I went to a very interesting talk today, extending a modern theory to an ancient example.

In 1907, Francis Galton went to the fair, and watched a weight-guessing contest, in which men put in tickets to guess the weight of meat that an ox would be when it was killed and dressed. The buyers were all sorts and conditions of men,  including professional farmers and butchers, and idle souls who came by and guessed their best. He thought this a fair analogue to democracy, and asked to see the cards afterwards. He found, that although the cards included estimates over a hundred pounds off, the median (1207 lb) was only nine pounds from the actual weight (1198 lb).  (Galton chose the median, as most analogous to the 50% + 1 result of democracy; the mean was 1197 lb, even closer.)

This is not what Galton expected, by the way; he was the snob who invented eugenics. It is to his credit that he published anyway.

This has recently become a hot topic in economics, called the "wisdom of crowds" with many experiments: one, to guess the number of jellybeans in a jar, had the mean estimate of a classful of students closer than all but one of them, IIRC. 

Our lecturer, Prof. Herman, of Hebrew University, had, however, a new example to propound: the Athenian direct democracy was also composed of all sorts of men, and made decisions through the collective decisions of a large random sample: although its decisions were not always perfect, they were good enough - if sometimes just barely good enough - for two centuries. 

He quotes sections from Aristotle, Plato, and Thucydides which argue for the wisdom of the crowd; in the last two, these are from speeches not expressing the author's view. (All of them, like most surviving Greek literature, disliked democracy, or preferred something else. Herman concludes that the Athenian democrats indeed argued for the wisdom of the many.
 
James Surowiecki and Scott Page have written books on the subject, offering Deep, Thoughtful, explanations, involving diversity of knowledge and approach (thirty people know more together than any one expert knows separately, and have more techniques for problem-solving), and information exchange.

What is truly striking, if I read correctly, is that neither of them discusses, even to refute, the obvious default explanation: the central limit theorem, from which follows: one way to get the average weight of a boxful of rocks is to draw out a committee of thirty rocks, weigh all of them, and take the average of the thirty. The weights of the committee may vary widely, but their average weight is likely to be quite close to the average of all the rocks, quite possibly closer than any of the thirty individual weights. 

This involves two assumptions: that the committee is large, and chosen randomly without bias.  If you vibrate the box, and shake the big rocks down to the bottom, the thirty on top will average light; if you pick a committee of one or two, they will be no closer to the grand average than any other rocks.

Similarly, if there is a large, randomly chosen bunch of people, their average opinion on the number of jelly beans in the jar will be close to the average opinion of all possible human beings. Unless there's some reason for people to guess fewer  (some optical illusion, for example) this average will be the number of beans in the jar. The conditions implied are the same the economists come up with: a large number of people, and as diverse as possible.

But then, few economists know much about mathematics: I have been convinced of this since I took Macro and they solved the problem of how to explain calculus right by explaining it wrong.

So with the United States, for forty years and more: we have had King Logs, who have done little, and so done little harm, and King Storks, who have done much, and made things that much worse. (This is not partisan: the elder Bush was as much a Log as Clinton, and Ford as much as Carter.)

Now, we are left with the contest between King Log, the second Democrat from the right, who has defeated Queen Log, the rightmost of the Democratic candidates. He faces King Stork, who would do many things, none of them helpful or clueful. I heartily support King Log; but I expect little of his administration.

I hope to be agreeably surprised.