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Concept

Condorcet jury theorem

The result that a majority of independent voters, each right more often than not, is right more often than any one of them. As the group grows the majority is almost surely right, and the theorem fails when the votes are correlated or each voter is more often wrong.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A majority of independent voters, more often right than any of them. The probability that a simple majority of n independent voters is right, for n from 1 to 201, when each voter is right with probability 0.45, 0.51, 0.55, 0.6, 0.7.

A majority wiser than its members

Condorcet's other theorem turns voting round: the voters no longer have preferences but judgements about a single fact, each a little more likely right than wrong. Then a simple majority of many of them is almost certainly right — 6,763 voters who are each right 51% of the time make a majority right 95% of the time. The theorem survives voters worse than a coin, if the average is better. It does not survive voters who share their mistakes, and when their skills differ the right rule weighs votes rather than counting them.

applied · Voting rules How often each procedure finds the right verdict, with 3 judges of competence 0.7. both true: liable: premises 61.5%, conclusion 48.5%; first only: not liable: premises 83.1%, conclusion 88.6%; second only: not liable: premises 83.1%, conclusion 88.6%; neither: not liable: premises 95.3%, conclusion 97.7%; average 80.7% against 80.9%.

Which vote finds the truth more often

A court that must decide two premises and their conjunction can vote on the premises or on the conclusion, and the two votes sometimes disagree. Suppose there is a right answer and each judge is more often right than wrong. Then the question has an exact answer: for three judges the conclusion vote is more often right when competence is below √½ and the premise vote above it, and in a large court the premise vote wins at any competence — while the conclusion vote turns out to be a built-in standard of proof.

applied · Judgement aggregation

Named alongside it

The objects these essays reach for when they reach for this one.

Binomial distributionIndependenceBayes' theoremBiasCorrelationJudgement aggregationLaw of large numbersMajority rulePairwise majorityProbability modelPropositionWeighted majority

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