Probability theory, not the very guide of life.

Abstract

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive integration, in part, at least, because of well-known capacity constraints on controlled thought. In this article, the authors show with computer simulations that when based on approximate knowledge of probabilities, as is routinely the case in natural environments, linear additive integration can yield as accurate estimates, and as good average decision returns, as estimates based on probability theory. It is proposed that in natural environments people have little opportunity or incentive to induce the normative rules of probability theory and, given their cognitive constraints, linear additive integration may often offer superior bounded rationality.

Evidence affects hypothesis judgments more if accumulated gradually than if presented instantaneously

“…A secondary finding evident in our data is that participants' responses were conservative relative to the Bayesian norm, as has been reported previously in the beads task (Anderson, 1981;Juslin, Nilsson, & Winman, 2009;Lopes, 1985;Shanteau, 1975). Such conservatism has been attributed to misaggregation of evidence over time, with the combined value of several sequential samples being a weighted average of their individual scale values (Anderson, 1981;Lopes, 1985;Shanteau, 1975).…”

Is there something special with probabilities? – Insight vs. computational ability in multiple risk combination

“…In this article, we undertake such a comparison with a special eye to the question of whether the propensity to rely on linear additive combination observed in studies of multiple-cue judgment (e.g., Brehmer, 1994;Juslin et al, 2009;Karelaia & Hogarth, 2008) extends also too formally similar probability combination tasks. Although the different combination strategies often correlate highly in these tasks, and despite the presence of considerable individual differences, by the use of computational modeling and residual analysis we have been able to detect some systematic differences between the tasks.…”

“…It has accordingly been proposed that the inclination for linear additive combination observed in research on multiple-cue judgment might be an important-and often neglected-contributor to biases observed in tasks that require multiplicative probability combination, like the medical diagnosis task (Juslin, Nilsson, Winman, & Lindskog, 2011;Juslin et al, 2009;Nilsson et al, 2009). In this article, we thus explore the relationship between these two tasks in greater detail.…”

“…In such a process, multiplicative (configural) cue combination requires that the adjustment made in view of a cue depends not only on this cue, but also on the cues considered previously in the sequence, which requires taxing working memory resources. Because many probability rules, including the rules for conjunctions and base-rate problems, involve multiplication, people are bound to have difficulties with these problems (see Juslin et al, 2009Juslin et al, , 2011. From this point of view, we predict that, from long experience with stochastic events, people do have qualitative insight into many of the probability laws (e.g., that the base-rate is relevant to the (posterior) probability in a base-rate problem, or that conjunctions of events tend to have a low probability and disjunctions of events a high probability).…”

Uncertainty and its perception: experimental study of the numeric expression of uncertainty in two decisional contexts

“…They often associate uncertainty to the concepts of possibility and probability (Juslin et al 2009). In their inquiries, uncertainty is also analyzed together with the following (Luxton and Wenzlaff 2005):…”