Discussion Overview
The discussion revolves around the Sleeping Beauty problem, specifically focusing on how Sleeping Beauty should assign her credence to the outcome of a coin toss when she is awakened. The conversation explores various interpretations of credence, the implications of anthropic reasoning, and the role of betting odds in determining probabilities.
Discussion Character
- Debate/contested
- Conceptual clarification
- Exploratory
- Mathematical reasoning
Main Points Raised
- Some participants argue that credence does not need to follow betting odds, citing sources that support this view.
- One participant suggests that Sleeping Beauty, as an epistemically sound reasoner, would assign a probability of 1/3 to heads based on the outcomes of the coin tosses and her awakening conditions.
- Another participant proposes a modified procedure involving two coins to illustrate the problem, asserting that the prior probabilities must be considered when she is awakened.
- Some participants express agreement on the conclusion that the probability of heads should be 1/3, while others challenge the clarity and necessity of the proposed modifications to the original problem.
- There is a debate over the meaning of "new information" and its role in influencing credence, with some arguing that the awakening itself does not provide surprising information that would alter her credence assignment.
Areas of Agreement / Disagreement
Participants generally agree that the probability of heads should be 1/3, but there are multiple competing views on how to arrive at that conclusion and the relevance of betting odds and new information. The discussion remains unresolved regarding the clarity and implications of the proposed modifications to the problem.
Contextual Notes
Some participants note that the original problem's details, such as the order of awakenings and the implications of being awakened, are not clearly defined, leading to different interpretations of how credence should be assigned.