Objective and Subjective Solomonoff Probabilities in Quantum Mechanics

TL;DR

This paper explores how algorithmic probability can be generalized to support both objective and subjective interpretations of quantum probabilities, with applications to thought experiments like Sleeping Beauty and Replicator.

Contribution

It introduces a general framework for generative probability, extending algorithmic probability to Bayesian and subjectivist quantum interpretations.

Findings

Framework successfully applies to quantum thought experiments

Bridges objective and subjective probability in quantum mechanics

Provides new insights into quantum probability modeling

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.