Revealing the Beauty behind the Sleeping Beauty Problem

TL;DR

This paper provides a clear probability-theoretic analysis of the Sleeping Beauty problem, demonstrating that Bayesian inference and the Reflection Principle remain consistent when considering an additional random experiment.

Contribution

It introduces a novel approach by analyzing an extra random experiment to clarify the conditional probabilities involved in the problem.

Findings

No inconsistency in the problem's probabilities

Bayesian inference remains valid

Reflection Principle holds true

Abstract

A large number of essays address the Sleeping Beauty problem, which undermines the validity of Bayesian inference and Bas Van Fraassen's 'Reflection Principle'. In this study a straightforward analysis of the problem based on probability theory is presented. The key difference from previous works is that apart from the random experiment imposed by the problem's description, a different one is also considered, in order to negate the confusion on the involved conditional probabilities. The results of the analysis indicate that no inconsistency takes place, whereas both Bayesian inference and 'Reflection Principle' are valid.