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 _1over 5_ of _S_, and you own _1over 5_ of _neg S_, then you can trade these to the market-maker for _1over 5_ of a dollar. (So for example, if the current price of a share of _S_ is _50¢_, and the current price of a share of _neg S_ is _45¢_, then you can arbitrage by buying _1over5_ of a share of both (cost _10¢_+_9¢_=_19¢_) and cashing these in to the market maker for _20¢_.) This forces the market to converge towards _text{price}(S)+text{price}(neg S) = $1_ for all _S_ [...]

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.