Lottery paradox, DNA evidence and other stories: How to accept uncertain statements

TL;DR

This paper discusses the challenges of accepting uncertain statements using probability, illustrating with paradoxes like the lottery paradox and DNA evidence cases, highlighting philosophical differences in probabilistic reasoning.

Contribution

It provides an overview of the problem of accepting uncertain statements and compares different inference schools without formal decision theory.

Findings

Lottery paradox illustrates logical issues in accepting high-probability statements.

DNA evidence case shows differences between frequentist, Bayesian, and likelihood approaches.

Highlights the complexity of probabilistic reasoning in uncertain situations.

Abstract

I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic selection that highlights the problem of accepting uncertain statements. Without going into a formal decision theory, there are simple intuitive rational bases for doing that, for instance based on high probability alone. The lottery paradox shows the logical problem of accepting uncertain statements based on high probability. The DNA evidence story is an example of the use probabilistic reasoning in court, where philosophical differences between the schools of inference -- the frequentist, Bayesian and likelihood schools -- lead to substantial differences in the quantification of evidence.