Interestingly, people seem to treat currency as nonlinear! Conventional wisdom has it that lotteries are a tax on the stupid (although Greg Egan considers them a tax on hope, which is closer to the mark). But here's another way of analysing why people buy lottery tickets (note: I don't).

Money is nonlinear. The utility function for having $X is not linear in X! Rather, for very low values of X it is much shallower. If you see a penny somewhere, often you won't bother to pick it up. But the cost of doing so is far less than 1 penny. The point is you don't expect to be able to get 1/100th the utility of $1 out of 1 cent (of course this does not apply to 100 cents; just to a single cent). So you don't mind losing 1 penny.

Lotteries are the same. I buy a ticket for $5 which with probability 10-6 will get me $2.5M. WHY? Well, evidently I don't think the loss of $5 is so great, compared to a gain of $2499995. With $2.5M, I could buy houses, invest wisely, etc.; with $5, I can't do any of that. They're just not the same sort of commodity!


this nonlinearity is the reverse of that in dragoon's writeup. There, more money is worth less as you get more of it; but in reality, more money is worth more as you get more of it. This has an obvious bearing about the fairness of capitalism.