Jordan Ellenberg at Quomodocumque links to an old article he wrote about the expected value of lottery tickets. Despite the fact that the article is in Slate, it is free of knee-jerk contrarianism, and this so disturbs the fundamental order of the universe that I feel like I have to supply some of my own. I claim, therefore, that playing the lottery can be quite rational in cost-benefit terms, even if the expected monetary value of the ticket is negative, and one is risk averse. (And what God died and left expected utility in charge?)
The benefit to playing the lottery comes entirely between buying the ticket, and when the winner is revealed. During this interval, someone who has bought the ticket can entertain the idea that they might win, and pleasantly imagine how much better their life could be with the money, what they would do with it, etc. It's true that in some sense you always could just make yourself think about "what if I had $280 million?", but many people find it very hard to get their imaginations going on sheer will-power. A plausible and concrete path to the riches, no matter how low the probability, serves as a hook on which to suspend disbelief. In this regard, indeed, lottery tickets are arguably quite cost-effective. If a $1 lottery ticket licenses even one hour of imagining a different life, I don't see how people who spend $12 for two or three hours of such imagining at a movie theater, or $25 for ten hours at a bookstore, are in any position to talk.
Despite having held this idea for years, I have never played the lottery, because I couldn't begin to make myself believe.
Update, next day: ... and in any case, I was, of course, raised to regard lotteries as (in the words of one of my teachers) a tax on people who are bad at math, and I'm at least as much a creature of such internalized class expectations as anyone else.
None of this is to deny that some people spend more than they can afford on lottery tickets (just as some people do on books), and would be happier in the long run not buying them. It's also not to say that imagining what one would do with lottery winnings is just as good as consuming works of art, or for that matter any other diversion. (Though many who are otherwise eager to incant de gustibus non est disputandum become strangely absolutist about this.) It is to say that lottery tickets look a lot better as imagination-fueling consumption goods than as investments.
Posted by crshalizi at December 31, 2010 19:43 | permanent link