Related papers: 2-Dimensional Euclidean Preferences
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…
We prove that there is an absolute constant $ C$ such that for every $ n \geq 2 $ and $ N\geq 10^n, $ there exists a polytope $ P_{n,N} \subset \mathbb{R}^n $ with at most $ N $ facets that satisfies…
In the traditional voting manipulation literature, it is assumed that a group of manipulators jointly misrepresent their preferences to get a certain candidate elected, while the remaining voters are truthful. In this paper, we depart from…
We construct a 5D, N = 2 Euclidean theory of supergravity coupled to vector multiplets. Upon reducing this theory over a circle we recover the action of 4D, N = 2 Euclidean supergravity coupled to vector multiplets.
Recommender systems can automatically recommend users with items that they probably like. The goal of them is to model the user-item interaction by effectively representing the users and items. Existing methods have primarily learned the…
3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today…
In this paper we address the problem of electing a committee among a set of $m$ candidates and on the basis of the preferences of a set of $n$ voters. We consider the approval voting method in which each voter can approve as many candidates…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…
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…
Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63.…
We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete positive solution of the open problem in dimension two.…
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 preference matrix $M$ has an entry for each pair of candidates in an election whose value $p_{ij}$ represents the proportion of voters that prefer candidate $i$ over candidate $j$. The matrix is rationalizable if it is consistent with a…
Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's…
In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional…
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…
Pull voting is a classic method to reach consensus among $n$ vertices with differing opinions in a distributed network: each vertex at each step takes on the opinion of a random neighbour. This method, however, suffers from two drawbacks.…
In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account…
We systematically compile an exhaustive catalogue of multiview varieties and anchored multiview varieties arising from projections of points and lines in 1, 2, and 3-dimensional projective space. We say that two such varieties are…
We give simple criteria for the singularities appearing on surfaces codimension less than or equal to two. As applications, we give conditions for codimension two singularities that appear in ruled surfaces and center maps of surfaces in…