This seems to be a misapplication of Bayesian reasoning. Suppose I believe this argument, and as such, assign 99.9% to “no god, many worlds”. Then suppose I had some absolutely reliable knowledge that god didn’t exist. This argument stops working and I now believe “no god, collapse postulate” at 50% and “no god, many worlds” at 50%. Imagine that I am about to get that perfectly reliable knowledge about the existence of god. I am almost sure that I will get “no god”. I know that, given “no god”, I will assign 50% credence to collapse postulates. I currently assign <0.1% to collapse postulates. Something has gone wrong.
The Bayesian irrelevance theorem states that
The likelihood ratio of any two hypothesis depends only on those hypothesis ability to predict the data, and the likelihood ratio in the prior.
In other words, if you have 3 possible theories, X, Y and Z, and you want to compare X and Y, then you don’t need to know anything about Z. To compare X with Y, compare their priors and their ability to predict data as if Z didn’t exist.
This will give you the ratio of the likelihood of X and Y.
So, to compare the two hypothesis, “no god, many worlds” and “no god, collapse postulate” you only need to think about these theories, what their priors are, and what updates you can make.
Depending on how you handle anthropic reasoning, you might or might not make an update towards many worlds.
This seems to be a misapplication of Bayesian reasoning. Suppose I believe this argument, and as such, assign 99.9% to “no god, many worlds”. Then suppose I had some absolutely reliable knowledge that god didn’t exist. This argument stops working and I now believe “no god, collapse postulate” at 50% and “no god, many worlds” at 50%. Imagine that I am about to get that perfectly reliable knowledge about the existence of god. I am almost sure that I will get “no god”. I know that, given “no god”, I will assign 50% credence to collapse postulates. I currently assign <0.1% to collapse postulates. Something has gone wrong.
The Bayesian irrelevance theorem states that
The likelihood ratio of any two hypothesis depends only on those hypothesis ability to predict the data, and the likelihood ratio in the prior.
In other words, if you have 3 possible theories, X, Y and Z, and you want to compare X and Y, then you don’t need to know anything about Z. To compare X with Y, compare their priors and their ability to predict data as if Z didn’t exist.
This will give you the ratio of the likelihood of X and Y.
So, to compare the two hypothesis, “no god, many worlds” and “no god, collapse postulate” you only need to think about these theories, what their priors are, and what updates you can make.
Depending on how you handle anthropic reasoning, you might or might not make an update towards many worlds.