The Shannon Challenge in the Sleeping Beauty Problem Quantifying ``New Information''

The Sleeping Beauty problem remains a highly contested paradox in formal epistemology. The thirder resolution, famously championed by Adam Elga, argues that Beauty’s credence that a fair coin landed Heads shifts from 1/2 on Sunday to 1/3 upon awakening. This paper challenges the mathematical legitimacy of this epistemic shift by applying Claude Shan- non’s Information Theory. We demonstrate that the experimental protocol—specifically the amnesiac awakening—functions mathematically as a perfectly predictable, constant signal. Because a constant signal carries zero entropy, it cannot share mutual information with any conceivable random variable, whether objective (the coin toss) or indexical (her temporal location). Consequently, Beauty receives exactly zero bits of Shannon information upon waking. Without quantifiable data transmission to trigger a Bayesian update, her mathe- matical prior cannot be altered, firmly supporting the strict halfer (1/2) position.