This was just before the release of Kahneman's new book Thinking, Fast and Slow, which is an excellent read.
I will tell you a riddle. It's better if I project it, but I think you can follow me. And anyway, you're not supposed to get it right, so it really doesn't matter. There is a town in which 85 percent of the cabs are green and 15 percent are blue. And there was a hit-and-run accident involving a cab at night, and there a witness. Conditions of visibility were so-so, and the witness basically said, "I'm 80 percent sure that it was a blue cab, one of the smaller company."
And people are asked, presented that problem, and they're asked what is your probability that the cab involved in the accident was blue. Hundreds of people have been asked this question, and the most frequent answer is 80 percent. You know, there was a witness there. He was tested, and actually, you know, we say that under the visibility conditions, he was 80 percent accurate when he said green or when he said blue.
They go with the witness. Actually, this is the wrong answer. The correct answer is slightly less than 50 percent that it's blue, because the base rate continues to be relevant. The number of cabs continues to be relevant. Very hard to see it. You don't see it. I'm not going to explain it now. I mean, some of you do, but that's because you studied base theorem somewhere else, but if you didn't have the mathematics, why not trust the witness.
Now, let me tell you a variation on that story, and all of you, I think, will immediately feel the difference. There are two cab companies in the city: 50 percent of the cabs are green and 50 percent of the cabs are blue. But 85 percent of the accidents involve green cabs. Now, there was a witness, and the rest of the story is the same. Do you feel the difference? Nobody wants to ignore the fact that 85 percent of the accidents are caused by green cabs. I mean, the drivers in that company must be insane. This is the way that people see it. You immediately infer a causal propensity. You make a causal inference from that statistic, and now that is used.
When people combine that with a witness, they get roughly the correct answer. So there is a real profound difference between the way our mind deals with arbitrary statistics and with causal stories. And sometimes statistics enable us to make a causal story, because, as in this case, you immediately felt that something must be wrong with the green drivers, and then you use it.
Continue Reading. Buy Kahneman's book.