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Applied

A rule for choosing, stated exactly, and what it forces on whoever adopts 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.

5 figures · new