With an inherently probabilistic interpretation of QM, flipping a quantum coin has to be treated linearly by our rational agent
Why? I understand that the people here tend to think that’s a good idea, but it doesn’t allow for Dutch book betting like violating Bayes’ Theorem does.
And all coins, when you get down to it, are quantum.
Not exactly. If we were to make a bet on the millionth digit of pi, or the accuracy of string theory, or whether or not there is a particle with a mass in a certain range, the result would be the same in every Everett branch.
The thing I am asserting without bothering to back it up is called the expected utility hypothesis.
It’s equivalent to having different priors and doing it linearly (although you might have to involve infinitesimal probabilities to get it to work exactly right). That does raise the question of whether those things really can be considered separate.
Why? I understand that the people here tend to think that’s a good idea, but it doesn’t allow for Dutch book betting like violating Bayes’ Theorem does.
Not exactly. If we were to make a bet on the millionth digit of pi, or the accuracy of string theory, or whether or not there is a particle with a mass in a certain range, the result would be the same in every Everett branch.
The thing I am asserting without bothering to back it up is called the expected utility hypothesis.
Fair enough. I believe you get the point though.
It’s equivalent to having different priors and doing it linearly (although you might have to involve infinitesimal probabilities to get it to work exactly right). That does raise the question of whether those things really can be considered separate.
Yes, though the result of the bet (i.e. your observations) would be different in an infinitesimal fraction of them.
/useless nitpick that doesn’t actually change your point