework in which…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
We show in section 1 that the Ax-Kochen isomorphism theorem requires the continuum hypothesis. Most of the applications of this theorem are insensitive to set theoretic considerations. (A probable exception is the work of Moloney.) In…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
In this paper, we study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. Our aim is to construct knot homologies categorifying…
Conjoint experiments randomize multidimensional profiles, offering a powerful design for recovering structural preference parameters -- including marginal rates of substitution, willingness to pay, and the distribution of preferences across…
The definition of preferences assigned to individuals is a concept that concerns many disciplines, from economics, with the search of an acceptable outcome for an ensemble of individuals, to decision making an analysis of vote systems. We…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set $X$ crucially hinges on the associated equivalence relation $=_{X}$.…
In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work…
A multicriteria group choice problem is considered in the paper. The model includes a set of feasible alternatives, a vector criterion, and n preference relations of the decision makers (DMs). Each preference relation is a cone relation…
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as…
We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching…