Related papers: A Maximum Theorem for Incomplete Preferences
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…
This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous…
Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
We propose a new determinacy hypothesis for transfinite games, use the hypothesis to extend the perfect set theorem, prove relationships between various determinacy hypotheses, expose inconsistent versions of determinacy, and provide a…
This paper introduces the axiom of Negative Dominance, stating that if a lottery $f$ is strictly preferred to a lottery $g$, then some outcome in the support of $f$ is strictly preferred to some outcome in the support of $g$. It is shown…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…
Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double…
In this work, we reformulate the problem of existence of maximal elements for preference relations as a variational inequality problem in the sense of Stampacchia. Similarly, we establish the uniqueness of maximal elements using a…
Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity…
Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple…
Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of…
Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…
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…
We propose and axiomatize a new model of incomplete preferences under uncertainty, which we call \textit{hope-and-prepare preferences}. An act is considered more desirable than an other act when, and only when, both an optimistic…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
We propose a model of incomplete \textit{twofold multiprior preferences}, in which an act $f$ is ranked above an act $g$ only when $f$ provides higher utility in a worst-case scenario than what $g$ provides in a best-case scenario. The…
The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…