We all know that lotteries are a really terrible investment strategy. There are various theories for why people buy tickets anyway; the two main ones are
- People are stupid and can’t do math.
- People are not buying an investment, they’re buying a few moments’ thrill and excitement.
Both these theories seem pretty good to me, but I’ve got another which I’ve never seen suggested. I wonder if the usual calculation, “Pay 1 dollar, average return 75 cents” (or whatever it is) gets the expected utility return, as opposed to the dollar return, wrong. If you lose in the lottery, you’re out a dollar which, presumably, you could afford to lose. But if you win, you get (say) a million dollars, all in one chunk. It seems to me that this million might have a very high utility, so that the proper calculation is (1 dollar*1utility/$) to get (epsilon chance of 1 million dollars (=75 cents) times 2M utility/M$), for a total expected return of 1.5. With a million dollars, most people (at least in the lottery-buying public) could solve a whole host of day-to-day problems: Fix the car, move to a better neighbourhood, pay down their mortgage.
Suppose I offer you this deal: You pay me a dollar, and I will pay you back 125 cents. A great investment, right? In dollars it’s certainly a lot better than your average lottery. In utility, though, how much do you really care about an extra quarter? Even if I were stupid enough to give you this deal for a full thousand dollars, and you actually had a thousand lying around to invest, how many problems is a free 250 dollars going to solve?
I think the usual calculation doesn’t take into account the benefit of getting a really huge chunk of money all at once, and out of proportion to your usual income. Most people’s problems are scaled to their income, so getting ten years’ money in a day means, in effect, blowing all your problems out of the water – short, at least, of a really bad drug or gambling habit.
Me, I don’t do lotteries; they’re sort of boring. But if you do, perhaps you’re not irrational after all. 🙂