By ET

There is a widely acclaimed saying in China:

“Three stinky cobblers working together can outsmart Zhuge Liang”

[Zhuge Liang is the most famous military strategist in Chinese history, he is a household name, and is considered as an incarnation for wisdom]

It generally talks about the power of aggregated knowledge, which is the foundation of the political systems such as the congress, the senete, etc.

British scientist Francis Galton, as other British elites, believed that only a few elites can have the capacity to organize and maintain a stable society. To prove his point, he randomly sampled 800 people, asking them to guess the weight of an ox. To his surprise, the average guess 1,197 pounds is amazingly close to the real number 1,198 pounds. He concluded after that experiment:

under the right circumstances, groups are remarkably intelligent, and are often smarter than the smartest people in them. Groups do not need to be dominated by exceptionally intelligent people in order to be smart. Even if most of the people within a group are not especially well-informed or rational, it can still reach a collectively wise decision.

In mathematics terms, this is simply the law of larger numbers, which states that: the average of a randomly selected sample from a large population is likely to be close to the average of the whole population. What happened in the Ox experiment is that some people overestimated the weight, and some underestimated it, the law of large numbers pulls the estimates toward the middle, which, as it shows, is amazingly close to the real number.

This, however, is not the whole story!

As we know, in teams, the performance of a team is severely influenced by the least capable member. In military situations, sometimes all it takes to win a battle is to attack the weakest point of the enemy. There is a wooden barrel theory stating that the capacity of a barrel is determined not by the longest wooden bar, but by the shortest. This is in contradition to the previous story about wisdom of the crowd. The lower bound means much more in this case!

Talking about estimating numbers, there is an interesting theory in economics called the winner’s curse. The winnner’s curse happens in auctions. Suppose there is a potential oil field for bidding, several companies are competing for the right to drill the oil. Each of them sends out the best analyst to estimate the value of the field. Similar to the Ox experiment, some will overestimate, and some will underestimate. But different from the Ox story, here, the winner will be the one who has the highest estimation. By the law of large numbers, this winning company will most probably overestimate the value. Then although it wins the auction, it may not get the profit as expected.

In all the above stories, the elite (whoever deviates from the average) loses. If you are near the average… hehe, sorry, by definition, you are not elite. Then why the society values the elites so much? In what circumstances elites are needed? Under what conditions, the elite person, the average person, the least capable person is most important?

I wanted to write more, linking everything to the information flow discussed in Hayek’s 1945 seminal paper “the use of knowledge in society”, but I need to get back to work. Let me try to finish this sometime later…

Until next time!

[I appologize for the long title :-p]

By ET This entry was posted on Thursday, September 14th, 2006 at 3:57 am and is filed under General, Random Thoughts, Technology. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.