Thursday, 25 August 2011

When the Majority is Right: Condorcet Meets Who Wants to be a Millionaire

This is academic autobiography

A couple of times recently, I have been taken back to work I did in the 1970s on the justification for majority voting, both in government and the legal system (jury trials)

The first writers to treat the matter seriously were Rousseau and Condorcet, the latter - among other talents - a mathematician specialising in the theory of probabilities.

Condorcet showed that majority voting is a good guide to truth:

(1) the more enlightened (knowledgeable) is each individual voter, with a minimum requirement that they be more likely to be right than wrong on any one occasion (p = greater than 0.5)

(2) provided that when voting, voters are trying to give the right answer

(3) and provided that they vote independently of each other - if one voter follows the lead of another, that simply reduces the effective number of voters

If these conditions are met, then in a majority vote the probability of the majority being right increases (and quite dramatically, heading towards p = 1 [certainty])the larger the vote gap between majority and minority.

Since I did the work in the 1970s, the TV quiz show Who Wants to be a Millionaire? has come along and it demonstrates Condorcet's theorem perfectly. When a contestant Asks The Audience to select the right answer from four possible answers, he or she can safely assume:

(1) that the Audience is quite knowledgeable- Quiz show live audiences are likely to contain a high proportion of people good at quizzes
(2) members of the audience have no motive to give answers they believe to be untrue (they enjoy giving right answers!)
(3) they vote independently of each other using push-button consoles with little or no time to consult the person sitting next to them

Hey Presto, the audience's choice of right answer will, almost certainly, BE the right answer. If some researcher checked back over Ask the Audience choices, I think they would rarely find that the Audience got it wrong. Ask the Audience is a No Brainer if you don't know the answer yourself.

There is more serious stuff in my essay "Majoritarianism" on my website

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