Contrasting stochastic and support theory accounts of subadditivity

Abstract

Numerous studies have found that likelihood judgment typically exhibits subadditivity in which judged probabilities of events are less than the sum of judged probabilities of constituent events. Whereas traditional accounts of subadditivity attribute this phenomenon to deterministic sources, this paper demonstrates both formally and empirically that subadditivity is systematically influenced by the stochastic variability of judged probabilities. First, making rather weak assumptions, we prove that regressive error (or variability) in mapping covert probability judgments to overt responses is sufficient to produce subadditive judgments. Experiments follow in which participants provided repeated probability estimates. The results support our model assumption that stochastic variability is regressive in probability estimation tasks and show the contribution of such variability to subadditivity. The theorems and the experiments focus on within-respondent variability, but most studies use between-respondent designs. Numerical simulations extend the work to contrast within- and between-respondent measures of subadditivity. Methodological implications of all the results are discussed, emphasizing the importance of taking stochastic variability into account when estimating the role of other factors (such as the availability bias) in producing subadditive judgments.