Related papers: Six Candidates Suffice to Win a Voter Majority
In many real-world applications of committee elections, the candidates are associated with certain attributes and the chosen committee is required to satisfy some constraints posed on the candidate attributes. For instance, when dress…
We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the…
We study two-stage committee elections where voters have dynamic preferences over candidates; at each stage, a committee is chosen under a given voting rule. We are interested in identifying a winning committee for the second stage that…
For a finite set of non-zero natural numbers that contains at least one element different from 1 and the least common multiple of any of its subsets, there exists a subset of at least half of its members which has a common divisor larger…
Theoretical results underpinning the Wisdom of Crowds, such as the Condorcet Jury Theorem, point to substantial accuracy gains through aggregation of decisions or opinions, but the foundations of this theorem are routinely undermined in…
The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in…
The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently…
In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space,…
Apportionment is the problem of distributing $h$ indivisible seats across states in proportion to the states' populations. In the context of the US House of Representatives, this problem has a rich history and is a prime example of…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of…
We study the problem of minimizing metric distortion in multi-winner elections, where a committee of size $k$ is selected from a set of candidates based on voters' ordinal preferences. We assume that voters and candidates are embedded on a…
This paper introduces Propose or Vote (PoV), a democratic procedure for collective decision-making and elections that does not rely on a central mechanism designer. In the first stage, members of a polity choose whether to become…
We present a polynomial-time algorithm for computing an optimal committee of size $k$ under any given Thiele voting rule for elections on the Voter Interval domain (i.e., when voters can be ordered so that each candidate is approved by a…
Metric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate. Voters…
Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule…
This paper deals with interactions between committee members as they rank a large list of applicants for a given position and eventually reach consensus. We will see that for a natural deterministic model the ranking can be described by…
We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which…
Consider a set $V$ of voters, represented by a multiset in a metric space $(X,d)$. The voters have to reach a decision -- a point in $X$. A choice $p\in X$ is called a $\beta$-plurality point for $V$, if for any other choice $q\in X$ it…
In this paper we study several monotonicity axioms in approval-based multi-winner voting rules. We consider monotonicity with respect to the support received by the winners and also monotonicity in the size of the committee. Monotonicity…