Related papers: Matrix Rationalization via Partial Orders

Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all…

We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…

A multicriteria group choice problem is considered in the paper. The model includes a set of feasible alternatives, a vector criterion, and n preference relations of the decision makers (DMs). Each preference relation is a cone relation…

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…

Multi-winner voting is the process of selecting a fixed-size set of representative candidates based on voters' preferences. It occurs in applications ranging from politics (parliamentary elections) to the design of modern computer…

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…

Even though proportional representation is a fundamental goal in multiwinner voting and a plethora of proportionality notions has been introduced, the normative justifications for choosing one notion over another remain poorly understood.…

We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are to be selected. In particular we focus on the axiomatic property called extended…

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…

In the Shift Bribery problem, we are given an election (based on preference orders), a preferred candidate $p$, and a budget. The goal is to ensure that $p$ wins by shifting $p$ higher in some voters' preference orders. However, each such…

The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…

We consider spatial voting where candidates are located in the Euclidean $d$-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location…

Many democratic political parties hold primary elections, which nicely reflects their democratic nature and promote, among other things, the democratic value of inclusiveness. However, the methods currently used for holding such primary…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

We all have preferences when multiple choices are available. If we insist on satisfying our preferences only, we may suffer a loss due to conflicts with other people's identical selections. Such a case applies when the choice cannot be…

Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

In light of the classic impossibility results of Arrow and Gibbard and Satterthwaite regarding voting with ordinal rules, there has been recent interest in characterizing how well common voting rules approximate the social optimum. In order…