The two envelopes paradox in non-Bayesian and Bayesian statistics

TL;DR

This paper uses quantum language, a framework inspired by quantum mechanics, to clarify and resolve the two envelopes paradox in both Bayesian and non-Bayesian statistics, offering a deeper understanding of the problem.

Contribution

It introduces quantum language as a novel approach to analyze the two envelopes paradox, providing a unified and clearer resolution in both statistical paradigms.

Findings

Quantum language offers a definitive resolution to the paradox.

The paradox is a simple probability puzzle exaggerated by traditional interpretations.

Discussion includes the St. Petersburg paradox related to the envelopes problem.

Abstract

The purpose of this paper is to clarify the (non-Bayesian and Bayesian) two-envelope problems in terms of quantum language (or, measurement theory), which was recently proposed as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). The two envelopes paradox is only a kind of high school student's probability puzzle, and it may be exaggerated to say that this is an unsolved problem. However, since we are convinced that quantum language is just statistics of the future, we believe that there is no clear answer without the description by quantum language. In this sense, the readers are to find that quantum language provides the final answer (i.e., the easiest and deepest understanding) to the two envelope-problems in both non-Bayesian and Bayesian statistics. Also, we add the discussion about St. Petersburg two-envelope paradox.