Sleeping Beauty in One or Many Worlds: A Defense of the Halfer Position

TL;DR

This paper defends the Halfer position in the Sleeping Beauty Problem, arguing that both quantum and classical versions support a credence of 1/2, challenging the Thirder view and defending the Many-Worlds Interpretation.

Contribution

It provides a novel defense of the Halfer position in SBP, extending the argument to quantum MWI and refuting major classical arguments for the Thirder position.

Findings

Correct credence in quantum SBP is 1/2 without unjustified renormalization.

Refutes four major classical arguments for the 1/3 credence.

Supports the consistency of MWI with SBP.

Abstract

The Sleeping Beauty Problem (SBP) is a long-standing puzzle in classical probability theory and has been used to challenge the Many-Worlds Interpretation (MWI) of quantum mechanics, since both involve objective determinacy combined with subjective uncertainty about certain events. A common concern is that MWI yields a different answer to the quantum version of SBP than the widely supported Thirder position in the classical case. We argue that this concern is unwarranted. We show that in both the quantum and classical versions of SBP, the correct credence is given by the Halfer position. In the quantum (MWI) SBP, we show that if no unjustified renormalization is introduced, the correct credence is 1/2. We then extend this result to the classical SBP by refuting four major arguments for 1/3. First, we reject the Proportion Argument by distinguishing event weight from probability. Second, we rebut Elga's Variant Argument by extending an earlier critique that identifies the implicit introduction of additional information; we further clarify this point by constructing a new variant and explaining why the Principle of Indifference is inapplicable, drawing an analogy with a mistake by d'Alembert in the history of probability theory. Third, we identify a flaw in the Technicolor Beauty Variant Argument, which arises from treating overlapping events as disjoint. Finally, we argue that causal decision theory is inappropriate for SBP, rendering the Thirders vulnerable to a Dutch Book. Our results support the consistency of MWI under the challenge posed by SBP and suggest that the dominant position on SBP needs careful reconsideration.