Related papers: Condorcet-Consistent Choice Among Three Candidates
Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. Perhaps one of the most important desirable properties in this context is Condorcet-consistency, which requires that a voting rule should…
Condorcet's paradox is a fundamental result in social choice theory which states that there exist elections in which, no matter which candidate wins, a majority of voters prefer a different candidate. In fact, even if we can select any $k$…
Proponents of Condorcet voting face the question of what to do in the rare case when no Condorcet winner exists. Recent work provides compelling arguments for the rule that should be applied in three-candidate elections, but already with…
In an election where $n$ voters rank $m$ candidates, a Condorcet winning set is a committee of $k$ candidates such that for any outside candidate, a majority of voters prefer some committee member. Condorcet's paradox shows that some…
We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver,…
The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…
In a single winner election with several candidates and ranked choice or rating scale ballots, a Condorcet winner is one who wins all their two way races by majority rule or MR. A voting system has Condorcet consistency or CC if it names…
A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to…
A cornerstone of social choice theory is Condorcet's paradox which says that in an election where $n$ voters rank $m$ candidates it is possible that, no matter which candidate is declared the winner, a majority of voters would have…
A Condorcet voting scheme chooses a winning candidate as one who defeats all others in pairwise majority rule. We provide a review which includes the rigorous mathematical treatment for calculating the limiting probability of a Condorcet…
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large…
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…
We analyze the susceptibility of instant runoff voting (IRV) to a lesser-studied paradox known as a \emph{reinforcement paradox}, which occurs when candidate $X$ wins under IRV in two distinct elections but $X$ loses in the combined…
The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying…
Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no…
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")…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
A Condorcet cycle election is an election (often called a Social Welfare Function, or SWF) between three candidates, where each voter ranks the three candidates according to a fixed cyclic order. Maskin showed that if such a SWF obeys the…
We initiate the work towards a comprehensive picture of the smoothed satisfaction of voting axioms, to provide a finer and more realistic foundation for comparing voting rules. We adopt the smoothed social choice framework, where an…
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…