Condorcet's jury theorem

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The theorem was first expressed by the Marquis de Condorcet.

It states that where the average chance of a member of a voting group making a correct decision is greater than fifty percent the chance of the group as a whole making the correct decision will increase with the addition of more members to the group.

[edit] Example

An innocent man is accused of murder on the border between England and Scotland. All other considerations aside, he would be wiser to hand himself in in Scotland than England. This is because, given exactly the same evidence, a jury of fifteen persons is more likely to reach a true verdict than a jury of twelve.

The logic behind the claim is based on probability.

Imagine throwing a weighted coin, with a 51% chance of landing heads. If you threw it three times, and it landed tails three times, you'd not be too surprised. If you threw it ten times and it game up tails all those times, knowing it had a 51% chance of coming up heads, you'd raise an eyebrow. If it came up tails 100 times, you'd be safe in concluding that it did not indeed have a 51% chance of coming up heads, but a 100% chance of landing tails.

The more iterations of a probabilistic outcome there are, the more likely that the distribution of outcomes will conform with the base probability.

In a voting group, therefore, where members have an average chance of reaching a true decision above fifty percent, the more times votes occur, the more likely it will be that an overall majority will come to that decision. Individual probabilities turn into a group probability that is greater.

This raises two linked questions - is there a correct decision to be had? and what is a fifty one percent chance of finding it?

The latter is easier to answer. A fifty percent chance of reaching an answer to any question, where there are two choices, is a blind guess. Any answer based on true information correctly processed must have a greater than fifty percent chance of being correct. The only way to go below fifty percent chance is to either have incorrect information or badly processed information.

As to the claims that an answer is true, that will vary. Whether a person killed another is reducible to a true or false dichotomy. Whether higher or lower taxes are right for the economy is a much more complex question.

[edit] External links

Christin List and Robert Goodin. Epistemic democracy : generalizing the Condorcet Jury Theorem. Retrieved on 8th December, 2006..