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I think the 'many worlds' assumption is much more than a technicality yet it has no solid theoretical foundations. The sunrise problem asks for the probability that the sun will rise tomorrow given that the sun has previously risen on $(N-1)$ consecutive days without fail.

The many worlds assumptions involves supposing that the the probability $p$ is uniformly distributed among an infinite number of worlds. This essentially leads to a calculation of the expected probability that the sun rises tomorrow, which gives us $\hat{p} = N/(N+1)$.

But, I argue that this 'many worlds' assumption has no solid theoretical foundations.

Aidan Rocke
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  • Please amplify this post--questions need to stand on their own and be intelligible without migrating to another page. – whuber Jul 07 '15 at 13:14
  • What is the "many worlds assumption"? – whuber Jul 07 '15 at 17:20
  • Thank you for the clarifications. I would be interested in a reference documenting this interpretation of the "many worlds assumption," because it is not the familiar one of quantum mechanics (which you would find dominating the top hits in Web searches). It sounds much closer to Laplace's "principle of insufficient reason." Who exactly has renamed it and why? – whuber Jul 07 '15 at 20:28
  • What constitutes "a solid theoretical foundation" here? An established physical theory? An established meta-physical one? One logically deducted from a premise? – Momo Jul 07 '15 at 21:08
  • @whuber The principle of insufficient reason is a Bayesian method for deriving uninformed priors. But, the 'many worlds' idea is a contrived method developed by frequentists to solve such problems.

    As I see it, the bayesian arguments are sound whereas the frequentist argument(that lead to the same conclusion) is unreasonable. My question is where do these 'extra' worlds come from??

     – Aidan Rocke Jul 07 '15 at 22:09
  • @Momo I mean an established physical theory or one that can be deducted from a reasonable premise. With a data stream consisting of nothing more than historical sunrises, we can't expect a statistician to come up with a sophisticated data model without any more prior knowledge.

    But, the frequentist that pulls the 'many worlds' out of a hat has a lot to explain.

     – Aidan Rocke Jul 07 '15 at 22:12
  • "I mean an established physical theory or one that can be deducted from a reasonable premise." I'm not sure this is the right SE for it, or if physics.SE would be better for that - they have this http://physics.stackexchange.com/questions/10140/are-many-worlds-and-the-multiverse-really-the-same-thin. I suppose the frequentist concept is more meta-physical (or should I say non-empirical) like "counterfactual" and to a certain degree "data generating process" for populations. – Momo Jul 08 '15 at 11:04
  • The "many worlds" assumption is not a standard frequentist assumption, so no frequentist would need to "abandon" it. Arch-frequentist von Mises would say that the probability you're talking about is not a well defined problem in the frequentist sense. If I remember correctly he even writes explicitly that for problems like this, the Bayesian approach is fine. – Christian Hennig Jun 05 '22 at 16:20
  • By the way, my personal view is that one can set up a model for "many worlds" in order to give a frequentist interpretation to such probabilities, as models are idealisations and don't have to be "really true". However in order to use it for scientific reasoning, it needs to be well argued and defended, and that's very hard in this situation (as you state, I don't see a solid foundation for it), so that going back to what von Mises wrote seems sensible here. – Christian Hennig Jun 05 '22 at 16:23
  • @Aidan Rocke Please provide the reference showing a frequentist has used the many worlds assumption to calculate the probability that the sun will rise tomorrow. – Graham Bornholt Jun 18 '22 at 11:15

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From Wikipedia

In the frequentist interpretation, probabilities are discussed only when dealing with well-defined random experiments.

The sunrise problem is not a well defined experiment. So the answer is that a "frequentist" will not be dealing with that problem.

As far as "frequentists" exist. It is not something like a religion like a statistician uses either only frequentist methods or only Bayesian methods. A scientist or a statistician is using whatever tool, frequentist or Bayesian, they prefer, like and/or is best applicable. They can use both.

But let's put all that asside. When we bluntly apply a frequentist approach to the problem then we could use for instance model the situation 'the event of a sunrise on a particular day' as a Bernoulli distribution with a parameter $p$ and each day an independent event from the others (which is absurd, but that is because the sunrise problem is absurd). Then the frequentist could compute the likelihood and determine the maximum, which is $p=1$. One could also compute a confidence interval, which the rule of three would state as $1-3/n$ to $1$, where $n$ is the number of days that the sun has risen.

It is unclear why the many worlds are needed and where this comes from? Maybe to turn this into a well-defined (thought) experiment with a long run frequency of failed and successful estimations? Yes that seems artificial, but the frequentist approach should not have been used in the first place.

Sextus Empiricus
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