Judgment errors in naturalistic numerical estimation.

People estimate numerical quantities (such as the calories of foods) on a day-to-day basis. Although these estimates influence behavior and determine wellbeing, they are prone to two important types of errors. Scaling errors occur when people make mistakes reporting their beliefs about a particular numerical quantity (e.g. by inflating small numbers). Belief errors occur when people make mistakes using their knowledge of the judgment target to form their beliefs about the numerical quantity (e.g. by overweighting certain cues). In this paper, we quantitatively model numerical estimates, and in turn, scaling and belief errors, in everyday judgment tasks. Our approach is unique in using insights from semantic memory research to specify knowledge for naturalistic judgment targets, allowing our models to formally describe nuanced errors in belief not considered in prior research. In Studies 1 and 2, we find that belief error models predict participant estimates and errors with very high out-of-sample accuracy rates, significantly outperforming the predictions of scaling error models. In fact, the best-fitting belief error models can closely mimic the inverse-S shaped patterns captured by scaling error models, suggesting that the types of responses previously attributed to scaling errors can be seen as errors of belief. In Studies 3 to 8, we find that belief error models are also able to predict people's responses in semantic judgment, free association, and verbal protocol tasks related to numerical judgment, and thus provide a good account of the cognitive underpinnings of judgment.