The mysterious letter

It is fascinating to see how strong our intuitions fail us. One such example is the survivor bias. Our belief in certain astrologer or certain medicine is mainly because we hear so many people telling us that it works. The fact is, it might be random – but people for whom it doesn’t work don’t go around telling that it didn’t work.

Have you seen some very affluent neighborhoods and noticed how there is not a single poor  person living there? It is mainly because the price to live in that neighborhood self selects only the rich ones – those who can’t afford can’t don’t show up there.

This interesting example is from Nassim Taleb’s book “Fooled by Randomness”:
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The mysterious letter

You get an anonymous letter on January 2 informing you that the market will go up during the month. It proves to be true, but you disregard it owing to the well-known January effect (stocks have gone up historically during January). Then you receive another one on February 1 telling you that the market will go down. Again it proves to be true. Then you get another letter on March 1 – same story. By July you are intrigued by the prescience of the anonymous person and you are asked to invest in a special offshore fund. You pour all your savings into it. Two months later, your money is gone. You go spill your tears on your neighbor’s shoulder and he tells you that he remembers that he received two such mysterious letters. But the mailings stopped at the second letter. He recalls that the first one was correct in its prediction, the other incorrect.

What happened? The trick is as follows. The con operator pulls 10,000 names out of a phone book. He mails a bullish letter to one half of the sample, and a bearish one to the other half. The following month he selects the names of the persons to whom he mailed the letter whose prediction turned out to be right, that is, 5,000 names. The next month he does the same with the remaining 2,500 names, until the list narrows down to 500 people. Of these there will be 200 victims. An investment in a few thousand dollars’ worth of postage stamps will turn into several millions.

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What happened here – how did those fall victim to this scam? Because of the survior bias. All the victims are from the lot for whom the predictions turned true consistently. They didn’t see the other 50% for whom it was wrong. This builds a bias in their minds that gets reinforced by the 5th month – strong enough that they believe the next prediction will turn out to be right.

Our mind can be tricked easily to see a pattern that doesn’t exist.



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