Revisiting the Sleeping Beauty problem
This work addresses a long-standing philosophical and mathematical puzzle with implications for probability theory and decision-making, but it is incremental as it builds on existing debates without introducing a fundamentally new paradigm.
The paper tackles the Sleeping Beauty probability riddle by analyzing it mathematically to identify probability distributions from the experiment's rules, showing that both halfer and thirder solutions arise from different probability spaces, and proposes an information-based criterion to decide between them.
The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer approach, and the thirder approach. The main reason for disagreement in the literature is connected to the use of different probability spaces to represent the same probabilistic riddle. In this work, we analyse the problem from a mathematical perspective, identifying probability distributions induced directly from the thought experiment's rules. The precise choices of probability spaces provide both halfer and thirder solutions to the problem. To try and decide on which approach to follow, a criterion involving the information available to Sleeping Beauty is proposed.