Never say "not": Impact of negative wording in probability phrases on imprecise probability judgments

Abstract

Effective translations between numerical and verbal representations of uncertainty are a concern shared by researchers in cognitive science and psychology, with applications to real-world risk management and decision support systems. While there is a substantial literature on such translations for point-wise probabilities, this paper contributes to the scanty literature on imprecise probability translations. Reanalysis of Budescu et al.'s [1] data on numerical interpretations of the Intergovernmental Panel on Climate Change [2] fourth report's verbal probability expressions (PEs) revealed that negative wording has deleterious effects on lay judgements. Budescu et al. asked participants to interpret PEs in IPCC report sentences, by asking them to provide lower, "best" and upper estimates of the probabilities that they thought the authors intended. There were four experimental conditions, determining whether participants were given any numerical guidelines for translating the PEs into numbers. The first analysis focuses on twelve sentences in Budescu et al. that used the PE "very likely," "likely," "unlikely," or "very unlikely". A mixed beta regression modelling the lower, "best" and upper estimates revealed a less regressive mean and less dispersion for positive than for negative wording in all three estimates, for both the "very likely" and "likely" sentence sets. The Budescu et al. data also included a task asking for context-free translations of these PEs, and a similar pattern of results was found for that task. Negative wording therefore resulted in more regressive estimates and less consensus regardless of experimental condition. The second analysis focuses on two statements that were positive-negative duals. Appropriate pairs of responses were assessed for conjugacy and additivity. A large majority of respondents were appropriately super- and sub-additive in their lower and upper probability estimates. A mixed beta regression model of these three variables revealed that respondents were suprisingly close to obeying the conjugacy relationships for lower and upper probabilities.