The math that explains why a crowd of laymen can outdo a small group of experts

The fact that groups consistently outperform individuals is well documented. This outcome rests on the statistical principle of the Law of Large Numbers. According to an enlightening article in Cal. Mgt. Rev., Vol. 50, Fall 2007 at 153, “This principle further states that a large group of laymen can even beat a small number of experts.” The article explains this counter-intuitive result as follows:

“Let the margins of error be x and y for an expert and a layman respectively. Naturally x<y. If n laymen work together, and they have independent sources of knowledge, then The Law of Large Numbers states that the margin of error of the group is yl√n = 4xl√16 = x. Hence, a group of 64 layman can beat the expert by a factor of two.” QED

Somehow, a three-lawyer law department is not at risk of being supplanted by 192 non-lawyers. If they tried, we would invoke the Law of Large Legal Spend Numbers.