Monday, January 28, 2008

Why buying a lottery ticket may be rational

Economists often puzzle about why people, in particular poor people, buy so many lottery tickets. Think about it, we generally consider that people are averse to risk, and lotteries certainly do not reward risk, as a substantial part revenues are essentially taxed away. So why do people buy lottery tickets?

John Laitner argues that this is because of the means tests poor people face: buying a lottery ticket will not make them any poorer as they will still stay eligible for social assistance. If they win, however, they can escape poverty for good. Thus, they win in expected terms. In a sense it is about the dream of escaping poverty, and it is close to free.

John Morgan argues that lotteries, as long as they help in providing a public good, can replace efficiently taxation. Lotteries work better that voluntary contributions. John Morgan and Martin Sefton confirm this in a laboratory environment. Rob Moir, also in experiments, shows that this reasoning may collapse if there other public goods to be financed.

Bruyneel, Dewitte, Franses and Dekimpe try to show that people play lottery more when depressed, say, because of reduced sunlight. Thus lottery is fun, especially when life is not fun.

But I do not think economists can be convinced of buying lottery tickets yet...


Vilfredo said...

I buy lottery tickets because my wife tells me to, not because I want to. Does this count as rational?

Acad Ronin said...

One intersting way to gamble is via lottery-linked deposit accounts. These are savings accounts (in banks) that carry a stochastic interest rate. That is, each week or month, the bank offering the account holds a drawing and awards large prizes to a small number of account holders, though most account holders get nothing. (Principal is safe; the foregone fixed interest is the de facto price of the lottery ticket.) These accounts have proved to be quite popular, especially in poor countries, where they have mobilized savings that people would otherwise hold under their mattresses.

BreadBox said...

The "Premium bonds" in the UK are (or at least used to be) an example of acad_ronin's method of gambling. An interesting method because they are government run, and are being used to entice people to save in government bonds.

As for lotteries, I have long thought that if I could tell my bank to buy me a lottery ticket every week, with some sort of pre-arranged manner to determine the randomly selected numbers, I would happily do so: I would forgo the addiction to gambling, wouldn't miss a dollar or so a week at all: and if I won, it would be life changing.

I have long believed that one of the problems of economics is the non-linearity of value of money. We don't perceive ten million dollars to be worth ten million times the worth of a dollar, because to do so we would have to be able to perceive ratios like ten million to one: and this is something the average individual has *no* conception of.


Bruce Webb said...

Those economists have never been poor.

When I was a typically cash strapped graduate student or in the first couple of years working when I was stuck in an entry level wage I would pick up the occasional lottery ticket. Not as a realistic ticket out of poverty but simply because for a buck you could buy three days and nights of dreams. As I lay in bed at night I would plan for what I would do should lightning strike. Good bye student loans, hello three months in Wales and Ireland. I got hours of entertainment for that buck.

On the other hand people think nothing of dropping $150 a ticket to watch a 60's has been rock group or that same amount to attend the symphony for a couple of hours. On a entertainment hour per dollar basis adjusted for income small amounts of lotto tickets do become economically rational.

The problem of course comes with the 'If one ticket is good, ten tickets must be ten times better'. Well no because it doesn't actually purchase you more entertainment hour, you get less of the only rational product you are buying per dollar spent.

But lets not confuse innumeracy with irrationality. The rational calculations for things like smoking do not break down on simple economic principles.