I'm not sure there's a way to frame it as maximization of some value. Here's basically the axiom of the decision theory: if strategy A results in higher wealth than strategy B with probability 1 (en.wikipedia.org/wiki/Almost_su), then I prefer strategy A to strategy B.
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It turns out that under certain assumptions (most unrealistically: infinite time), having the above heuristic means that at each step, I need to maximize the rate of growth of my wealth.
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But that log appears in the OUTPUT of the theory, not as an input assumption (the way it does in Bernoulli's theory of log utility of wealth).
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Yes - even if you aren't *deliberately* trying to maximize the expectation of anything, it may be possible to construct a random variable X whose EV you are equivalently but *inadvertently* maximizing
(I think may be doing this fairly explicitly now)
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And it may be reasonable to call this random variable X your 'utility'
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I think "utility" has misleading connotations because historically it has been used to refer to subjective preferences and circumstances (like what I would be able to spend that wealth on)
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sure, thus why I tried renaming it 'qwer'
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As long as we agree that the "quer" value is an instrumental value and that my real goal is almost-surely-beating-any-other-strategy (and maximizing EV(qwer) is my tactic to get there), I think we're in agreement
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ah ok, yeah so we're not on the same page then:
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Replying to @danrobinson and @elliot_olds
(I agree with @GaussianProcess)
There are 2 different threads here.
A) how risk seeking should you be?
B) should there exist some function F that you're trying to maximize the EV of?
on (A) I disagree with you but don't think it's obvious, and isn't the primary thing here.