bogdanb comments on On dollars, utility, and crack cocaine - Less Wrong

13 Post author: PhilGoetz 04 April 2009 12:00AM

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Comment author: Eliezer_Yudkowsky 04 April 2009 03:58:23AM 11 points [-]

1) Lottery tickets are bought using income that is after tax, after debt, and after loss of government benefits.

2) Many people buy more than one lottery ticket; they spend hundreds of dollars per year or more.

3) There was a period during which poor folks had reason to legitimately distrust banks and played the illegal numbers game as a sort of stochastic savings mechanism, up to 600-to-1 payouts on 1000-to-1 odds, which meant they did get large units of cash occasionally. Post-FDIC this is no longer a realistic motive and the odds on the government lotteries are worse.

4) Yes, your life can suck, yes, the lottery can seem like the only way out. But this is not a reasoned decision based on having literally no better life-improving use for hundreds of after-tax dollars. It is based on the lure and temptation of easy money to a mind that can't multiply.

5) Those who buy tickets will not win the lottery. If you think the chance is worth talking about, you've fallen prey to the fallacy yourself. In ordinary conversation odds of one in a hundred million of being wrong would correspond to a Godlike level of calibrated confidence. Therefore I say simply, "You WILL NOT win the lottery!" with far more confidence than I say that the Sun will rise tomorrow (since something could always... happen... overnight). On a statistical basis, before selective reporting, lottery winners are nonexistent - you would never encounter one if you lived in the ancestral environment and had no newspapers. The lottery is simply a lie.

Comment author: bogdanb 04 April 2009 01:13:58PM 3 points [-]

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.