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naraburns  nihil supernum  1yr ago (text post)   Edited 1yr ago   34391 thread views

Culture War Roundup for the week of November 14, 2022

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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.

COWEN: Should a Benthamite be risk-neutral with regard to social welfare?

BANKMAN-FRIED: Yes, that I feel very strongly about.

COWEN: Okay, but let’s say there’s a game: 51 percent, you double the Earth out somewhere else; 49 percent, it all disappears. Would you play that game? And would you keep on playing that, double or nothing?

BANKMAN-FRIED: With one caveat. Let me give the caveat first, just to be a party pooper, which is, I’m assuming these are noninteracting universes. Is that right? Because to the extent they’re in the same universe, then maybe duplicating doesn’t actually double the value because maybe they would have colonized the other one anyway, eventually.

COWEN: But holding all that constant, you’re actually getting two Earths, but you’re risking a 49 percent chance of it all disappearing.

BANKMAN-FRIED: Again, I feel compelled to say caveats here, like, “How do you really know that’s what’s happening?” Blah, blah, blah, whatever. But that aside, take the pure hypothetical.

COWEN: Then you keep on playing the game. So, what’s the chance we’re left with anything? Don’t I just St. Petersburg paradox you into nonexistence?

BANKMAN-FRIED: Well, not necessarily. Maybe you St. Petersburg paradox into an enormously valuable existence. That’s the other option.

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.

COWEN: Are there implications of Benthamite utilitarianism where you yourself feel like that can’t be right; you’re not willing to accept them? What are those limits, if any?

BANKMAN-FRIED: I’m not going to quite give you a limit because my answer is somewhere between “I don’t believe them” and “if I did, I would want to have a long, hard look at myself.”...

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.

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.

Correction: the probability that SBF will destroy the world under these circumstances is 0.49 + 0.51*0.49 + 0.51^2 * 0.49 + 0.51^3 * 0.49 + ... + 0.51^(n-1) * 0.49, where n is however many times he plays that game. That's cumulative probability of the geometric distribution.

(Whereas 0.49^n goes to 0 as n goes to infinity.)

Or 1-0.51^n

Yeah I stand corrected, wrote this early in the morning.

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