I mean I think the “gamble her money” interpretation is just a different question. It doesn’t feel to me like a different notion of what probability means, but just betting on a fair coin but with asymmetric payoffs.
The second question feels closer to actually an accurate interpretation of what probability means.
Probability is not some vaguely defined similarity cluster like “sound”. It’s a mathematical function that has specific properties. Not all of them are solely about betting.
We can dissolve the semantic disagreement between halfers and thirders and figure out that they are talking about two different functions p and p’ with subtly different properties while producing the same betting odds.
This in itself, however, doesn’t resolve the actual question: which of these functions fits the strict mathematical notion of probability for the Sleeping Beauty experiment and which doesn’t. This question has an answer.
I mean I think the “gamble her money” interpretation is just a different question. It doesn’t feel to me like a different notion of what probability means, but just betting on a fair coin but with asymmetric payoffs.
The second question feels closer to actually an accurate interpretation of what probability means.
https://www.lesswrong.com/posts/Mc6QcrsbH5NRXbCRX/dissolving-the-question
Probability is not some vaguely defined similarity cluster like “sound”. It’s a mathematical function that has specific properties. Not all of them are solely about betting.
We can dissolve the semantic disagreement between halfers and thirders and figure out that they are talking about two different functions p and p’ with subtly different properties while producing the same betting odds.
This in itself, however, doesn’t resolve the actual question: which of these functions fits the strict mathematical notion of probability for the Sleeping Beauty experiment and which doesn’t. This question has an answer.