The Lottery is Some Kind of Tax

Richard Posner reconsiders, as a part of a larger conversation, whether the lottery is really a "Tax on Stupidity":
As for the "tax on stupidity," it is of course irresistible to finance as much
as government as possible by a system of voluntary taxation, which is what a
state lottery is. And I don’t think "stupid" is the right word to describe all
or even most of the people who buy lottery tickets. I do think that some of them
consider themselves "lucky" and so in effect recalculate the odds in their
favor. That is stupid; in a game of chance, "luck" is randomly distributed. Some
people, though, simply enjoy risk. Others like to daydream, and a daydream is
more realistic if there is some chance it may come true, even if a very small
chance. And finally and most interestingly, there are people whose marginal
utility of income is U-shaped rather than everywhere declining. Usually we think
of it as declining: my second million dollars confers less utility on me than my
first million, and that is why I would not pay a million dollars for a lottery
ticket that gave me a 50.1 percent or probably even an 80 percent probability of
winning $2 million. But maybe I lead a rather drab life, and this might make
such a gamble rational even if it were not actuarially fair. Suppose that for a
$2 lottery ticket I obtain a one in a million chance of winning $1 million. It
is not a fair gamble because the expected value of $1 million discounted by
.000001 is $1, not $2. But if having $1 million would transform my life, the
expected utility of the gamble may exceed $2, and then it is rationally
I've heard it called a "Stupid Tax" or a "Tax on Those Who Are Bad at Math," before, and I've generally agreed with those characterizations, but I like Posner's framing it as a "system of voluntary taxation." Of course, no one buys a lotto ticket out of altruism -- perhaps it is better called a "system of unintended-yet-voluntary taxation." But it is voluntary, and you do know where it's going. I suppose if we extrapolate on that, Las Vegas is a forum for unintended-yet-voluntary charity. Sounds nice (kind of).

But Posner's later point indicates that, as far as subjective personal experiences go, buying a lottery ticket may be downright rational. If your life sucks and you know that, given your skills and position in life, it is very unlikely that you will ever accumulate the kind of wealth the lotto offers, the cost of the ticket in exchange for the chance is a very good deal, especially when that dollar wouldn't have gotten you all that far in savings anyway. Perhaps it should be called a "Tax on Despair."