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One curious thing I noticed about SBF on the Tyler Cowen podcast is that he had a very odd idea about the St. Petersburg Paradox. At the time, I found myself very much unable to steel man this.
I'll just interject here that to me, this sounds completely insane. For those less familiar with decision theory, this not an abstruse philosophical question - it's simply a mathematical fact with probability approaching 1 (specifically, 0.49^n for large n), SBF will destroy the world.
At the time I found this odd. Does SBF not understand Kelly betting? This twitter thread, unearthed from 2 years ago, suggests maybe he doesn't?
https://twitter.com/breakingthemark/status/1591114381508558849
I don't see how he, or Caroline, or the rest of his folks got to where they did without understanding kelly. Pretty sure you don't get to be a junior trader at Jane St. without understanding it.
My best attempt at a steelman is that because he's altruistic, the linear regime of his utility function goes a lot further than for Jeff Bezos or someone else with an expensive car collection. As in, imagine each individual has a sequence of things they can get with diminishing marginal utility - $u_0 > u_1 > ... > u_n > ...$, $u_n \rightarrow 0$ and each thing has unit cost. A greedy gambler has sublinear utility since they first buy u_0, then u_1, etc. By definition, $\sum_{i=0}^N u_i < N u_0$.
But since SBF is buying stuff for everyone, he gets $N u_0$.
Then again, this is still clearly wrong - eventually he runs out of people who don't have $u_0$, and he needs to start buying $u_1$. His utility is still diminishing.
Is there some esoteric branch of decision theory that I'm unfamiliar with - perhaps some strange many worlds interpretation - which suggests this isn't crazy? Is he just an innumerate fraud who truly believes in EA, but didn't understand the math?
I would love any insights the community can share.
I'm not sure how much his whole group were into LessWrong, specifically, during its height, but the St. Petersburg Paradox was a pretty significant area of focus. See here for an early reference (with most interesting discussion going under the lifespan paradox), or more recently this.
I expect that part of the confusion comes because the St Petersburg Paradox requires you to continue playing and is usually framed in limits to benefits, hence the preferred emphasis on the Lifespan Paradox in the LessWrong literature. And for the same reasons that limited rounds make the traditional St. Petersburg Paradox valueless even at fairly low stakes, limited rounds here are easier to come up with world-situations where the total expected value is high rather than provably zero. That's part of why it's a paradox! Making a 49-51 world-ending bet once, or even some countable number of times, is still bad -- as a non-philosophy question, the answer is "reserve" -- but it isn't as obviously bad as making it until you certainly lose.
That said, I don't know about the Kelly Bet side. Kelly isn't about utility or diminishing returns on money; it uses logarithms because it's trying to demonstrate geometric growth, not because of any philosophical or ideological statement about bounds of return (explicitly: that "The reason has nothing to do with the value function which he attached to his money"). But Kelly assumed infinite repetition, (indeed, referencing St Petersburg). If you aren't in that game, then :
BreakingTheMarket references this in this page that they linked to in their post. You can reject the arithmetic mean entirely -- BTM does, and I'll take it to the ends of refusing gambling -- but it's not clearly obvious and clearly losing.
It's just a stupid gamble. But you can get very far in business by making stupid gambles.
Do you know the definitive Lesswrong approach to robust decision theories? Specifically, how do they manage outliers and infinities, to ensure that in the majority of timelines the world ends up "good enough"? Or do they prefer expected value maximization that much.
I don't think there's a Definitive LessWrong Approach, though for Yudkowskian reasons there's been a lot of skepticism of any reasoning where rare high payoffs or costs aren't given some level of a harsh eye. On the flip side, a lot of early Pascal's Mugging discussion was in the context of cryonics, and I think had a bit of a thumb on the pro-unlikely-benefit side. Most of the big successes in recent Decision Theory work has focused on analysis and coordination in different scopes; I think the most common approach for infinities in the short term was simply to fight any probabilities at epsilon or near epsilon.
I think they want a generalizable and mathematic solution to the problem, but I don't know if it's been solved. Bostrom had some good attempts at a solution, but most of his solutions had distortionary effects or other problems.
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