Correlation
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
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.
Drawn without putting back
Every concentration bound on this shelf assumes the draws are independent. A real sample is not: a pollster does not ring the same person twice, and every ball taken from an urn changes what is left in it. The dependence runs the helpful way. Wassily Hoeffding proved in 1963 that a sample drawn without replacement is at least as concentrated as one drawn with it, for every convex measure of spread at once — and the variance falls by an exact factor that reaches zero when the whole urn is taken.
Named alongside it
The objects these essays reach for when they reach for this one.
Binomial distributionBayes' theoremConcentration inequalityCondorcet jury theoremConvexityHoeffding inequalityIndependenceLaw of large numbersMoment generating functionPairwise majorityProbability modelSampling