相关论文: The one-dimensional Euclidean domain: Finitely man…

We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only…

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…

Spatial models of preference, in the form of vector embeddings, are learned by many deep learning and multiagent systems, including recommender systems. Often these models are assumed to approximate a Euclidean structure, where an…

Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and…

A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has…

We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of…

Eliciting the preferences of a set of agents over a set of alternatives is a problem of fundamental importance in social choice theory. Prior work on this problem has studied the query complexity of preference elicitation for the…

We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.

For multidimensional Euclidean type spaces, we study convex choice: from any choice set, the set of types that make the same choice is convex. We establish that, in a suitable sense, this property characterizes the sufficiency of local…

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…

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…

This paper uncovers tight bounds on the number of preferences permissible in identified random utility models. We show that as the number of alternatives in a discrete choice model becomes large, the fraction of preferences admissible in an…

An ordinal preference domain is a subset of preference orders that the voters are allowed to cast in an election. We introduce and study the notion of outer diversity of a domain and evaluate its value for a number of well-known structured…

We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS), which includes Linkages and Frameworks. Each representation corresponds to a choice of Cayley parameters and yields a…

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…

In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree…

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…

We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.

Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…