Fermian guesstimation can boost the wisdom-of-the-inner-crowd.

How can people's ability to make accurate estimations be boosted? Psychological research on the wisdom-of-the-inner-crowd suggests that people's judgments improve when they use a simple consider-the-opposite-strategy, dubbed-inspired by Enlightenment philosopher Hegel-dialectical-bootstrapping: A person generates a first estimate (thesis), then rejects it and generates another one (anti-thesis), and finally integrates both (synthesis). Yet, the wisdom-of-the-inner-crowd-phenomenon comes with controversy concerning its measurement, robustness, and moderators. We (1) introduce a novel class of strategies to elicit the wisdom-of-the-inner-crowd. These strategies root in physics, where Nobel-laureate Enrico Fermi used back-of-the-envelope guesstimation, for instance, when assessing the explosive yield of the first tested nuclear bomb. Fermian strategies prescribe decomposing an estimation problem into subtasks, solving the subtasks separately, and ultimately integrating those solutions into a final estimate. In an experiment using a new task-environment, we find (2) that a similarity-based Fermian-strategy boosts the wisdom-of-the-inner-crowd even more than consider-the-opposite does, (3) that the provision of a memory aid differentially affects those two strategies' performance, and (4) that data trimming matters. Moreover, and for the first time, we document (5) overprecision in wisdom-of-the-inner-crowd estimations. Finally, we (6) replicate previous results, including that the collective intelligence of two persons still outperforms asking oneself twice.

From washing hands to washing consciences and polishing reputations.

While Lee and Schwarz propose grounded procedures of separation as an explanation for physical cleansing in various domains (e.g., washing one's hands), we suggest that separation can also account for behavioral cleansing aimed at washing consciences and polishing reputations. We discuss this extension in terms of degrees of behavioral cleansing, motivations, and intentions behind cleansing, and social settings.

Natural frequencies improve Bayesian reasoning in simple and complex inference tasks.

Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions-three cue values, three hypotheses, two cues, or three cues-by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought.

Visual aids improve diagnostic inferences and metacognitive judgment calibration.

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 healthrelevant numerical information while helping them assess the quality of their own risk comprehension.

Toward an ecological analysis of Bayesian inferences: how task characteristics influence responses.

In research on Bayesian inferences, the specific tasks, with their narratives and characteristics, are typically seen as exchangeable vehicles that merely transport the structure of the problem to research participants. In the present paper, we explore whether, and possibly how, task characteristics that are usually ignored influence participants' responses in these tasks. We focus on both quantitative dimensions of the tasks, such as their base rates, hit rates, and false-alarm rates, as well as qualitative characteristics, such as whether the task involves a norm violation or not, whether the stakes are high or low, and whether the focus is on the individual case or on the numbers. Using a data set of 19 different tasks presented to 500 different participants who provided a total of 1,773 responses, we analyze these responses in two ways: first, on the level of the numerical estimates themselves, and second, on the level of various response strategies, Bayesian and non-Bayesian, that might have produced the estimates. We identified various contingencies, and most of the task characteristics had an influence on participants' responses. Typically, this influence has been stronger when the numerical information in the tasks was presented in terms of probabilities or percentages, compared to natural frequencies - and this effect cannot be fully explained by a higher proportion of Bayesian responses when natural frequencies were used. One characteristic that did not seem to influence participants' response strategy was the numerical value of the Bayesian solution itself. Our exploratory study is a first step toward an ecological analysis of Bayesian inferences, and highlights new avenues for future research.

Chances and risks in medical risk communication.

Communication between physicians and patients in everyday life is marked by a number of disruptive factors. Apart from specific interests, mistakes, and misunderstandings on both sides, there are main factors that contribute to the risk in risk communication. Using the example of mammography screening, the current work demonstrates how the meaning of test results and the informative value of measures taken to reduce risk are often misunderstood. Finally, the current work provides examples of successful risk communication.

Societal perspectives on risk awareness and risk competence.

Medical risks can be assessed by objectifiable therapeutic features; however, these risks are also characterised to a considerable degree by individual and social values. People tend to strive towards both freedom as well as safety; in a medical context, these two aims are taken into account by shared decision-making models and by stricter regulations in the pharmaceutical sector. Media reports on medical risks are caught between providing information and economic interests, and this conflict particularly complicates rational discussions about unexpected risks (for instance, in the field of natural medicine). Thus, it is necessary to create the type of information culture which allows differentiating between real and less pronounced risks.

Natural frequencies facilitate diagnostic inferences of managers.

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in terms of probabilities or percentages. Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates. The present research replicates the beneficial effect of natural frequencies with four tasks from the domain of management, and with management students as well as experienced executives as participants. The percentage of Bayesian responses was almost twice as high when information was presented in natural frequencies compared to a presentation in terms of percentages. In contrast to most tasks previously studied, the majority of numerical responses were lower than the Bayesian solutions. Having heard of Bayes' rule prior to the study did not affect Bayesian performance. An implication of our work is that textbooks explaining Bayes' rule should teach how to represent information in terms of natural frequencies instead of how to plug probabilities or percentages into a formula.

Choice deferral can arise from absolute evaluations or relative comparisons.

When choosing among several options, people may defer choice for either of 2 reasons: because none of the options is good enough or because there is uncertainty regarding which is the best. These reasons form the basis of the 2-stage, 2-threshold (2S2T) framework, which posits that a different kind of processing corresponds to these 2 reasons for choice deferral: absolute evaluations and relative comparisons, respectively. Three experiments are reported in which each type of processing was triggered in different conditions either via different payoff structures or different degrees of attribute knowledge. The effects of the 3 main independent variables (the size of the choice set, the utility of the best option, and the number of competitive options) differed depending on the payoff structure or attribute knowledge conditions in ways predicted by the 2S2T framework. Implications for consumer decision making, marketing, and eyewitness identification are discussed.

Processes models, environmental analyses, and cognitive architectures: quo vadis quantum probability theory?

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.

Visual representation of statistical information improves diagnostic inferences in doctors and their patients.

Doctors and patients have difficulty inferring the predictive value of a medical test from information about the prevalence of a disease and the sensitivity and false-positive rate of the test. Previous research has established that communicating such information in a format the human mind is adapted to-namely natural frequencies-as compared to probabilities, boosts accuracy of diagnostic inferences. In a study, we investigated to what extent these inferences can be improved-beyond the effect of natural frequencies-by providing visual aids. Participants were 81 doctors and 81 patients who made diagnostic inferences about three medical tests on the basis of information about prevalence of a disease, and the sensitivity and false-positive rate of the tests. Half of the participants received the information in natural frequencies, while the other half received the information in probabilities. Half of the participants only received numerical information, while the other half additionally received a visual aid representing the numerical information. In addition, participants completed a numeracy scale. Our study showed three important findings: (1) doctors and patients made more accurate inferences when information was communicated in natural frequencies as compared to probabilities; (2) visual aids boosted accuracy even when the information was provided in natural frequencies; and (3) doctors were more accurate in their diagnostic inferences than patients, though differences in accuracy disappeared when differences in numerical skills were controlled for. Our findings have important implications for medical practice as they suggest suitable ways to communicate quantitative medical data.

The impact of affect on willingness-to-pay and desired-set-size.

What role does affect play in economic decision making? Previous research showed that the number of items had a linear effect on the willingness-to-pay for those items when participants were computationally primed, whereas participants' willingness-to-pay was insensitive to the amount when they were affectively primed. We extend this research by also studying the impact of affect on nonmonetary costs of waiting for items to be displayed and of screening them in a computer task. We assessed these costs by asking participants how many items they desired to see before making their selection. In our experiment, the effect of priming on desired-set-size was even larger than on willingness-to-pay, which can be explained by the fact that the nonmonetary costs, waiting time, were real, whereas willingness-to-pay was hypothetical. Participants also reported their satisfaction with the choosing process and the chosen items; no linear or nonlinear relationship was found between the self-determined desired-set-size and satisfaction.

Fast and frugal heuristics are plausible models of cognition: reply to Dougherty, Franco-Watkins, and Thomas (2008).

M. R. Dougherty, A. M. Franco-Watkins, and R. Thomas (2008) conjectured that fast and frugal heuristics need an automatic frequency counter for ordering cues. In fact, only a few heuristics order cues, and these orderings can arise from evolutionary, social, or individual learning, none of which requires automatic frequency counting. The idea that cue validities cannot be computed because memory does not encode missing information is misinformed; it implies that measures of co-occurrence are incomputable and would invalidate most theories of cue learning. They also questioned the recognition heuristic's psychological plausibility on the basis of their belief that it has not been implemented in a memory model, although it actually has been implemented in ACT-R (L. J. Schooler & R. Hertwig, 2005). On the positive side, M. R. Dougherty et al. discovered a new mechanism for a less-is-more effect. The authors of the present article specify minimal criteria for psychological plausibility, describe some genuine challenges in the study of heuristics, and conclude that fast and frugal heuristics are psychologically plausible: They use limited search and are tractable and robust.

Inferences under time pressure: how opportunity costs affect strategy selection.

Do the inference strategies people select depend on the magnitude of time pressure? Is this dependency modified by the type of time pressure? These questions are addressed in three experimental studies in which participants made inferences after having searched for information on a computerized information board. In Study 1, time pressure was induced indirectly by imposing opportunity costs of being slow, a form of time pressure that is common in daily life but that has rarely been examined in the literature. A simple lexicographic heuristic (LEX) achieved the best fit in predicting participants' inferences. Studies 2 and 3 induced high time pressure either indirectly by imposing opportunity costs in terms of time or directly by limiting the time for each choice. Regardless of how time pressure was induced, under high time pressure the inferences could be best predicted with LEX, whereas under low time pressure a weighted linear model that integrates all available information predicted the inferences best. We conclude that people select strategies adaptively depending on characteristics of the situation.

When one cue is not enough: combining fast and frugal heuristics with compound cue processing.

One-reason decision-making heuristics as proposed by Gigerenzer, Todd, and the ABC Research Group (1999) have been shown to perform accurately. However, such strategies cannot deal with compound cues. We propose the Take The Best Configural Cue (TTB-Configural) as a fast and frugal heuristic that processes compound cues. In a series of three experiments, we analysed whether participants used this heuristic when making cue-based inferences on which of two alternatives had a higher criterion value. In two of the experiments, two cues were amalgamated into a valid compound cue by applying the AND or the OR logical rule, respectively. In the third experiment, there was no valid compound cue. Within each experiment, we also manipulated causal mental models through instructions. In the configural causal model, cues were said to act through the same causal mechanism. In the elemental causal model, cues were said to act through different causal mechanisms. In the neutral causal model, the causal mechanism was not specified. When a highly valid compound existed, and participants had a configural causal model, for the majority of them the strategy that could best account for their choices was TTB-Configural. Otherwise, the strategy that best predicted their choices was the Take The Best (TTB) heuristic.

The role of representative design in an ecological approach to cognition.

Egon Brunswik argued that psychological processes are adapted to environmental properties. He proposed the method of representative design to capture these processes and advocated that psychology be a science of organism-environment relations. Representative design involves randomly sampling stimuli from the environment or creating stimuli in which environmental properties are preserved. This departs from systematic design. The authors review the development of representative design, examine its use in judgment and decision-making research, and demonstrate the effect of design on research findings. They suggest that some of the practical difficulties associated with representative design may be overcome with modern technologies. The importance of representative design in psychology and the implications of this method for ecological approaches to cognition are discussed.

How to keep children safe in traffic: find the daredevils early.

Crossing the street in front of oncoming vehicles poses serious danger to young children. But is each young pedestrian similarly at risk? The authors aimed to identify children who are particularly prone to making risky and potentially harmful crossing decisions. They used a simple game involving risk to classify 5- to 6-year-olds as risk takers or risk avoiders. Children classified as risk takers made more crossing decisions at a busy 1-way street than risk avoiders, tolerated shorter time intervals between initiation of the crossing decision and arrival of the next vehicle, and were more likely to cause a (hypothetical) accident. Finally, they made decisions more quickly than risk avoiders. The authors discuss the implication of these results for traffic safety programs.

Research on hindsight bias: a rich past, a productive present, and a challenging future.

In this introduction to the present issue, we give a brief description of the phenomenon. Subsequently, we discuss the major theoretical accounts, focusing on how these are related to the papers included in the issue.

Hindsight bias: how knowledge and heuristics affect our reconstruction of the past.

Once people know the outcome of an event, they tend to overestimate what could have been anticipated in foresight. Although typically considered to be a robust phenomenon, this hindsight bias is subject to moderating circumstances. In their meta-analysis, Christensen-Szalanski and Willham (1991) observed that the more experience people have with the task under consideration, the smaller is the resulting hindsight bias. This observation is one benchmark against which the explanatory power of process models of hindsight bias can be measured. Therefore, we used it to put the recently proposed RAFT model (Hoffrage, Hertwig, & Gigerenzer, 2000) to another test. Our findings were consistent with the "expertise effect." Specifically, we observed-using computer simulations of the RAFT model-that the more comprehensive people's knowledge is in foresight, the smaller is their hindsight bias. In addition, we made two counterintuitive observations: First, the relation between foresight knowledge and hindsight bias appears to be independent of how knowledge is processed. Second, even if foresight knowledge is false, it can reduce hindsight bias. We conclude with a discussion of the functional value of hindsight bias.