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.
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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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dude I literally tried to define a made up word because you kept bending words to mean nonstandard things and you responded by disagreeing with the definition of a word I just made up?
also:
almost surely is not the only thing that matters!
outliers matter.
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I'm not disagreeing with the definition of the word qwer! I am disagreeing that you are trying to maximize the EV of anything.
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Like, fine, to be pedantic:
a) if only one sequence will end up happening, there are no interaction effects between them
b) So you have a set of possible outcomes and probabilities o_i and p_i
c) because of (a), U = sum_i[p_i*f(o_i)] for some function f
d) (cont'd)
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f here is whatever wacky nonlinear function you want.
d) define qwer == f(o_i)
e) you are trying to maximize the EV of qwer
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I think we diverge at (c) in the prior tweet, or (e) here.
This is in some senses an ideological disagreement, not a mathematical one.
You're saying, "hey, I don't know what outcome I'm going to see, so what I'm going to do is weight each by their probability and sum."
(ctd.)
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On the other hand, we're saying, "hey, I don't know what outcome I'm going to see, so what I'm going to do is pick a strategy that will lead to better outcomes for me with probability 1."
You're absolutely correct that we miss out on some extremely good outcomes this way.
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When I was first learning about this, the frustrating part was that I got taught starting in Econ 101 and then as a professional trader that EV is *the* thing that matters.
But! It's just a particular number. I now believe maximizing another number fits my preferences better.
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really glad that you're phrasing this clearly!
FWIW I think that the paper fails pretty badly to make this prominent. It's a key assumption underpinning it.
I do object a bit to "probability 1". That is not a meaningful statement in practice, rather it's "high probability".
It’s probability = 1. en.m.wikipedia.org/wiki/Almost_su
The arguable bit here isn’t that—it’s the infinite time assumption
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yes -- if time goes on infinitely!
which is not going to happen in the actual practical cases people without infinite lives face.
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Hey, clarity is what we aim for😉
This is definitely one of those things that is so weird it's very hard to signpost enough.
I did try several times, most especially in 2.3 (and to provide resources in 2.5) but it's clear I could have hit it harder.
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You're also right about probability 1, it's only probability 1 *in the limit as time goes to infinity,* which of course by definition never happens.
In the explainer, I say "almost surely as time goes on," but you're right that there's some detail elided there.
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Furthermore, this is just one rabbit hole which doesn't address my other objections (which are that the assumptions in the paper missed a ton of key points and make no sense in practice, with this just being one example)
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Thank goodness, I was worried we wouldn't have anything to talk about on the podcast.
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