Thank you. Actually, my point was this: there is value to a gamble that isn't measured by the expected value. The expected value argues that playing the lottery isn't going to make them rich. But keeping the dollar isn't going to make them rich either. At least spending their dollar playing the lottery gives them the chance of being rich.
When I made this argument I was actually thinking of impossible gambles that are made on the scale of evolution, say. For every million that make a gamble and fail, (for example, to escape an island), eventually one wins and validates the gambles of all (survives the journey and populates the continent).
I was reluctant to provide this example because I definitely don't want to imply that it's an evolutionary advantage or a justified sacrifice for the good of the group. (yuck) Perhaps an analogy from economics will balance -- you can demand more for an opportunity that can't be purchased any other way.
There is at least one parallel in evolution. Many bacteria have heat shock proteins that inhibit DNA proofreading. That means that they respond to stress by increasing their mutation rate. It will probably kill them, but if the entire colony does it, it's more likely to survive.
It's not quite the same. If you count the payoff to the bacteria to include the lives of all its descendants, then it may still be "rational".
But maybe it is the same. Presumably, we instinctively act in a way that counts the utility of all our descendants in our utility functions.
The lottery came up in a recent comment, with the claim that the expected return is negative - and the implicit conclusion that it's irrational to play the lottery. So I will explain why this is not the case.
It's convenient to reason using units of equivalent value. Dollars, for instance. A utility function u(U) maps some bag of goods U (which might be dollars) into a value or ranking. In general, u(kn) / u(n) < k. This is because a utility function is (typically) defined in terms of marginal utility. The marginal utility to you of your first dollar is much greater than the marginal utility to you of your 1,000,000th dollar. It increases the possible actions available to you much more than your 1,000,000th dollar does.
Utility functions are sigmoidal. A serviceable utility function over one dimension might be u(U) = k * ([1 / (1 + e-U)] - .5). It's steep around U=0, and shallow for U >> 0 and U << 0.
Sounds like I'm making a dry, academic mathematical point, doesn't it? But it's not academic. It's crucial. Because neglecting this point leads us to make elementary errors such as asserting that it isn't rational to play the lottery or become addicted to crack cocaine.
For someone with $ << 0, the marginal utility of $5 to them is minimal. They're probably never going to get out of debt; someone has a lien on their income and it's going to be taken from them anyway; and if they're $5 richer it might mean they'll lose $4 in government benefits. It can be perfectly reasonable, in terms of expected utility, for them to play the lottery.
Not in terms of expected dollars. Dollars are the input to the utility function.
Rationally, you might expect that u(U) = 0 for all U < 0. Because you can always kill yourself. Once your life is so bad that you'd like to kill yourself, it could make perfect sense to play the lottery, if you thought that winning it would help. Or to take crack cocaine, if it gives you a few short intervals over the next year that are worth living.
Why is this important?
Because we look at poor folks playing the lottery, and taking crack cocaine, and we laugh at them and say, Those fools don't deserve our help if they're going to make such stupid decisions.
When in reality, some of them may be making <EDITED> much more rational decisions than we think. </EDITED>
If that doesn't give you a chill, you don't understand.
(I changed the penultimate line in response to numerous comments indicating that the commenters reserve the word "rational" for the unobtainable goal of perfect utility maximization. I note that such a definition defines itself into being irrational, since it is almost certainly not the best possible definition.)