I haven’t followed your arguments all the way here but I saw the comment
If I am understanding correctly, you are saying if the sleeping beauty problem does not use a coin toss, but measures the spin of an election instead, then the answer would be different.
and would just jump in and say that others have made a similar arguments. The one written example I’ve seen is this Master’s Thesis.
I’m not sure if I’m convinced but at least I buy that depending on how the particular selection goes about there can be instances were difference between probabilities as subjective credences or densities of Everett branches can have decision theoretic implications.
The link point back to this post. But I also remember reading similar arguments from halfer before, that the answer changes depending on if it is true quantum randomness, could not remember the source though.
But the problem remains the same: can Halfers keep the probability of a coin yet to be tossed at 1⁄2, and remain Bayesian. Michael Titelbaum showed it cannot be true as long as the probability of “Today is Tuesday” is valid and non-zero. If Lewisian Halfer argues that, unlike true quantum randomness, a coin yet to be tossed can have a probability differing from half, such that they can endorse self-locating probability and remains Bayesian. Then the question can simply be changed to using quantum measurements (or quantum coin for ease of expression). Then Lewisian Halfers faces the counter-argument again: either the probability is 1⁄2 at waking up and remains at 1⁄2 after learning it is Monday, therefore non-Bayesian. Or the probability is indeed 1⁄3 and updates to 1⁄2 after learning it is Monday, therefore non-halving. The latter effectively says SSA is only correct in non-quantum events and SIA is correct only for quantum events. But differentiating the cases between quantum and non-quantum events is no easy job. A detailed analysis of a simple coin toss result can lead to many independent physical causes, which can very well depend on quantum randomness. What shall we do in these cases? It is a very assumption-heavy argument for an initially simple Halfer answer.
Edit: Just gave the linked thesis a quick read. The writer seems to be partial to MWI and thinks it gives a more logical explanation to anthropic questions. He is not keen on the notion of treating probability/chance as that a randomly possible world becomes actualized, but considers all possible worlds ARE real (many-worlds), that the source of probability (or “the illusion of probability” as the writer says) is from which branch-world “I” am in. My problem with that is the “I” in such statements is taken as intrinsically understood, i.e. has no explanation. It does not give any justification on what the probability of “I am in a Heads world” is. For it to give a probability, additional assumptions about “among all the physically-similar agents across the many-branched worlds, which one is I” is needed. And that circles back to anthropics. At the end of the day, it is still using anthropic assumptions to answer anthropic problems, just like SIA or SSA.
I have argued against MWI in anthropics in another post. If you are interested.
I haven’t followed your arguments all the way here but I saw the comment
and would just jump in and say that others have made a similar arguments. The one written example I’ve seen is this Master’s Thesis.
I’m not sure if I’m convinced but at least I buy that depending on how the particular selection goes about there can be instances were difference between probabilities as subjective credences or densities of Everett branches can have decision theoretic implications.
Edit: I’ve fixed the link
The link point back to this post. But I also remember reading similar arguments from halfer before, that the answer changes depending on if it is true quantum randomness, could not remember the source though.
But the problem remains the same: can Halfers keep the probability of a coin yet to be tossed at 1⁄2, and remain Bayesian. Michael Titelbaum showed it cannot be true as long as the probability of “Today is Tuesday” is valid and non-zero. If Lewisian Halfer argues that, unlike true quantum randomness, a coin yet to be tossed can have a probability differing from half, such that they can endorse self-locating probability and remains Bayesian. Then the question can simply be changed to using quantum measurements (or quantum coin for ease of expression). Then Lewisian Halfers faces the counter-argument again: either the probability is 1⁄2 at waking up and remains at 1⁄2 after learning it is Monday, therefore non-Bayesian. Or the probability is indeed 1⁄3 and updates to 1⁄2 after learning it is Monday, therefore non-halving. The latter effectively says SSA is only correct in non-quantum events and SIA is correct only for quantum events. But differentiating the cases between quantum and non-quantum events is no easy job. A detailed analysis of a simple coin toss result can lead to many independent physical causes, which can very well depend on quantum randomness. What shall we do in these cases? It is a very assumption-heavy argument for an initially simple Halfer answer.
Edit: Just gave the linked thesis a quick read. The writer seems to be partial to MWI and thinks it gives a more logical explanation to anthropic questions. He is not keen on the notion of treating probability/chance as that a randomly possible world becomes actualized, but considers all possible worlds ARE real (many-worlds), that the source of probability (or “the illusion of probability” as the writer says) is from which branch-world “I” am in. My problem with that is the “I” in such statements is taken as intrinsically understood, i.e. has no explanation. It does not give any justification on what the probability of “I am in a Heads world” is. For it to give a probability, additional assumptions about “among all the physically-similar agents across the many-branched worlds, which one is I” is needed. And that circles back to anthropics. At the end of the day, it is still using anthropic assumptions to answer anthropic problems, just like SIA or SSA.
I have argued against MWI in anthropics in another post. If you are interested.