Stocks and Reasoning About Others' Reasoning
The problem of guessing 80 percent of the average guess is a bit like Keynes's description of the investors' task. What makes it tricky is that anyone insightful enough to cut to the heart of the problem and guess 0 right away is almost certain to be wrong, since different individuals will engage in different degrees of meta-reasoning about others' reasoning. (This may be sour grapes for my disastrous misadventure in the stock market.) Some, to increase their chances, will choose numbers a little above or a little below the natural guesses of 40 or 32 or 25.6 or 20.48. There will be some random guesses as well and some guesses of 50 or more. Unless the group is very unusual, few will guess 0 initially.
If a group plays this game only once or twice, guessing the average of all the guesses is as much a matter of reading the others' psychologies as it is of following an idea to its logical conclusion. Gauging investors is often as important as gauging investments and is likely to be more difficult as well.
Finally, the recent SEC settlement to reform the investment industry reminds us of an unpleasant aspect of this market/contest analogy. It's not uncommon that some of the market's formerly prettiest contestants — WorldCom, Tyco, Adelphia, Global Crossing, and HealthSouth — turn out on closer inspection to have pimples and pustules all over their corporate faces.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the forthcoming A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.