I agree. Rounding has always been ridiculous to me. Methodologically, “Make your best guess given the evidence, then round” makes no sense. As long as your estimates are better than random chance, it’s strictly less reliable than just “Make your best guess given the evidence”.
Credences about credences confuse me a lot (is there infinite recursion here? I.e. credences about credences about credences...). My previous thoughts have been give a credence range or to size a bet (e.g. “I’d bet $50 out of my $X of wealth at a Y odds”). I like both your solutions (e.g. “if I thought about it for an hour...”). I’d like to see an argument that shows there’s an optimal method for representing the uncertainty of a credence. I wouldn’t be surprised if someone has the answer and I’m just unaware of it.
I’ve thought about the coin’s 50% probability before. Given a lack of information about the initial forces on the coin, there exists an optimal model to use. And we have reasons to believe a 50-50 model is that model (given our physics models, simulate a billion coin flips with a random distribution of initial forces). This is why I like your “If I thought about it more” model. If I thought about the coin flip more, I’d still guess 49%-51% (depending on the specific coin, of course).
I agree. Rounding has always been ridiculous to me. Methodologically, “Make your best guess given the evidence, then round” makes no sense. As long as your estimates are better than random chance, it’s strictly less reliable than just “Make your best guess given the evidence”.
Credences about credences confuse me a lot (is there infinite recursion here? I.e. credences about credences about credences...). My previous thoughts have been give a credence range or to size a bet (e.g. “I’d bet $50 out of my $X of wealth at a Y odds”). I like both your solutions (e.g. “if I thought about it for an hour...”). I’d like to see an argument that shows there’s an optimal method for representing the uncertainty of a credence. I wouldn’t be surprised if someone has the answer and I’m just unaware of it.
I’ve thought about the coin’s 50% probability before. Given a lack of information about the initial forces on the coin, there exists an optimal model to use. And we have reasons to believe a 50-50 model is that model (given our physics models, simulate a billion coin flips with a random distribution of initial forces). This is why I like your “If I thought about it more” model. If I thought about the coin flip more, I’d still guess 49%-51% (depending on the specific coin, of course).