Simplifying the anthropic impossibility result

LessWrong is reporting on a simplified proof by Stuart Armstrong of an impossibility theorem in probability theory. In the Duplicates Sleeping Beauty thought experiment — where an observer might be cloned — no probability system can satisfy both standard Bayesian reasoning and the basic inclusion-exclusion principle. Armstrong shows that every attempt to make the math work violates one rule or another. The result highlights a deep puzzle for how observers should update their beliefs when they could be one of many copies of themselves.

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