# Is there an economic analysis of the rationality of buying lottery tickets?

It's quite clear that the expected return on a lottery ticket is less than 1.

However, I think it can still be argued that buying lottery tickets is still a economically rational decision by consumers.

There are a few lines of reasoning:

• The consumer isn't just buying an expected payout, they're buying 'a dream'. Much like watching a fantasy movie or reading a book is an economically rational decision, (even though the story isn't 'real'), the thoughts of 'what would I do if I won the lottery' is a commodity that the consumer is buying.
• The value of a lottery payout is worth more than its face value. When analysing the expected return on an ordinary decision, we assume that the return is given in the same context. (For example when Bob is choosing between Stock A, Stock B or saving his money in the bank, regardless of which payout he gets, the rest of his circumstances stay the same). Winning the lottery means, for most us, that we'd quit our jobs, which is worth more than just the payout itself.
• It also needs to be considered that the cost of the lotto ticket is often mitigated by that it can also be partially considered as charity.

The question is - is this subject well considered in economics?

Perhaps a good answer would iterate the economic reasoning of buying lottery tickets.

NB. I'm planning asking a separate follow up question regarding point two, question at what lottery payout the expected return increases.

• This is not a problem, if the person buying lottery are risk loving. The real problem is that Von Neumann-Morgenstein expected utility fails to rationalize behavior of buying insurance and lottery at the same time. This problem dissipates when taking ambiguity aversion into account. Apr 8 '15 at 2:07
• I've heard playing the lottery described as a "inverse insurance". If nothing happens and you don't use the insurance, the money is lost. But if something happens and you do use the insurance, the returns are much higher than your investment. Much like a lottery. Apr 9 '15 at 21:29

There are definitely economic justifications for playing the lottery, even if all (I hope) players understand that it is unlikely to pay off.

One such justification is that what you actually buy when purchasing a lottery ticket is the fantasy of winning.

Here are a few sources. Lotterys are relatively well understood in economics.

• The Economics of Lotteries: A Survey of the Literature(pdf) - is an excellent article covering basically your entire question. It discusses the microeconomic forces at play, particularly income elasticity and risk aversion.

• This source (note: this is now a dead link) has some excellent lecture notes on the market for risk. I recommend it highly. Some basic points are:

• people don't want actuarialy fair games, often they would decline a coin flip with a payoff of \$1mil for a win and a cost of \$1m for a loss. Also, an actuarialy favourable game isn't necessarily desirable. If the payoff was \$1.1m people would still decline the game as the cost is just so high. In that sense, a lottery has an advantage. The payoff can be huge but the cost in the event of losing is almost negligible. • Lastly, this source is an article from the NY times. Definitely relevant, highlighting similar points to the first two articles but is a lot more accessible. • Nice references. Jun 4 '15 at 9:24 I want to add some other justifications for buying lottery tickets: • general risk-seeking behavior (which is probably pretty rare) • risk-seeking when it comes to low monetary values (Cumulative prospect theory) • Cognitive biases, e.g., • with respect to probabilities (over-weighting low probabilities, Knightian unicertainty) • the money (under-weighting small amounts) • Gambler's fallacy (I've lost so often, I have to win now) • focusing effect (John has won \$ 10 000 in the lottery last year and Jane \$1000 this year) • Jumps in the utility function (e.g., I am on a fair, have only \$ 2 on me, but I really want to buy this cotton candy for \\$ 3), (probably also rare)
• additional (non-monetary) benefit through lotteries (e.g., doing something good (charity) or likes the "thrill" of gambling) (in my opinion the most important reason)

Your mentioned reasons fit very well into the additional benefit category (buying a dream or "cost of the lotto ticket is mitigated") or into the the jumps in the utility function (quitting the job).

• Should "over-weighting high probabilities" read "over-weighting very low probabilities" by any chance? And ISTM that you don't need jumps in the utility function: it just needs to be convex rather than linear in part. Jun 4 '15 at 8:23
• @EnergyNumbers Thanks! Of course it has to be low probabilities. And you don't need jumps, but jumps work (and the example is easier to explain). I think the reason why we avoid jumps is only to make things tractable or easier not because we think they are not there. Jun 4 '15 at 9:04

You might find a very old paper interesting:

Milton Friedman and Leonard Savage, "Utility Analysis of Choices Involving Risk", Journal of Political Economy 1948, pages 279–304.

This famous paper asked how the fact that the same individuals buy lottery tickets, and buy insurance, could be reconciled with the economic theory of expected utility maximization.

Nothing in this paper is related to the political views for which Milton Friedman later became well-known.