Related papers: What majority decisions are possible

This article aims to present a unified framework for ranking-based voting rules based on the use of depth functions on permutations, as a counterpart of deepest voting rules on evaluation introduced in Aubin et al. [2022]. It introduces the…

Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…

We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…

I study the relationship between diversity preferences and the choice rules implemented by institutions, with a particular focus on the affirmative action policies. I characterize the choice rules that can be rationalized by diversity…

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class;…

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…

Researchers in psychology characterize decision-making as a process of eliminating options. While statistical modelling typically focuses on the eventual choice, we analyze consideration sets describing, for each survey participant, all…

A method is given for determining a mixed social choice out of a paired-comparison matrix. The method combines a projection procedure introduced in previous papers of the same authors and a classical method due to Zermelo. The resulting…

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should…

We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…

We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…

The statistical properties of pairwise majority voting over S alternatives is analyzed in an infinite random population. We first compute the probability that the majority is transitive (i.e. that if it prefers A to B to C, then it prefers…

The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…

We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them.

In a parking function, a lucky car is a car that parks in its preferred parking spot and the parking outcome is the permutation encoding the order in which the cars park on the street. We give a characterization for the set of parking…

We consider the approval-based model of elections, and undertake a computational study of voting rules which select committees whose size is not predetermined. While voting rules that output committees with a predetermined number of winning…

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…

We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We…