State lotteries: Part 1
David Brooks wrote a column last week in which he worries about the deterioration of cultural values related to intelligent use of money. This got responses on the Becker-Posner blog. All three articles make good points, but I got hung up on a sub-debate occurring between Brooks and Posner on the question of state lotteries. This is one of my pet peeve idiotic government policies, and I wanted to write something about it. As I started writing, it became clear to me that this was longer than one post, so I’m breaking it up into a several-post series.
My ultimate goal is to argue that states should not have state lotteries, giving fair consideration to arguments for the other side. Today’s goal, though, is to show a smaller point — a lemma, for the mathematicians out there — that from the point of view of the typical lottery customer, playing is irrational.
The most obvious value of a lottery ticket, the chance to win, doesn’t even come close to making it worth buying. Typically the expected value of the lottery ticket is something like half the cost of buying it. It is an idiotic way to try to get rich. Proponents of the lottery tend instead to point to more intangible things. Maybe the suspense of playing the lottery has entertainment value. Maybe it gives people hope and the chance to dream.
I find these arguments unconvincing. I’m sure playing the lottery is suspenseful and that people playing it dream about what they’d do if they had the money. I’m sure some people buy lottery tickets because they like the suspense or the daydreaming it brings even though they know the payoff is incredibly not worth the price. I just don’t believe these people account for an appreciable portion of lottery tickets sold. My main reason for believing this is just common sense, but it’s also backed up by they way lotteries are advertised. Those writing the ads presumably use focus groups and so forth to see what message it is that makes people play. The slogans they come up with aren’t things like “It’s fun and suspenseful” or “What a great way to donate to your state government.” What they do emphasize is the chance of winning. California uses “Dreams do come true.” New York uses “Hey, you never know” and “All it takes is a little bit of luck.” Pennsylvania uses “You have to play to win.” (In the interest of fairness and giving credit where credit is due, Illinois seems to be an exception here, emphasizing the fun of playing with “Have a ball”. I only checked a handful of states, so there are probably other exceptions, but the trend is clear.)
The “allowing people to dream” benefit is on particularly weak ground. If all you need in order to daydream about being rich is a non-zero probability of that happening, you don’t need to buy a lottery ticket. You could get rich by discovering oil in your backyard or a priceless antique in your attic. You could find and return a cat whose grateful billionaire owner makes you the sole beneficiary in their will. If however, you need a reasonable possibility of becoming rich in order to daydream about it, the lottery ticket is insufficient, as the chances of winning any of the big prizes are mind-numbingly small. In other words, buying a lottery ticket so that you can dream requires just as bad an understanding of the odds as buying one to make money does.
There’s one more potential reason for the lottery being rational that I want to deal with. It’s Posner’s hypothetical U-shaped marginal utility curve. That one, though, involves some complicated economics, so I’m going to push it to tomorrow’s post.
Update: Installments two and three have been posted.
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[...] Yesterday I started a multi-post series on why state lotteries are dumb. I tried to show that it was irrational to play the lottery. As I said yesterday, though, I left one potential counterargument to deal with today. [...]
[...] posts, this is the third part of a series on the problems I see with state lotteries. In parts one and two, I give what I hope is a convincing argument that playing the lottery is irrational for the [...]