math-lab

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Condorcet jury theorem

Three people answer the same three cases. The picture is one run, not the long-run chance.

Three jurors answer the same three cases. A case is one question with a right answer and a wrong answer. Juror 1's button shows only that person's answers: right or wrong on case 1, case 2, and case 3.

The majority button asks all three the same cases. On a case, the majority is whatever at least 2 of them said.

If each person is right a little more often than wrong, a bigger group gets more sure. One person at 60% is right 60% of the time. Three people together are right about 65% of the time. This picture is one run you can read. It does not draw that percent.

Each person is right about 60% of the time, on their own, and they do not copy one another.

One person is then right 60% of the time. Three people, taking the majority, are right about 65% of the time. More people push that chance toward 100%.

This board is one run of three cases, so you can see right and wrong. It is not the 60% and it is not the 65%.

If each person is wrong more often than right, or they all share one bias, a bigger group does not get more sure.