Objective and Subjective Solomonoff Probabilities in Quantum Mechanics

Abstract: Algorithmic probability has shown some promise in dealing with the probability problem in the Everett interpretation, since it provides an objective, single-case probability measure. Many find the Everettian cosmology to be overly extravagant, however, and algorithmic probability has also provided improved models of subjective probability and Bayesian reasoning. I attempt here to generalize algorithmic Everettianism to more Bayesian and subjectivist interpretations. I present a general framework for applying generative probability, of which algorithmic probability can be considered a special case. I apply this framework to two commonly vexing thought experiments that have immediate application to quantum probability: the Sleeping Beauty and Replicator experiments.