Inference by Multiple Identical Observers

TL;DR

This paper develops a probability framework for inference problems involving multiple identical observers, allowing for precise comparison of different solutions to such problems.

Contribution

It introduces a formal model for analyzing inference with multiple identical observers within Kolmogorov probability spaces, clarifying debates like the Sleeping Beauty problem.

Findings

Provides a rigorous probability framework for multiple observers

Enables precise comparison of competing inference solutions

Clarifies the structure of observer-based inference problems

Abstract

We consider models for inference which involve observers which may have multiple copies, such as in the Sleeping Beauty problem. We establish a framework for describing these problems on a probability space satisfying Kolmogorov's axioms, and this enables the main competing solutions to be compared precisely.