In the Land of the Perma-Bear and the Perma-Bull
When the Facts Change, Change Your Mind
TIME FOR ANOTHER GAME FOR YOU TO PUZZLE OVER.
Imagine two urns filled with millions of poker chips. In one of the urns, 70 percent of the chips are red and 30 percent are blue. In the other, the ratio is reversed, so we have 70 percent blue and 30 percent red chips. Suppose one of the urns is chosen randomly and a dozen chips are drawn from it: eight red chips and four blue chips. What are the chances that the chips came from the urn with mostly red chips? (Give your answer as a percentage.)
If you are like most people, you have probably just said a figure between 70 and 80 percent. Surprisingly, the correct answer is actually a whopping 97 percent. To arrive at this answer you would need to apply Bayes Theorem, a relatively simple formula which shows how the probability that a theory is true is affected by a new piece of evidence. However, very few people solve this problem correctly. They end up being too conservative.
This tendency towards conservatism isn’t just seen in odd mathematical problems. It rears its head in the real world as well. Doug Kass of Seabreeze wrote an article for RealMoney Silver on May 27, 2009, which summed up the problem of conservatism very well. In this piece, Kass warns of the dangers of being a perma-bull—always bullish on the market—or a perma-bear—always negative on the market.
I have often written that both perma-bears and perma-bulls are ...