Why playing the lottery can be a rational thing to do

Benedict Carey finds a 2000 paper by Lloyd Cohen, which is well worth rediscovering. From the abstract:

The central purpose of this paper is to show that lottery play is not economically irrational and uninformed. The paper presents a theory of lottery tickets not as misguided inputs into wealth production as some critics believe but as valuable inputs in creating a sense of open-ended possibility, specifically the possibility of escaping one’s current life by acquiring great wealth.

Cohen has some interesting ideas surrounding the idea that lotteries are a regressive tax:

The regressivity or progressivity of the tax implicit in the monopoly rents collected by the state turns on the question of whether it is the universe of lottery players who pay the tax or just the winners. Imagine that $10,000,000 is wagered at $10 a person from 1,000,000 people and a single winner is paid $4,000,000 and the state keeps $6,000,000 as a tax/rent. Who has paid this $6,000,000, the 1,000,000 purchasers or the one winner?

It’s certainly true that people who play the lottery are almost certain to lose money. But Cohen’s insight is that playing the lottery is not therefore automatically irrational. People like me love to calculate the expected gain or loss from buying a lottery ticket: back in 2005 I wrote a little post on the subject at MemeFirst. A commenter then came along:

Personally, I can afford a dollar (or equivalent) every now and then to keep the dream of international playboyery alive.

In other words, as Carey puts it:

Like a throwaway lifestyle magazine, lottery tickets engage transforming fantasies: a wine cellar, a pool, a vision of tropical blues and white sand.

People don’t invest the money they spend on lottery tickets. They spend it, and get those transforming fantasies in return. Cohen even manages to put this in economic terms:

In all things economic, there is a diminishing marginal something. In the case of ” belief in possibilities,” the most initially steeply diminishing marginal utility is that of probability. That is, one requires some real finite probability to support a belief in the possibility of escape, and while the more the better, the falloff in gain from additional probability is precipitous. On the other hand what is indispensable is a scenario that could conceivably be realized that satisfies the conditions of the hoped for fundamental transformation of one’s life.

Cohen even manages to use his theory to explain not only why one would expect the poor to play the lottery more than the rich, but also why one would expect the middle-aged to play the lottery more than the young, and so on. It’s all rather appealing — as a work of theory.

Does Cohen’s argument stand up against the kind of people who would abolish lotteries? It’s certainly true that those people rarely stop to spend much time considering the real benefit that lottery-players obtain from merely buying tickets even if they don’t win the lottery. Economists, who like to assume that individuals are economically rational (more or less), will move quickly to the conclusion that playing the lottery can therefore be a rational thing to do. Such a conclusion has the pleasant side effect of avoiding the opposite conclusion, which is that poor people are stupid and should be protected from themselves.

On the other hand, the money which poor people lose spend on playing the lottery is large enough to really make a difference to the communities in which that money is lost spent. Maybe the solution is for local lotteries to be set up, with the help of insurance companies who will insure against a tiny chance of an enormous payout. Lotteries have historically been organised on a statewide or nationwide basis because they payouts have historically had to come directly from ticket sales. But it’s very easy to envisage a lottery with an enormous jackpot ($100 million, say) which never generates anywhere near that amount of money in revenues. If such a lottery spent all its profits in the neighborhoods where the lottery tickets were bought, lotteries would be more defensible.

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16 Responses to Why playing the lottery can be a rational thing to do

  1. Ape Man says:

    Being a working class dude myself, I have to say that I think that Mr. Cohen is full of it.

    Sure, the poor saps who buy lottery tickets get to dream. You can construe the dreams as a benefit if you want to. But at what cost?

    For example, a lot more poor people smoke then rich people. I could write up an argument showing that this is rational on economic grounds. After all, poor people will not earn as much over their lifetimes as rich people. Thus there is less cost associated with them shortening their lives. Moreover, being poor, they have a smaller range of available pleasures then rich people. Therefore, in purely economic terms it is understandable that more poor people would smoke then rich people.

    But is it desirable that anyone should smoke?

    I have the same question with the lottery.

    As a side note, from what I see my co-workers doing, I would say that most of the lottery revenue comes from people who spend significant portions of their income on the lottery. It seems to me that the people around me either spend thousands of dollars a year on the lottery or they don’t play at all. This changes a little when the prizes reach record size. But still, if I had to guess by what I see around me I would say that lottery derives most of its revenue from people who are spending money that they can’t afford to lose.

    Anyone know of a scientific study that on the subject?

  2. Brad DeLong says:

    But isn’t it much more rewarding to anchor your fantasies in your belief in leprechauns, or in your descent from Xena? And it’s much cheaper in the long run too!

  3. Ironman says:

    It’s not so much where lottery monies are spent – it’s more that over time, they don’t pay for themselves if run by the state.

    Some points to consider. First, the state of California has a for its schools because too many people are winning the state lottery too often to drive revenues from the program high enough to cover the expected costs of the programs its mandated to support.

    Now, add to that the costs of the state having to cope with the unintended consequences of legalized gaming, and its very possible it may be losing money. One wonders if Illinois’ recent decision to wasn’t driven by such calculations.

    Finally, there’s the matter of what really motivates people to play the lottery. My best thinking is what that comes down to is only expressed as the – it’s actually a combination of the cost of a ticket, the odds of winning and the taxes that have to be paid on the winnings. I believe we see that in the various levels of the prizes that it takes for “lottery fever” to kick in as people adjust to the odds of winning every time the games are changed.

    That math doesn’t change for the national, local or state level. You’re certainly welcome to adapt the default data at our to design your ideal local lottery.

  4. Stefan says:

    I’d love to know if there is data that correlates church attendance with lottery playing.

    On the one hand, religion is a lottery where the payoff comes after you’re dead. Perhaps. So the religious might be more prone to playing lotteries, as the impulse is the same.

    On the other hand, perhaps non-church-goers are more likely to play the lottery, as they would like their winnings in this life, thank you very much.

    Finally, it is probably rational for those bad at maths to play the lottery, as their innumeracy allows them to have the happy belief they have a chance of winning. But for those of us cursed with the knowledge of expected returns, we are not able to gain that same benefit, so we don’t play.

  5. Caravaggio says:

    Interesting discussion. Here’s a relevant quote from “Dumb and Dumber”:

    Lloyd: What are the chances of a guy like you and a girl like me… ending up together?

    Mary: Well, that’s pretty difficult to say.

    Lloyd: Hit me with it! I’ve come a long way to see you, Mary. The least you can do is level with me. What are my chances?

    Mary: Not good.

    Lloyd: You mean, not good like one out of a hundred?

    Mary: I’d say more like one out of a million.


    Lloyd: So you’re telling me there’s a chance.

  6. Caravaggio says:

    I forgot to add my thought that many people play lotteries in syndicates of friends or work-colleagues. Part of this is because of the the increased probability of a win, but the other part is the fear of being left behind if the syndicate wins the bog prize.

  7. Ape Man says:


    I would be amazed if there was data that correlated church attendance to lottery playing. Especially if you adjusted for income.

    Statistically, most people who go to church regularly either behave no differently then those who do not go to church, or they behave more conservatively. Conservatively in this context means that they don’t drink, gamble, or sleep around. So if anything I would expect there to be a negative correlation.

    On a personal note, most of the religious people that I know do not play the lottery as a matter of moral principle.

    Also, if you will pardon an observation from someone who is “religious” himself, I think you are a little off target comparing religion to a lottery.

    Granted, there are plenty of people out there for whom the lottery example has a lot of explicatory power. This is what makes Billy Graham so popular. But when you wondered about lottery playing correlating with church attendance, you are talking about people for whom being “religious” is the governing meme of their life. For such people, the lottery example breaks down.

    For one thing, people who are only looking for lottery like return on religion will rationally chose a course that will bring them maximum psychological befits for minimal investment. This explains why most people in America are Christians who rarely if ever go to Church, read their bibles, pray, or do any other religious type things.

    On the other hand, truly religious people invest massive amounts into their beliefs for the same psychological befits (at least, as far as the after life is concerned). Take the Amish for example. To me, a lottery like example does not do a very good job of explaining the Amish way of life.

    I would suggest that religious people have a different sense of aesthetics then non-religious people (I am not using non-religious to mean atheist, but rather, those for whom religion does not govern their life). In other words, what they find to be beautiful (or meaningful) differs from non-religious people. I don’t think that this difference in aesthetics can be explained by their view of the afterlife.

    For example, religious people will generally have more children then non-religious people. This is true even of those who do not have religious objections to birth control and who do not believe that having more children will benefit them in the after life. Thus, I don’t think you can say that the extra children come about because of their belief in the afterlife. Rather, I think the extra children and the belief in the after life flows from the same aesthetic sense that leads them to become religious.

  8. Andrew says:

    The person wondered about the correlation because they are both based on the idea of what “could” be possible, but in all logical reasoning isn’t worth it.

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  10. PowerBall says:

    I would be amazed if there was data that correlated church attendance to lottery playing. Especially if you adjusted for income.

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  14. investing says:

    I think you are so wrong about this. The lottery is the worst thing that you can do.

  15. Marc Anderson says:

    Nothing sophisticated is needed to show that playing the lottery is entirely rational. Remember that economics don’t dictate what people should find pleasurable (i.e., what gives them “utility”). If buying a ticket, and having an infinitessimal chance of winning any # of dollars, gives them more utility than other uses of that same money, then that is perfectly rational behavior. Many economists are ridiculously narrow-minded regarding rationality…

  16. Marc Anderson says:

    Sorry for the typo in my last point. It should have been “economics doesn’t”. I guess better spell-checking wasn’t rational behavior, or else I would have done it (ha ha).

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