Related papers: Choice functions on posets
Choice functions over a set $X$ that satisfy the Outcast, a.k.a. Aizerman, property are exactly those that attach to any set its maximal subset relative to some total order of ${2}^{X}$.
Let m>2 be an integer. We show that ZF + "For every integer n, Every countable family of non-empty sets of cardinality at most n has an infinite partial choice function" is not strong enough to prove that every countable set of m-element…
Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It…
Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice…
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the M\"obius function and topology of such pattern posets.…
If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…
We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions.…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
We establish formulas for the number of all downsets (or equivalently, of all antichains) of a finite poset P. Then, using these numbers, we determine recursively and explicitly the number of all posets having a fixed set of minimal points…
Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential "voters". The question is, what choice…
This paper introduces an alternative approach to proving the existence of choice functions for specific families of sets within Zermelo-Fraenkel set theory (ZF) without assuming any form on the Axiom of Choice (AC). Traditional methods of…
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…
We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function,…
Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We investigate a certain class of posets arising from semilattice actions. Let $S$ be a semilattice with identity. Let $S$ act on a set $C$. For $c,d\in C$ put $c\leq d$ iff there is some $s\in S$ with $ds=c$. Then $(C,\leq)$ is a poset.…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…