Groups and Wisdom II

January 16, 2007
Posted by Jay Livingston

The Wisdom of Crowds by James Surowiecki begins with the story of Francis Galton at the fair. Galton, whose life spans much of the 19th century, was among other things, a statistician. He also believed in improving the human race by selective breeding. In fact, he coined the term eugenics.

At the fair, Galton noticed people submitting their guesses on the weight of an ox. Galton the statistician kept track of all the guesses— some 800 in all— and computed the group mean. Galton the eugenicist assumed that the guesses of the ignorant would detract from the overall accuracy, while the guesses of farmers and butchers would be closest to the actual weight.

When all the entries were in, the mean of the group guesses was 1197 pounds; the ox’s weight, 1198 pounds. Not even the savviest ox breeder came closer than the group as a whole.
I teach a general intro course for majors, and the first concept I want them to grapple with is the social fact. I usually start with Durkheim and suicide rates. But this semester I'm thinking of doing variations on a theme by Galton for the first day of class.

1. Bring a jar filled with M&Ms.
2. Have students pass the jar around and submit a piece of paper with their name and their guess as to the number of M&Ms. (Maybe announce that there will be a prize so as try to prevent wise-ass guesses.)
3. Collect the guesses but announce that there’s going to be one more player, the group itself, i.e., the mean of all guesses.
4. Maybe ask them to speculate on whose guess will be closest or how they think the group will do compared with the guesses of the smartest students or the students who eat a lot of M&Ms and are therefore more familiar with the subject.
5. Record the guesses, compute the mean, announce the right answer.
6. If Galton is looking down and blessing this experiment, the group mean should be closer than any individual guess, even that of the most experienced M&M eater.
I’m not sure if this really gets across the point about social facts. It does show that there is something about a group that makes it different from just the sum of its individuals, but it requires no interaction, no social influence.

On the other hand, there’s a moral to the story that I like: in order for the group to be so smart, we need the contributions of everyone, even those whose guesses were farthest off. The same principle will hold true for discussion throughout the semester. So don’t suppress an idea just because you think you don’t know enough about the topic.

Now all I need is an M&M-counting machine.