How Much More Probable is "Much More Probable"? Verbal Expressions for Probability Updates

TL;DR

This paper investigates how natural language probability phrases correspond to numerical probability updates, finding that phrases like 'much more likely' best match fixed probability differences, with a 72% accuracy in user interpretation.

Contribution

It extends prior work by analyzing the correspondence between probability update phrases and numerical changes, proposing that fixed probability differences best explain phrase usage.

Findings

Fixed probability difference best explains phrase usage

Eight phrases used to describe probability updates

72% accuracy in phrase-to-numerical correspondence

Abstract

Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic phrases. This study extends that work to the correspondence between changes in probabilities (updates) and relative probability phrases, such as "much more likely" or "a little less likely." Subjects selected such phrases to best describe numerical probability updates. We examined three hypotheses about the correspondence, and found the most descriptively accurate of these three to be that each such phrase corresponds to a fixed difference in probability (rather than fixed ratio of probabilities or of odds). The empirically derived phrase selection function uses eight phrases and achieved a 72% accuracy in correspondence with the subjects' actual usage.