Algorithmic Probability as a Common Foundation for Quantum Interpretation

The Born rule has remained a perpetual puzzle in the quantum foundations community. The Gleason-Busch Theorem proves the rule, given the assumption of a certain type of non-contextuality, an assumption that only some are willing to grant as obvious. I analyze these issues in terms of two thought experiments from the literature: the Sleeping Beauty problem and the Replicator Copies experiment, showing that differing interpretations can be understood in terms of how they interpret these two (non-quantum) thought experiments, the major division being between those who count ontic (metaphysical) entities, and those who count subjective states. For instance, I argue that wave function realists (such as Everettians) need to be ontic counters to be consistent, yet Everett himself was not. I argue further that algorithmic probability is our best way forward towards resolving the interpretation of quantum probabilty, by providing a common foundation for all four of the above schools, each of which differs in the nature of the computing language used to formulate its algorithms. I would argue that, by using algorithmic probability as a common foundation, those debating quantum interpretations stand a better chance of understanding each other, and may perhaps avoid talking past each other.