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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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I am mostly a person who uses Kelly and not a theoretician, but the Kelly formula is definitely derived from the principle of maximizing $E[\ln(S)]$ with S=wealth. That has the obvious philosophical interpretation of diminishing marginal utility, unless I'm missing something/
I assume that what SBF is talking about is he instead maximizes $E[S]$ which is quite different.
I did find this which attempts to defend kelly from the perspective of volatility drag rather than diminishing utility: https://www.lesswrong.com/posts/zmpYKwqfMkWtywkKZ/kelly-isn-t-just-about-logarithmic-utility
Will need to read it more carefully.
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