Where did you get your ideas of statistics, may I ask? The "what frequentists do" and "what bayesians do" isn't even part of mathematics, in the mathematics you learn the formulae, where those come from, and actually see how either works. Can't teach that in a post, you'll need several years studying.
You learn "what frequentists do" and "what bayesians do" predominantly from people whom can't actually do any interesting math and instead resort to some sort of confused meta for amusement.
Also: nobody actually uses Solomonoff induction, it's uncomputable.
The frequentism is seeing the probability as the limit of infinitely many trials. Nothing more, nothing less. You can do trials on Turing machine if you wish. If you read LessWrong you'd be thinking frequentism is some blatant rejection of the Bayes rule or something. The LessWrong seem to be predominantly focussed on meta of claiming itself to be less wrong than someone else, usually wrongly.
I've had a bit of success with getting people to understand Bayesianism at parties and such, and I'm posting this thought experiment that I came up with to see if it can be improved or if an entirely different thought experiment would be grasped more intuitively in that context:
I originally came up with this idea to explain falsifiability which is why I didn't go with say the example in the better article on Bayesianism (i.e. any other number besides a 3 rolled refutes the possibility that the trick die was picked) and having a hypothesis that explains too much contradictory data, so eventually I increase the sides that the die has (like a hypothetical 50-sided die), the different types of die in the jar (100-sided, 6-sided, trick die), and different distributions of die in the jar (90% of the die are 200-sided but a 3 is rolled, etc.). Again, I've been discussing this at parties where alcohol is flowing and cognition is impaired yet people understand it, so I figure if it works there then it can be understood intuitively by many people.