Degree in a Fortune Cookie

Degree in a Fortune Cookie

I used to attend a health club in the middle of the day and chat with an interesting Eastern European fellow with two Ph.D. degrees, one in physics (statistical no less), the other in finance. He worked for a trading house and was obsessed with the anecdotal aspects of the markets. He once asked me doggedly what I thought the stock market would do that day. Clearly I gave him a social answer of the kind “I don’t know, perhaps lower”—quite possibly the opposite answer to what I would have given him had he asked me an hour earlier. The next day he showed great alarm upon seeing me. He went on and on discussing my credibility and wondering how I could be so wrong in my “predictions,” since the market went up subsequently. The man was able to derive conclusions about my ability to predict and my “credibility” with a single observation. Now, if I went to the phone and called him and disguised my voice and said, “Hello, this is Doktorr Talebski from the Academy of Lodz and I have an interrresting prrroblem,” then presented the issue as a statistical puzzle, he would laugh at me. “Doktorr Talevski, did you get your degree in a fortune cookie?” Why is it so?

Clearly there are two problems. First, the quant did not use his statistical brain when making the inference, but a different one. Second, he made the mistake of overstating the importance of small samples (in this case just one single observation, the worst possible inferential mistake a person can make). Mathematicians tend to make egregious mathematical mistakes outside of their theoretical habitat. When Tversky and Kahneman sampled mathematical psychologists, some of whom were authors of statistical textbooks, they were puzzled by their errors. “Respondents put too much confidence in the result of small samples and their statistical judgment showed little sensitivity to sample size.” The puzzling aspect is that not only should they have known better, “they did know better.” And yet . . .

I will next list a few more heuristics. (1) The availability heuristic, which we saw in Chapter 3 with the earthquake in California deemed more likely than catastrophe in the entire country, or death from terrorism being more “likely” than death from all possible sources (including terrorism). It corresponds to the practice of estimating the frequency of an event according to the ease with which instances of the event can be recalled. (2) The representativeness heuristic: gauging the probability that a person belongs to a particular social group by assessing how similar the person’s characteristics are to the “typical” group member’s. A feminist-style philosophy student is deemed more likely to be a feminist bank teller than to be just a bank teller. This problem is known as the “Linda problem” (the feminist’s name was Linda) and has caused plenty of academic ink to flow (some of the people engaged in the “rationality debate” believe that Kahneman and Tversky are putting highly normative demands on us humans). (3) The simulation heuristic: the ease of mentally undoing an event—playing the alternative scenario. It corresponds to counterfactual thinking: Imagine what might have happened had you not missed your train (or how rich you’d be today had you liquidated your portfolio at the height of the NASDAQ bubble). (4) We discussed in Chapter 3 the affect heuristic: What emotions are elicited by events determine their probability in your mind.