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The Geometric Expectation — LessWrong

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There is a pattern that shows up in many of the toys we like to play with around here: the pattern of maximizing the expected logarithm. Nash bargaining is a method for aggregating preferences without a means to directly compare them. When Nash bargaining, you are maximizing the expected logarithm of utility, where the expectation is over uncertainty about which person you are. Kelly betting is an extremely useful tool for not putting all your future wealth in one basket. When Kelly betting, you are maximizing the expected logarithm of your wealth. The log scoring rule is a very natural way to extract beliefs. When maximizing your log score, you are maximizing the expectation of the logarithm of the probability you assign to the right answer. This is one example of a general pattern. Maximizations of expected logarithms show up all over information theory, often phrased as minimizing the negative of the expected logarithm. Why does maximization of the expected logarithm keep showing up

x The Geometric Expectation — LessWrong Geometric Rationality Logic & Mathematics Kelly Criterion Rationality World Modeling Frontpage 179 The Geometric Expectation by Scott Garrabrant 23rd Nov 2022 5 min read 22 179 A Suspicious Pattern There is a pattern that shows up in many of the toys we like to play with around here: the pattern of maximizing the expected logarithm. Nash bargaining is a method for aggregating preferences without a means to directly compare them. When Nash bargaining, you are maximizing the expected logarithm of utility, where the expectation is over uncertainty about whi

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