People frequently dismissively refer to lotteries as a “math tax” — but I believe this oversimplifies the cognitive error that allows people to conceive of a lottery as being a worthwhile risk.
The actual error has nothing to do with mathematics, but with groups and belonging. The error stems not from the possibility of winning, but from seeing actual winners on TV or in the papers. When you see a winner, that person temporarily becomes “real” to you, and the fact that they won the lottery means that “someone you know” won the lottery. I believe that human beings have no cognitive capacity to grasp how many people there actually are — we all live in a world with maybe 200 actual people in it — and everyone else is just a statistic. I think that emotionally it is impossible to “feel” that as many as a thousand people exist — much less a million or hundred million. So, when we read that people have actually won the lottery, we calculate the odds in our gut, which says then that one of my people have won the lottery, so the odds feel about one in a hundred or so. We then modify this in our explanation because we know rationally that it is more than this, but the excitement we feel on listening to the numbers, or on going through our purses and wallets if we hear that the winning ticket has been lost, that is based on the physical intuition that “someone I know” won — and so that it could possibly be me.
While I agree that it is offensively stupid, on reflection, to play the lottery — I think it is worse when people who have calculated the odds of that look on the behavior of other human beings, behavior which in every way is just as irrational as ones own behavior, and pass judgment on it as if that behavior was more simply motivated than it is.
In my opinion, the dork that smugly refers to the lottery as a “math tax” is a bigger idiot than the person who plays the lottery, because he is relying on an intuitive model of human decision making, while at the same time castigating another person for relying on an intuitive model of games of chance. And if overlooking the implausibility of the lottery is evidence of stupidity, then what kind of gross insanity is it to pretend that the model of “rational self interest operating with clear information” can be used to explain any kind of human behavior.
That is the kind of thing that causes lottery players to look down on statisticians.
——————–Other posts on the Math Tax
Dangerous Intersection Post on the Math Tax
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