PSA— According to expected-utility theory, utility values are:
ALWAYS affine as functions of probabilities, but
almost NEVER affine as functions of money
(except approximately, with caveats and assumptions that are usually wishful thinking on economists’ part)
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Even famous authors in adjacent fields often see some implication from expected-utility theory (𝔼U) to something like “𝔼$”, and then either —correctly reject 𝔼$ by absurd counterexamples, & incorrectly conclude the vNM axioms must be wrong —believe vNM & so bite the 𝔼$ bullet
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Corollary PSA: NEVER design an AI to maximize 𝔼$, even the most primitive trading bot—not just because there are more important values than monetary values—but because even with respect to money alone, it’s absurdly risk-insensitive!
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People criticize Kelly betting for being too risky, but Kelly betting is equivalent to maximizing 𝔼(log(b+$)), which is already way more risk-averse than 𝔼($).
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“putting money to work” is the mistaken wisdom here. for most money, you want it to work *inside a warchest*
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