About point 5: I’ve encountered this idea quite often. And I agree, but only if “win the lottery” means winning the big prize.
I’ve never seen the consideration* that, in addition to the one (or, statistically, fewer than one) “jackpot”, there are in most lotteries relatively large numbers of consolation prizes.
(*: this doesn’t mean that it’s absent; it may be included in the general calculations, but I’ve never seen the point being made explicit.)
In terms of expected dollars this part doesn’t change much (it’s still sub-unitary, since lotteries don’t generally go bankrupt), but in terms of expected utility as discussed in the post, and in particular with respects with your fifth point, it seems very significant. On the monetary side, even payoffs of a few hundred dollars may have highly “distorted” utilities for some persons. And on the epistemological side, probabilities of one in a few thousand (even more for lower payoffs) are much more relevant than one in a hundred million.
That doesn’t mean that lottery players actually do the math—or base their decisions on more than intuition—but at such relatively lower levels of uncertainty it’s not as obvious that the concept is completely invalid. Also, I expect there would be many takers for any winner-takes-all lottery, too, but I’d be surprised if the number wasn’t significantly lower, all else being equal.
About point 5: I’ve encountered this idea quite often. And I agree, but only if “win the lottery” means winning the big prize.
I’ve never seen the consideration* that, in addition to the one (or, statistically, fewer than one) “jackpot”, there are in most lotteries relatively large numbers of consolation prizes.
(*: this doesn’t mean that it’s absent; it may be included in the general calculations, but I’ve never seen the point being made explicit.)
In terms of expected dollars this part doesn’t change much (it’s still sub-unitary, since lotteries don’t generally go bankrupt), but in terms of expected utility as discussed in the post, and in particular with respects with your fifth point, it seems very significant. On the monetary side, even payoffs of a few hundred dollars may have highly “distorted” utilities for some persons. And on the epistemological side, probabilities of one in a few thousand (even more for lower payoffs) are much more relevant than one in a hundred million.
That doesn’t mean that lottery players actually do the math—or base their decisions on more than intuition—but at such relatively lower levels of uncertainty it’s not as obvious that the concept is completely invalid. Also, I expect there would be many takers for any winner-takes-all lottery, too, but I’d be surprised if the number wasn’t significantly lower, all else being equal.