Audio note: this article contains 92 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Garrabrant Induction provides a somewhat plausible sketch of reasoning under computational uncertainty, the gist of which is "build a prediction market". An approximation of classical probability theory emerges. However, this is only because we assume classical logic. The version of Garrabrant Induction in the paper does this by allowing bets to be placed on all boolean combinations of sentences visible to the market. An earlier draft accomplished the same thing via special arbitrage rules, EG, if you own <span>_1over 5_</span> of <span>_S_</span>, and you own <span>_1over 5_</span> of <span>_neg S_</span>, then you can trade these to the market-maker for <span>_1over 5_</span> of a dollar. (So for example, if the current price of a share of <span>_S_</span> is <span>_50¢_</span>, and the current price of a share of <span>_neg S_</span> is <span>_45¢_</span>, then you can arbitrage by buying <span>_1over5_</span> of a share of both (cost <span>_10¢_</span>+<span>_9¢_</span>=<span>_19¢_</span>) and cashing these in to the market maker for <span>_20¢_</span>.) This forces the market to converge towards <span>_text{price}(S)+text{price}(neg S) = $1_</span> for all <span>_S_</span> [...]

The original text contained 5 footnotes which were omitted from this narration.

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First published:
November 22nd, 2025

Source:
https://www.lesswrong.com/posts/g8RBkTf9uGTq9ypub/market-logic-i

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Narrated by TYPE III AUDIO.

Market Logic I

LessWrong (30+ Karma)