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.
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.” But I will give you something a little weaker than that, which is an area where I think things get really wacky and weird and hard to think about, and it’s not clear what the right framework is, which is infinity.
All this math works really nicely as long as all the numbers are finite. As soon as you say, “What are the odds that there’s a way to be infinitely happy? What if infinite utility is a possibility?” You can figure out what that would do to expected values. Now, all of a sudden, we’re comparing hierarchies of infinity. Linearity breaks down a little bit here. Adding two things together doesn’t work so well. A lot of really nasty things happen when you go to infinite numbers from an expected-value point of view.
There are some people who have thought about this. To my knowledge, no one has thought about this and come away feeling good about where they ended. People generally think about this and come away feeling more confused.
This case (with our own universe, not a new one) appears in a Tyler Cowen interview of Sam Bankman-Fried: