[QUOTE=Garula]
It is certainly possible to construct a hypothetical scenario in which buying a lottery ticket is reasonable. Your financial situation could be such that you consider $1 for a ticket utterly inconsequential, but that the potential payout would be life changing. So the minuscule chance of winning would be greater than the $1. In reality, this virtually never applies since even though $1 is pretty small, is not actually as inconsequential as the chance of winning.
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That’s only true if you assume that each person’s utility function is flat or decreasing and you don’t assign any value to variance itself. And I’m not talking about the daydreaming, either. This is true even if you discover the results immediately (like with scratch-off tickets).
Consider two hypothetical lotteries that have mathematically equal odds, ie, your expected value from playing is 0. Each costs $1 to play, and one of them pays $2 1/2 the time, and the other pays $1 million 1/millionth of the time. Many more people would play the second lottery than the first because the utility of $1 million is more than 1 million times $1, so a smaller chance of a big payout is actually worth more than a bigger chance at a small payout. The difference between extreme outcomes is actually worth something to the player. When the payout is just right, it’s worth considerably bad odds, as the many people playing the lottery obviously demonstrate.
The usual claim is that one’s marginal utility is constantly decreasing, ie, that the first $x is worth more than the second $x, but I don’t think that’s true in general. I think that the utility curve decreases for a while, but then increases sharply in the “fuck you” money range, and then decreases again thereafter.
If I win $1million+ in the lottery, it changes my whole life. I no longer have to work at a particular job (I probably can’t just couch-surf forever, but I can take any path that strikes my fancy) If I win $10, $100, or $10,000, I get to see a movie, have a nice dinner out, or buy a fancier car, respectively. All great things, but they pale in comparison to the big score.
A while ago, there was a thread where people discussed the amount of money that they’d accept for a 1/n chance of killing themselves. Regardless of how large n was, very few people were willing to take the bet for $10 or $10000. But when it got to the $1 million+ range, people were willing to take some kind of risk. It was only a small risk, of course, since the potential downside is so great. But this does demonstrate that the marginal utility of money increases sharply at a certain point for most people.