Dutch-book resistant probability over centered worlds

A longstanding puzzle in decision theory: how do you rationally assign probabilities when your own position as an observer is uncertain? Sleeping Beauty captures the problem—you wake in an experiment not knowing if it's the first or second time. LessWrong author jessicata proposes a formal answer using 'centered worlds'—a framework that tags each possible universe state with information about who you are and when you are it. The main result: probability assignments that can't be exploited via Dutch books—sure-fire losing bets—must follow a pattern called centering-uniformity, where probabilities are weighted by how many times your exact observational scenario appears across different worlds. Applied to Sleeping Beauty, this yields a prediction some find counterintuitive: if you wake uncertain, assign one-third probability to Heads, not one-half. Per the Dutch-book analysis, this shift is rationally required—even though you've gained no new factual information, your shifted observer-location changes what you ought to believe.

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