Related papers: Condorcet's Jury Theorem with Abstention
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…
Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important…
Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability $p$, then the…
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size…
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 present theoretical and empirical results demonstrating the usefulness of voting rules for participatory democracies. We first give algorithms which efficiently elicit \epsilon-approximations to two prominent voting rules: the Borda rule…
We study two notions of stability in multiwinner elections that are based on the Condorcet criterion. The first notion was introduced by Gehrlein: A committee is stable if each committee member is preferred to each non-member by a (possibly…
The median voter theorem has long been the default model of voter behavior and candidate choice. While contemporary work on the distribution of political opinion has emphasized polarization and an increasing gap between the "left" and the…
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…
Elections where electors rank the candidates (or a subset of the candidates) in order of preference allow the collection of more information about the electors' intent. The most widely used election of this type is Instant-Runoff Voting…
Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…
The main idea of the {\em distance rationalizability} approach to view the voters' preferences as an imperfect approximation to some kind of consensus is deeply rooted in social choice literature. It allows one to define ("rationalize")…
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…
Majority voting (MV) is the prototypical ``wisdom of the crowd'' algorithm. Theorems considering when MV is optimal for group decisions date back to Condorcet's 1785 jury \emph{decision} theorem. The same error independence assumption…
We present a simple proof of a well-known axiomatic characterization of state-salient decision rules, using Weak Dominance Criterion and Global Independence of Irrelevant Alternatives. Subsequently we provide a simple axiomatic…
We conjecture that Borda count is the ranked choice voting method that best preserves the outcome of an election with randomly corrupted votes, among all fair voting methods with small influences satisfying the Condorcet Loser Criterion.…
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…
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…
Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…
It is well known, by the Gibbard-Satterthwaite Theorem, that when there are more than two candidates, any non-dictatorial voting rule can be manipulated by untruthful voters. But how strong is the incentive to manipulate under different…