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.