The Jury Theorem

By Ocean in Featured, History, Our Theory

Marquis de Condorcet devised what we now know as the Jury Theorem in 1785:

Dealing more with political science, the Jury Theorem states that with a majority vote, each person has the probability ‘p’ of making the correct decision. If the probability that each person makes the correct decision is over 50%, then the probability that a majority of ‘N‘ people vote the correct decision is over 50%, increasing and approaching 100% as ‘N‘ increases and approaches infinity.

It is quite apparent that the Jury Theorem is in agreement with the Dumb Agent Theory in its most simple form. Several Caveats are:

• The Jury Theorem assumes there are two decisions to make, a right and a wrong one (binary choice). This does not apply if there are more than 2 options, although a study has been performed by List and Goodin showing that it can.
• This also, like the Dumb Agent Theory, assumes that people are making their decisions independently. If ‘p‘ is >50%, but one person has influence over many other people, this can skew the result. We see this very often, especially with politics.
• Also, this assumes that each participant’s competence is greater than 1/2. In other words, if each person is more likely to vote incorrectly, then a majority will vote incorrectly, and the optimal number of voters would be 1. The interesting fact about the Dumb Agent Theory is that this doesn’t seem to be a necessary factor. Even if peoples’ results are across a wide spectrum, we need only take a mean of their choices to achieve an accurate result.

It is therefore interesting to compare the two slightly different theories. The Jury Theorem is also a step forward in explaining how the Dumb Agent Theory and Wisdom of Crowds works, although much of it is still a mystery.