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warbo comments on What are your contrarian views? - Less Wrong
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At the risk of looking even more like an idiot: Buying one $1 lottery ticket earns you a tiny chance - 1 in 175,000,000 for the Powerball - of becoming absurdly wealthy. The Powerball gets as high as $590,500,000 pretax. NOT buying that one ticket gives you a chance of zero. So buying one ticket is "infinitely" better than buying no tickets. Buying more than one ticket, comparably, doesn't make a difference.
I like to play with the following scenario. A LessWrong reader buys a lottery ticket. They almost certainly don't win. They have one dollar less to donate to MIRI and because they're not wealthy they may not have enough wealth to psychologically justify donating anything to MIRI anyway. However, in at least one worldline, somewhere, they win a half a billion dollars and maybe donate $100,000,000 to MIRI. So from a global humanity perspective, buying that lottery ticket made the difference between getting FAI built and not getting it built. The one dollar spent on the ticket, in comparison, would have had a totally negligible impact.
I fully realize that the number of universes (or whatever) where the LessWrong reader wins the lottery is so small that they would be "better off" keeping their dollar according to basic economics, but the marginal utility of one extra dollar is basically zero.
edit: Digging myself in even deeper, let me attempt to simplify the argument.
You want to buy a Widget. The difference in net utility, to you, between owning a Widget and not owning a Widget is 3^3^3^3 utilons. Widgets cost $100,000,000. You have no realistic means of getting $100,000,000 through your own efforts because you are stuck in a corporate drone job and you have lots of bills and a family relying on you. So the only way you have of ever getting a Widget is by spending negligible amounts of money buying "bad" investments like lottery tickets. It is trivial to show that buying a lottery ticket is rational in this scenario: (Tiny chance) x (Absurdly, unquantifiably vast utility) > (Certain chance) x ($1).
Replace Widget with FAI and the argument may feel more plausible.
There are ways to win a lottery without buying a ticket. For example, someone may buy you a ticket as a present, without your knowledge, which then wins.
No, it is much more likely that you'll win the lottery by buying tickets than by not buying tickets (assuming it's unlikely to be gifted a ticket), but the cost of being gifted a ticket is zero, which makes not buying tickets an "infinitely" better return on investment.