Beating the Crowd

Summary

Suppose you are participating in an auction for a box. Nobody knows exactly what is in the box, but they are bidding on it for various reasons; some think they can make money, some might have sentimental reasons, and others might just be having fun. You yourself are trying to make money. You asked around a bit, did some research, and think that you have a good estimate for the value of the box. You think it’s worth $10,000 and decide to bid $9,000. You won. How do you feel? Great? You made money (on average, you think)! But thinking about it a little more gives you pause. The rest of the world bid for this box and your bid beat all of them. Every single person who did their own research, and presumably thought just as hard as you, decided to bid less. Could it really be that you know more than all of them? You open the box, and find a $100 bill inside. It’s a bit of a contrived example, but it illustrates the point nonetheless. You might have had a reasonable confidence interval in isolation. But the very fact that you won the bid, that you were more aggressive than the rest of the world, shifts the probability of your decision actually being good vastly against you. Professional traders think very hard about this. It’s why firms like CitSec pay for order flow from brokers like Robinhood. It’s very simple: if you had to win an auction, you should want to win it against a random retail “trader” rather than a professional hedge fund. The question, then, is whether the world is usually correct with their hunches. Statistician Francis Galton tried to find out through a well-known experiment. He asked a group of people to independently guess the weight of a displayed ox. The average guess turned out to be within a couple of pounds of the correct weight. This seems surprising, but is logically consistent: in the absence of other information or opinions, one would have to assume the average human guesses any quantity correctly. To say anything else implies an opinion that ...