Related papers: Partial-conjugates and Dimensionality of Posets
We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…
We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial…
A partial group with $n+1$ elements is, when regarded as a symmetric simplicial set, of dimension at most $n$. This dimension is $n$ if and only if the partial group is a group. As a consequence of the first statement, finite partial groups…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
The notion of preferences plays an important role in many disciplines including service robotics which is concerned with scenarios in which robots interact with humans. These interactions can be favored by robots taking human preferences…
Partially ordered patterns (POPs) generalize the notion of classical patterns studied in the literature in the context of permutations, words, compositions and partitions. In this paper, we give a number of general, and specific enumerative…
We consider an extension of the setting of label ranking, in which the learner is allowed to make predictions in the form of partial instead of total orders. Predictions of that kind are interpreted as a partial abstention: If the learner…
We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the…
This paper studies preference aggregation under ambiguity when agents have incomplete preference relations due to imprecise beliefs. We introduce the "dual" of the Pareto principle, which respects unanimity among individuals, including…
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.…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
The Possible Winner (PW) problem, a fundamental algorithmic problem in computational social choice, concerns elections where voters express only partial preferences between candidates. Via a sequence of investigations, a complete…
The dimension of a partial order $P$ is the minimum number of linear orders whose intersection is $P$. There are efficient algorithms to test if a partial order has dimension at most $2$. In 1982 Yannakakis showed that for $k\geq 3$ to test…
Let $(P,\leq)$ be a finite poset (partially ordered set), where $P$ has cardinality $n$. Consider linear extensions of $P$ as permutations $x_1x_2\cdots x_n$ in one-line notation. For distinct elements $x,y\in P$, we define…
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…
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 consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…
In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and…
Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…