Yep, I'm with Dan here.
One way to view the question:
EV measures what happens when you make a ton of bets in parallel.
EV of log measures what happens when you compound a bunch of bets over time.
The reason is that multiplying <-> adding logs, so law of large numbers works
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Another way to look at it: maximizing EV(wealth) at the expense of log wealth results in the long run in some EXTREMELY HAPPY people in some possible worlds—but you are vanishingly unlikely to get to live in such a world.
It’s like utility monsters in ethics. Probability monster
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I actually agree with all of that. Here, by definition, you're asking "what maximizes EV[wealth]?"
In the world is (I think) referring to, I can always construct an LP with less than or equal linear loss than the zero-fee LP.
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Maybe the discontinuity at that fee introduces the confusion? At (not approaching) a zero fee, it can be proven trivially.
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Agreed, at zero fee you always do worse being an LP, and that discontinuity is key.
The only thing I'd add regards your previous tweet: we're not really asking about EV[Wealth], because EV actually doesn't tell us what will happen over time (!!) See ergodicityeconomics.com/lecture-notes/
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Yes, totally agree.
That said, EV[wealth] is still a well-defined objective function. And you can prove that the smallest fee that maximizes the objective is exactly enough to preclude rebalancing.
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My point here is that having a utility function that is linear in wealth does not mean that your utility function is linear in EV(wealth)
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yes it very much does imply that; that's how math works
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I think you think I'm objecting to the first step (EV[wealth]-maximizing -> EV[utility]-maximizing when utility linear in wealth) when actually I'm objecting to the latter step (EV[utility]-maximizing -> utility-maximizing)
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It is a tautology that I prefer having greater utility to having less.
It is NOT a tautology that I prefer a strategy with higher EV(utility) to one with lower
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ok so what do you mean by "utility" here?
I guess, if we want, we can sidestep this and blacklist the world 'utility'.
I'm going to define 'qwer' to be "the thing that I'm trying to maximize the EV of".
if qwer is linear in wealth then the paper doesn't apply.
I claim that, as an EA, qwer is in fact fairly linear in wealth if wealth << $20b.
Thus I claim that this paper doesn't apply to EAs worth much less than $20b.
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My point is that you're not trying to maximize EV of qwer at all.
You are trying to maximize qwer.
And whatever qwer is, maximizing expected growth in qwer means that you will ALMOST SURELY maximize qwer itself in the long run
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