There has been a probabilistic turn in contemporary cognitive science. Far and away, most of the work in this vein is Bayesian, at least in name. Coinciding with this development, philosophers have increasingly promoted Bayesianism as the best normative account of how humans ought to reason. In this paper, we make a push for exploring the probabilistic terrain outside of Bayesianism. Non-Bayesian, but still probabilistic, theories provide plausible competitors both to descriptive and normative Bayesian accounts. We argue for this general (...) idea via recent work on explanationist models of updating, which are fundamentally probabilistic but assign a substantial, non-Bayesian role to explanatory considerations. (shrink)

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts’ probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely (...) to invariably choose the category to which they assigned the higher probability of a target’s membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments. (shrink)

Visual aids can improve comprehension of risks associated with medical treatments, screenings, and lifestyles. Do visual aids also help decision makers accurately assess their risk comprehension? That is, do visual aids help them become well calibrated? To address these questions, we investigated the benefits of visual aids displaying numerical information and measured accuracy of self-assessment of diagnostic inferences (i.e., metacognitive judgment calibration) controlling for individual differences in numeracy. Participants included 108 patients who made diagnostic inferences about three medical tests on (...) the basis of information about the sensitivity and false-positive rate of the tests and disease prevalence. Half of the patients received the information in numbers without a visual aid, while the other half received numbers along with a grid representing the numerical information. In the numerical condition, many patients --especially those with low numeracy-- misinterpreted the predictive value of the tests and profoundly overestimated the accuracy of their inferences. Metacognitive judgment calibration mediated the relationship between numeracy and accuracy of diagnostic inferences. In contrast, in the visual aid condition, patients at all levels of numeracy showed high-levels of inferential accuracy and metacognitive judgment calibration. Results indicate that accurate metacognitive assessment may explain the beneficial effects of visual aids and numeracy --a result that accords with theory suggesting that metacognition is an essential part of risk literacy. We conclude that well-designed risk communications can inform patients about health-relevant numerical information while helping them assess the quality of their own risk comprehension. (shrink)

The Monty-Hall Problem ($MHP$) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view $MHP$ and its two-player extension ($MHP2$) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that $MHP2$ (studied here) be described in different terms than usually applied (...) and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge. (shrink)

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous (...) probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. (shrink)

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the use (...) of frequencies in a natural sampling framework —as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally-sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. (shrink)