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I think you're ignoring the fact that utility is non-linear with money. If you're kind of poor (not starving though), it makes sense to play the lottery. $10 a

I think you're ignoring the fact that utility is non-linear with money. If you're kind of poor (not starving though), it makes sense to play the lottery. $10 a month isn't going to cause you to starve, but there is a possibility you'll get a decent chunk of money (not jackpot perhaps, but enough to substantially improve your standing say). Whereas for someone who is well off, getting a few thousand dollars isn't such a big deal.

ZeroGravitas 17y ago
I think most people think the non-linear aspects of money work the other way round e.g. progressive taxes take more from the rich because they will miss it less. "Investing" small amounts to achieve a big pay-off also hits the problem that large windfalls aren't psychologically or socially very beneficial.
gjm11 17y ago
Ow ow ow. No. The usual reason for disagreeing with what you just said is that for most people the utility gain from (say) a 1/6000 probability of getting $3000 is less, not more, than the utility loss of certainly spending $1, and it only seems otherwise because we tend to round small utility differences to 0 mentally. I think this is correct. But here's another reason why you're wrong. First of all, let me correct something in the previous paragraph. Of course hardly anyone plays the lottery just once, so let's consider playing 10 times per month in a lottery whose tickets cost $1 and whose only prize is $3000, with probability 1/6000. (Oversimplification, of course; I'm going with basically the figures you mentioned, and a fairly typical 50% take for the people running the lottery). So, if you do that for a year then roughly speaking you are paying $120 for a 1/50 chance of getting $3000. So, suppose there's some person for whom the utilities really do work out the way you describe: getting $3000 with probability 1/50 is worth more than $120. And suppose that person could instead invest their money somewhere reasonably safe and get a return of 1% per annum over (inflation plus their temporal discount rate). For simplicity of exposition, I shall ignore inflation and discounting in what follows, so that's just an annual return of 1%. Then instead of spending $120 on the lottery over a year, they could invest ~ $119.40 over the same period, at the end of which they will have $120 which they can put into the lottery. Same result, less money spent. So. Unless your temporal discount rate is higher than the best rate of interest over inflation that you can get, playing the lottery now cannot be your best option -- at least, not if your motivation is that you think the utility gain from having more money when you win is worth the utility loss from having less money because you spent it. In less-crappy economic times than we've had recently, you can typically get a rate of return that's quite a bit better than inflation. In which case, unless your discount rate is really high, you should not play the lottery with the intention of increasing your net utility. (Of course, if your discount rate is really high, it follows that you should never save anything: anything you would save you should spend immediately on things that give you immediate pleasure, or put into the lottery at once.)
- shrikant 17y ago
  So, decide on basis of expectation calculations as opposed to mere probabilities?
  - gjm11 17y ago
    I certainly think working in terms of expected utility is sensible. But the person I was replying to didn't argue in terms of expectations, and it's not obviously mandatory to think in those terms. (For instance, you might assign more or less importance to very low-probability events than expected utility maximization would suggest. If you do that, then in the very very long run you lose; but none of us is likely to live that long, and I don't think it's clear that "if you live for a million years and consistently do X, then you can be Dutch-booked" is much of an argument against doing X.) So I didn't put my argument in terms of expectations, and I don't think it depends on using expectations.
- sunkencity 17y ago
  The logic is binary, either you have a possibility to win something (at all), or you are a complete loser. If you're poor, buy one lottery ticket where the draw is as far into the future as possible, or a scratch lottery ticket and don't scratch it until it's about to expire. As long as it is not decided, you are potentially a winner.
- randallsquared 17y ago
  Then instead of spending $120 on the lottery over a year, they could invest ~ $119.40 over the same period, at the end of which they will have $120 which they can put into the lottery. Same result, less money spent. Except that they lack the utility of playing the lottery for an entire year, which is already worth more than $120 to them, as we can see from the fact that they play the lottery in the first place. :)
  - gjm11 17y ago
    I happily concede that if you really enjoy playing the lottery then it can be eminently rational to do it. The person I was replying to wasn't making that argument, but a completely different one: that the utility from the potential winnings outweigh the costs for some poorer people. I think that's monstrously implausible.
kingkongrevenge 17y ago
Many working poor have an effectively zero probability of dramatically improving their financial situation. The odds of winning the lottery are higher than zero. Therefore, there is a sort of rationality to playing if you have correctly self assessed that you're stuck in near poverty. That said, it's deplorable government is running these programs. Only 40 years ago this was the illegal domain of mobsters and sleazeballs. Now the state has muscled in on the action is legitimizing the moral message that you can get something for nothing.

ZeroGravitas 17y ago

I think most people think the non-linear aspects of money work the other way round e.g. progressive taxes take more from the rich because they will miss it less. "Investing" small amounts to achieve a big pay-off also hits the problem that large windfalls aren't psychologically or socially very beneficial.

gjm11 17y ago

Ow ow ow. No. The usual reason for disagreeing with what you just said is that for most people the utility gain from (say) a 1/6000 probability of getting $3000 is less, not more, than the utility loss of certainly spending $1, and it only seems otherwise because we tend to round small utility differences to 0 mentally. I think this is correct. But here's another reason why you're wrong. First of all, let me correct something in the previous paragraph. Of course hardly anyone plays the lottery just once, so let's consider playing 10 times per month in a lottery whose tickets cost $1 and whose only prize is $3000, with probability 1/6000. (Oversimplification, of course; I'm going with basically the figures you mentioned, and a fairly typical 50% take for the people running the lottery). So, if you do that for a year then roughly speaking you are paying $120 for a 1/50 chance of getting $3000. So, suppose there's some person for whom the utilities really do work out the way you describe: getting $3000 with probability 1/50 is worth more than $120. And suppose that person could instead invest their money somewhere reasonably safe and get a return of 1% per annum over (inflation plus their temporal discount rate). For simplicity of exposition, I shall ignore inflation and discounting in what follows, so that's just an annual return of 1%. Then instead of spending $120 on the lottery over a year, they could invest ~ $119.40 over the same period, at the end of which they will have $120 which they can put into the lottery. Same result, less money spent. So. Unless your temporal discount rate is higher than the best rate of interest over inflation that you can get, playing the lottery now cannot be your best option -- at least, not if your motivation is that you think the utility gain from having more money when you win is worth the utility loss from having less money because you spent it. In less-crappy economic times than we've had recently, you can typically get a rate of return that's quite a bit better than inflation. In which case, unless your discount rate is really high, you should not play the lottery with the intention of increasing your net utility. (Of course, if your discount rate is really high, it follows that you should never save anything: anything you would save you should spend immediately on things that give you immediate pleasure, or put into the lottery at once.)

shrikant 17y ago
So, decide on basis of expectation calculations as opposed to mere probabilities?
- gjm11 17y ago
  I certainly think working in terms of expected utility is sensible. But the person I was replying to didn't argue in terms of expectations, and it's not obviously mandatory to think in those terms. (For instance, you might assign more or less importance to very low-probability events than expected utility maximization would suggest. If you do that, then in the very very long run you lose; but none of us is likely to live that long, and I don't think it's clear that "if you live for a million years and consistently do X, then you can be Dutch-booked" is much of an argument against doing X.) So I didn't put my argument in terms of expectations, and I don't think it depends on using expectations.
sunkencity 17y ago
The logic is binary, either you have a possibility to win something (at all), or you are a complete loser. If you're poor, buy one lottery ticket where the draw is as far into the future as possible, or a scratch lottery ticket and don't scratch it until it's about to expire. As long as it is not decided, you are potentially a winner.
randallsquared 17y ago
Then instead of spending $120 on the lottery over a year, they could invest ~ $119.40 over the same period, at the end of which they will have $120 which they can put into the lottery. Same result, less money spent. Except that they lack the utility of playing the lottery for an entire year, which is already worth more than $120 to them, as we can see from the fact that they play the lottery in the first place. :)
- gjm11 17y ago
  I happily concede that if you really enjoy playing the lottery then it can be eminently rational to do it. The person I was replying to wasn't making that argument, but a completely different one: that the utility from the potential winnings outweigh the costs for some poorer people. I think that's monstrously implausible.

kingkongrevenge 17y ago

Many working poor have an effectively zero probability of dramatically improving their financial situation. The odds of winning the lottery are higher than zero. Therefore, there is a sort of rationality to playing if you have correctly self assessed that you're stuck in near poverty. That said, it's deplorable government is running these programs. Only 40 years ago this was the illegal domain of mobsters and sleazeballs. Now the state has muscled in on the action is legitimizing the moral message that you can get something for nothing.