Related papers: Optimizing Voting Order on Sequential Juries: A Me…
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…
The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different…
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…
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…
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…
We discuss voting scenarios in which the set of voters (agents) and the set of alternatives are the same; that is, voters select a single representative from among themselves. Such a scenario happens, for instance, when a committee selects…
The Condorcet Jury Theorem or the Miracle of Aggregation are frequently invoked to ensure the competence of some aggregate decision-making processes. In this article we explore an estimation of the prior probability of the thesis predicted…
Condorcet's jury theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter's independent probability of voting for that outcome is greater than 0.5. Yet,…
There is a striking relationship between a three hundred years old Political Science theorem named "Condorcet's jury theorem" (1785), which states that majorities are more likely to choose correctly when individual votes are often correct…
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…
A group of privately informed agents chooses between two alternatives. How should the decision rule be designed if agents are known to be biased in favor of one of the options? We address this question by considering the Condorcet Jury…
Consider $2k-1$ voters, each of which has a preference ranking between $n$ given alternatives. An alternative $A$ is called a Condorcet winner, if it wins against every other alternative $B$ in majority voting (meaning that for every other…
We consider the problem of determining a binary ground truth using advice from a group of independent reviewers (experts) who express their guess about a ground truth correctly with some independent probability (competence). In this…
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…
In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under…
We study a mathematical model of voting contest with $m$ voters and $n$ candidates, with each voter ranking the candidates in order of preference, without ties. A Condorcet winner is a candidate who gets more than $m/2$ votes in pairwise…
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…
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…
A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…
We explore how the mechanics of collective decision-making, especially of jury deliberation, can be inferred from macroscopic statistics. We first hypothesize that the dynamics of competing opinions can leave a "fingerprint" in the joint…