On the relation between plausibility logic and the maximum-entropy principle: a numerical study

TL;DR

This paper investigates the relationship between plausibility logic and the maximum-entropy principle through numerical analysis of fifteen simple dice-throwing problems, exploring when each approach is appropriate and how they compare.

Contribution

It provides a numerical comparison of plausibility logic and maximum-entropy distributions across simple problems, clarifying their applicability and differences.

Findings

Maximum-entropy often aligns with plausibility logic in simple cases

Discrepancies occur when maximum-entropy yields unreasonable results

Plausibility logic can sometimes provide more appropriate answers

Abstract

What is the relationship between plausibility logic and the principle of maximum entropy? When does the principle give unreasonable or wrong results? When is it appropriate to use the rule `expectation = average'? Can plausibility logic give the same answers as the principle, and better answers if those of the principle are unreasonable? To try to answer these questions, this study offers a numerical collection of plausibility distributions given by the maximum-entropy principle and by plausibility logic for a set of fifteen simple problems: throwing dice.