Supplemental reading from stanford: https://plato.stanford.edu/entries/probability-interpret/

What scenarios doesn't frequentism work for? I had a quick skim through the Stanford entry and believe it said something to the effect that frequentism is a subset of Bayesianism. This seemed odd to me as aren't all probability methods subject to Bayesianism?

What scenarios doesn't frequentism work for? — Down The Rabbit Hole

Seems like frequentism is a bad fit for "What's the probability that Donald Trump wins the election?" for example.

It's not like there's a like-for-like set of comparable situations you can compare this future event to, like you would with coin flips for example - this next election will happen once and will be unique from all elections before and after it.

There is an excellent book called Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science
by Aubrey Clayton that points out some of the major flaws in frequentism as it is commonly put forth.

I think it's very accessible as far as math books go, and does a very good job explaining the history, even if it does sometimes seem to lurch close ad hominems in pointing out how many advocated of frequentism were social scientists trying to use statistics to advocate for eugenics.

However, I am not convinced, as Clayton seems to be, that Bayesian methods resolve the problem.

I actually think that the widespread use of information theory in the sciences (particularly physics) and as a tool to unify the sciences will make this question among the very most important questions in metaphysics in the future. If you're defining physical reality in terms of information, and defining causation in terms of computation and information transfer, then "what is information," becomes an essential question. But information is itself generally defined in terms of probability.

There is an argument that information doesn't "really" exist because in reality there is no "probability." For any system the measurements/interactions that can occur are just the measurements that do actually occur. Information is thus inherently "subjective." But since the concept is so foundational it seems that the consensus tends towards "well so much the worse for (that sort of) objectivity," and you even see arguments for information being more ontologically basic than matter or energy, the latter emerging from the former. Obviously, the merits of such positions, or even what they are saying, will depend on one's understanding of probability in the first place.

I feel like Bayesianism is the most general and all the others can be looked at reasonably well through a Bayesian lense. For instance, it seems there are many situations where it is natural to cash out Bayesian probabilities regarding the occurrence of events in terms of frequencies; and obviously this can be easily justified by the law of large numbers. Doesn't seem hard to me to connect it to propensities either, which I might also cash out in terms of talk about frequencies, at least counterfactually speaking.

Seems like frequentism is a bad fit for "What's the probability that Donald Trump wins the election?" for example.

It's not like there's a like-for-like set of comparable situations you can compare this future event to, like you would with coin flips for example - this next election will happen once and will be unique from all elections before and after it. — flannel jesus

I think we predict such probabilities almost exclusively from national and constituency polling, and projections based upon said national and constituency polling. At least here in the UK.
In any event, we judge probabilities based upon patterns of behaviour?

oh that's a good point, so there is a type of frequentism that goes into the analysis, but... is it exclusively frequentism? Do they also layer on additional types of analysis that aren't as obviously frequentist?

Maybe not, maybe it's just all obviously fitting into a frequentist paradigm and I'm a silly boy.

is it exclusively frequentism? Do they also layer on additional types of analysis that aren't as obviously frequentist? — flannel jesus

I can only think of patterns of behaviour being a basis for judging probability. Which I think the definition of frequentism fits.