If you have a group of people, and if each person is more than 50% likely to be right, the likelihood that the average answer will be right approaches 100% as the size of the group increases.Interesting. I had always wondered if crowds were wise, or better stated: when are crowds wise? I had never thought of it like this, but this is simple and gets at the heart of it. Although, how do you know if people are 50%+ likely to be right?
Here's a problem, though. If group members are less than 50% likely to be right, the likelihood that the average will be right approaches ZERO as the size of the group increases.
I think this has big implications on democracies. When should things go to referrendums, and when should things be decided by representatives? You could make a good case that things like gas taxes, the average voter is less than 50% likely to get it right. Whereas voters are probably over 50% in picking the better candidate, and the representative (because they can study the issue more closely) are probably over 50% in doing the right thing on the gas tax. Of course what does right mean here?
The other obvious implication is for Who Wants To Be A Millionaire. When should you ask the audience and when should you phone a friend? In one case you are using the wisdom of a crowd and the other the wisdom of 1 expert.
Via Lessig Blog