## 24 February 2016

### Playing the lottery might be your smartest move

David writes*

Voltaire called it a tax on stupidity. People who buy lottery tickets are often seen as stupid, naïve, or at the very least, (economically) irrational. They are often looked down upon because buying a lottery ticket would be an economically bad choice. This common belief is a logical outcome of expected utility theory: if the probability of winning times the pay-off is lower than the utility you lose by participating, you should not participate [pdf]. The obvious pay-off in the case of the lottery would be the prize money, and in that case, the probability of winning times the prize money is of course lower than the ticket prize, otherwise the lottery would not make any profit.

It is important to note for this theory however, that the pay-off is an expected utility value: people can never know how happy or unhappy they are going to be after something has happened, so they have to make an estimate of what the pay-off is going to be. That means that an economically rational choice is not necessarily the choice with the highest utility value, but the choice with the highest expected utility value based on the information with which the people make the choice.

Now often, playing the lottery is justified by a psychological factor, such as liking the thrill or wanting to have that incredibly small chance of never having to work again. There are however two reasons why even purely economically, it might be a rational choice. First of all, an information asymmetry plays a role. The extremely high pay-off is thrown into the face of the participants (and sadly also the people that do not participate) all the time, up to the point where you see an orange whale with a number on his back swim on your screen every 10 minutes when you are watching TV. The low probability is however just ‘low’, but a value is never really put on it. That means that people only know that it is about a huge number such as 20 million euros, and know that the probability is ‘low’, but not more than that. That means that their (unconscious) economic calculation might not show that buying the ticket is a bad idea, just that the ticket prize is relatively low and that the pay-off is huge, which might make it seem logical for them to participate. If the extremely low probability was thrown into their face equally as much as the high pay-off, perhaps many people would not participate.

Second of all, Kahneman and Tversky have explained [pdf] why people put a disproportionately high weight on low probability risks. People might be incredibly scared of flying, terrorists, or sharks, even though the risks are miniscule. This disproportionate value changes the outcome of an (unconscious) economic calculation as well, up to the point where the risk times the pay-off plus the added weight might be bigger than the ticket prize. That means that the outcome of the calculation would be that it is economically interesting to play the lottery. Although this added value is not in any way paid back, the only thing that matters is that people add that weight when they make the choice, because as I explained in the beginning, rationality is not about the outcomes but rather the expected outcomes.

Bottom Line People might make an economically rational decision to play the lottery, because their lack of information and disproportionate weight of the choice cripple their (unconscious) economic calculation. This does not mean you should go out and buy a lottery ticket, just that people who are playing might not be as stupid as they are often made out to be.

* Please comment on these posts from my microeconomics students, to help them with unclear analysis, other perspectives, data sources, etc.

1. David writes that it may be economically rational to buy a lottery ticket based on a couple of factors. However, it seems not economically rational to enter into a transaction not knowing the probability of the outcomes. So I don’t think he can call it economically rational, and at the same time say that people would likely choose not to buy lottery tickets if they realised the actual odds for and against winning. It’s rational if they know and still buy.

Second, placing “disproportionately high weight” on low probability risks is acting emotionally, rather than rationally. Rational behaviour places weight according to risk/probability.

Personally, I think that the rational reason for buying lottery tickets is the ability to sit on the tram and validly day dream about what you would do if you won the millions. I think people buy a warm, enjoyable feeling, and that is often the main payoff, for which they rationally buy (low cost) lottery tickets.

Actually winning is probably fairly accurately discounted by most people so they are also acting rationally in accepting the relatively poor odds:payoff ratio of most lotteries (how else do they pay for all those TV ads and other marketing).

2. Hey David! Considering the fact that yesterday afternoon I bought my first ever lottery ticket, I must say reading your first sentence wasn't necessarily a confidence boost :-) Pride aside however, I find it quite admirable that you're trying to find another explanation for such 'economically illogical' behavior than mere irrationality.

Though I think NM's comment on your article that it isn't 'economically rational to enter into a transaction not knowing the probability of the outcomes,' has some truth in it, I don't fully agree with his critique. Many games and situations with a chance to earn something have been made so bureaucratic and complicated that finding all information necessary to make a perfect decision requires time, effort, and infinite love for computer screens. Last December I spent half an hour looking up probability tables (they exist, online!) for the Dutch 'End Of the Year'-Lottery to mock my mother, who was planning on buying a lottery ticket, with her naivety. If I'd spent this half an hour washing my neighbor's cars, I could have made 7 euros - enough for two tickets!

As you state, 'people can never know how happy or unhappy they are going to be after something has happened, so they have to make an estimate of what the pay-off is going to be.' So, sadly, by trying to be super rational and estimating all odds that dark December evening, I actually missed a chance of acquiring much pleasure. Perhaps that's why I decided yesterday that I'd like to feel like a real and fully alive risk-taker for once - and maybe that short moment was worth 3,50 euros independent of the results :-)

3. Very interesting thoughts. I've been playing the online lottery ( Icelotto review) for several years already. It was for fun for me. As I see there is much more behind it. The thrill of expectation of huge winning is the most potent driving force for most of the players. Surely investing in lottery would be a bad idea but buying a ticket or two won't be harmful.

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