My "Payorian FairBot" was just the original FairBot

LessWrong has published a detailed mathematical proof showing that two different fairness conditions for game-theoretic agents—Löbian fairness and Payorian fairness—are mathematically equivalent. The post walks through both elementary and sophisticated formal proofs. The work builds on MIRI's proof-based prisoner's dilemma tournament, which encodes agents as formulas in Peano arithmetic. While this confirms that two seemingly distinct approaches are the same, the author notes an intriguing insight: the Payorian condition doesn't require Löb's theorem to establish equivalence, suggesting the two might diverge in weaker logical systems.

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