The impact of problem domain on Bayesian inferences: A systematic investigation.

Sparse (and occasionally contradictory) evidence exists regarding the impact of domain on probabilistic updating, some of which suggests that Bayesian word problems with medical content may be especially challenging. The present research aims to address this gap in knowledge through three pre-registered online studies, which involved a total of 2,238 participants. Bayesian word problems were related to one of three domains: medical, daily-life, and abstract. In the first two cases, problems presented realistic content and plausible numerical information, while in the latter, problems contained explicitly imaginary elements. Problems across domains were matched in terms of all relevant statistical values and, as much as possible, wording. Studies 1 and 2 utilized the same set of problems, but different response elicitation methods (i.e., an open-ended and a multiple-choice question, respectively). Study 3 involved a larger number of participants per condition and a smaller set of problems to more thoroughly investigate the magnitude of differences between the domains. There was a generally low rate of correct responses (17.2%, 17.4%, and 14.3% in Studies 1, 2, and 3, respectively), consistent with accuracy levels commonly observed in the literature for this specific task with online samples. Nonetheless, a small but significant difference between domains was observed: participants' accuracy did not differ between medical and daily-life problems, while it was significantly higher in corresponding abstract problems. These results suggest that medical problems are not inherently more difficult to solve, but rather that performance is improved with abstract problems for which participants cannot draw from their background knowledge.

Sensory and multisensory reasoning: Is Bayesian updating modality-dependent?

Bayesianism assumes that probabilistic updating does not depend on the sensory modality by which information is processed. In this study, we investigate whether probability judgments based on visual and auditory information conform to this assumption. In a series of five experiments, we found that this is indeed the case when information is acquired through a single modality (i.e., only auditory or only visual) but not necessarily so when it comes from multiple modalities (i.e., audio-visual). In the latter case, judgments prove more accurate when both visual and auditory information individually support (i.e., increase the probability of) the hypothesis they also jointly support (synergy condition) than when either visual or auditory information support one hypothesis that is not the one they jointly support (contrast condition). In the extreme case in which both visual and auditory information individually support an alternative hypothesis to the one they jointly support (i.e., double-contrast condition), participants' accuracy is not only lower than in the synergy condition but near chance. This synergy-contrast effect represents a violation of the assumption that information modality is irrelevant for Bayesian updating and indicates an important limitation of multisensory integration, one which has not been previously documented.

Nudging COVID-19 Vaccine Uptake by Changing the Default: A Randomized Controlled Trial.

BACKGROUND: Although vaccination against SARS-CoV-2 is considered the central strategy against the pandemic, uptake lags behind target rates. METHOD: To explore whether this rate could be enhanced by a nudging strategy that exploits the status quo bias, we conducted a randomized controlled trial in northern Italy comparing vaccination acceptance among 2000 adults, ages 50 to 59 years, who were either invited to set an appointment (opt-in group) or assigned an individual appointment (opt-out group). RESULTS: Results indicate a difference of 3.2 percentage points, which represents a 32% relative increase in the vaccination rate for the opt-out group compared with the opt-in group. CONCLUSIONS: A significant portion of those who remain unvaccinated may not hold strong beliefs against vaccination but rather tend to inaction and may therefore be nudged toward vaccination with a reduction of action required. HIGHLIGHTS: Reluctant adults (50-59 years), who had not yet received vaccines against COVID-19, were sent letters announcing appointment availabilityIn an RCT, the status quo option in the notices influenced the rate of vaccine acceptanceNudging via pre-scheduled appointments encouraged vaccine uptake more than invitations to schedule didSwitching the default option yielded a 32% relative increase (13.1% vs. 9.9%) in vaccination.

Interpolating causal mechanisms: The paradox of knowing more.

Causal knowledge is not static; it is constantly modified based on new evidence. The present set of seven experiments explores 1 important case of causal belief revision that has been neglected in research so far: causal interpolations. A simple prototypic case of an interpolation is a situation in which we initially have knowledge about a causal relation or a positive covariation between 2 variables but later become interested in the mechanism linking these 2 variables. Our key finding is that the interpolation of mechanism variables tends to be misrepresented, which leads to the paradox of knowing more: The more people know about a mechanism, the weaker they tend to find the probabilistic relation between the 2 variables (i.e., weakening effect). Indeed, in all our experiments we found that, despite identical learning data about 2 variables, the probability linking the 2 variables was judged higher when follow-up research showed that the 2 variables were assumed to be directly causally linked (i.e., C→E) than when participants were instructed that the causal relation is in fact mediated by a variable representing a component of the mechanism (M; i.e., C→M→E). Our explanation of the weakening effect is that people often confuse discoveries of preexisting but unknown mechanisms with situations in which new variables are being added to a previously simpler causal model, thus violating causal stability assumptions in natural kind domains. The experiments test several implications of this hypothesis. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

The Effect of Evidential Impact on Perceptual Probabilistic Judgments.

In a series of three behavioral experiments, we found a systematic distortion of probability judgments concerning elementary visual stimuli. Participants were briefly shown a set of figures that had two features (e.g., a geometric shape and a color) with two possible values each (e.g., triangle or circle and black or white). A figure was then drawn, and participants were informed about the value of one of its features (e.g., that the figure was a "circle") and had to predict the value of the other feature (e.g., whether the figure was "black" or "white"). We repeated this procedure for various sets of figures and, by varying the statistical association between features in the sets, we manipulated the probability of a feature given the evidence of another (e.g., the posterior probability of hypothesis "black" given the evidence "circle") as well as the support provided by a feature to another (e.g., the impact, or confirmation, of evidence "circle" on the hypothesis "black"). Results indicated that participants' judgments were deeply affected by impact, although they only should have depended on the probability distributions over the features, and that the dissociation between evidential impact and posterior probability increased the number of errors. The implications of these findings for lower and higher level cognitive models are discussed.

Public's understanding of swab test results for SARS-CoV-2: an online behavioural experiment during the April 2020 lockdown.

OBJECTIVE: Although widespread testing for SARS-CoV-2 is in place, little is known about how well the public understands these results. We aimed to provide a comprehensive overview of the general public's grasp of the accuracy and significance of the results of the swab test. DESIGN: Web-based behavioural experiment. SETTING: Italy during the April 2020 lockdown. PARTICIPANTS: 566 Italian residents. MAIN OUTCOME MEASURES: Participants' estimates of the SARS-CoV-2 prevalence; the predictive and diagnostic accuracy of the test; the behavioural impact of (positive vs negative) test results; the perceived usefulness of a short-term repetition of the test following positive or negative results; and rankings of causes for false positives and false negatives. RESULTS: Most participants considered the swab test useful (89.6%) and provided predictive values consistent with their estimates of test diagnostic accuracy and infection prevalence (67.0%). Participants acknowledged the effects of symptomatic status and geographical location on prevalence (all p<0.001) but failed to take this information into account when estimating the positive or negative predictive value. Overall, test specificity was underestimated (91.5%, 95% CI 90.2% to 92.8%); test sensitivity was overestimated (89.7%, 95% CI 88.3% to 91.0%). Positive results were evaluated as more informative than negative ones (91.6, 95% CI 90.2 to 93.1 and 41.0, 95% CI 37.9 to 44.0, respectively, p<0.001); a short-term repetition of the test was considered more useful after a positive than a negative result (62.7, 95% CI 59.6 to 65.7 and 47.2, 95% CI 44.4 to 50.0, respectively, p=0.013). Human error and technical characteristics were assessed as more likely to be the causes of false positives (p<0.001); the level of the viral load as the cause of false negatives (p<0.001). CONCLUSIONS: While some aspects of the swab for SARS-CoV-2 are well grasped, others are not and may have a strong bearing on the general public's health and well-being. The obtained findings provide policymakers with a detailed picture that can guide the design and implementation of interventions for improving efficient communication with the general public as well as adherence to precautionary behaviour.

The challenge of mental simulation in preference-sensitive treatment decisions.

This commentary discusses the importance for preference-sensitive treatment decisions of episodic future thinking, which is the capacity to mentally simulate and pre-experience what might occur in one's personal future. Our aim is to call attention to this important topic since patients confronted with preference-sensitive treatment decisions could benefit from professional support that promotes the construction of comprehensive and detailed mental simulations of what might affect their future well-being and satisfaction.

Fostering the Understanding of Positive Test Results.

Background: The majority of health-service users seem unable to properly compute the positive predictive value of medical tests. The research reported in the present study sought to investigate whether, and to what extent, probabilistic inferences about a positive test result can be improved by changing the traditional way in which probability judgments are elicited and medical information is presented. Methods: Online survey respondents were presented with a positive test result regarding a pregnant woman, and had to estimate the chances that her unborn baby had an anomaly (standard judgment), to apportion the numbers of chances for and against this hypothesis (distributive judgment), and to indicate whether the hypothesis that the baby had an anomaly was more or less likely than its alternative (relative judgment). Test sensitivity and information framing were also manipulated. Results: Irrespective of education and to some extent of numeracy, the majority of respondents produced correct distributive assessments of chances, which were in line with relative judgments and more accurate than standard ones. When information displayed exclusively positive test results, inferences resulted further improved and unaffected by test sensitivity. Conclusions: Simple communication strategies that prompt extensional reasoning on the relevant set of number of chances can help individuals to overcome probabilistic inference errors.

Mind the gap: Physicians' assessment of patients' importance weights in localized prostate cancer.

BACKGROUND: The management of localized prostate cancer is challenging because of the many therapeutic options available, none of which is generally acknowledged as superior to the others in every respect. The selection of the most appropriate treatment should therefore reflect patients' preferences. OBJECTIVE: The purpose of the following study was to pilot a new approach for investigating whether urologists who had previously provided patients with therapeutic advice actually knew their patients' importance weights concerning the relevant aspects of the treatments at issue. METHOD: Participants were patients recently diagnosed with localized prostate cancer (n = 20), urologists (n = 10), and non-medical professionals (architects, n = 10). These last served as a control group for the urologists and were matched to them for age and gender. Patients' importance weights were elicited by two standard methods (Direct Rating and Value Hierarchy). Each urologist was asked to estimate (with Direct Rating) his/her patient's importance weights. The same task was performed by a corresponding architect, who never met the patient and knew only the patient's age. Univariate and bivariate statistical analyses were performed to investigate the association between importance weights as elicited from patients and as estimated by urologists and architects, as well as to assess whether such agreement was attribute-dependent. RESULTS: Participants found both elicitation methods easy to use. The correlation between patients' actual importance weights and urologists' estimates was poor and comparable to that obtained between patients and architects. This result did not depend on the attribute considered, with the sole exception of the attribute "Effectiveness in curing the cancer", which was evaluated as the most important attribute by the majority of participants. CONCLUSION: These findings demonstrate the feasibility of the employed methodology and highlight the need to support preference-sensitive decisions in clinical practice by facilitating the elicitation of patients' importance weights, as well as their communication to physicians.

Double Conjunction Fallacies in Physicians' Probability Judgment.

We report the first empirical data showing a significant amount of double conjunction fallacies in physicians' probability judgments concerning prognosis and diagnosis. Our results support the hypothesis that physicians' probability judgments are guided by assessments of evidential impact between diagnostic conditions and clinical signs. Moreover, we show that, contrary to some influential views, double conjunction fallacies represent an experimentally replicable reasoning bias. We discuss how the phenomenon eludes major current accounts of uncertain reasoning in medicine and beyond and how it relates to clinical practice.

Generalized Information Theory Meets Human Cognition: Introducing a Unified Framework to Model Uncertainty and Information Search.

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma-Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism.

Children's quantitative Bayesian inferences from natural frequencies and number of chances.

Zhu and Gigerenzer (2006) showed that an appreciable number of Chinese children aged between 9 and 12years old made correct quantitative Bayesian inferences requiring the integration of priors and likelihoods as long as they were presented with numerical information phrased in terms of natural frequencies. In this study, we sought to replicate this finding and extend the investigation of children's Bayesian reasoning to a different numerical format (chances) and other probability questions (distributive and relative). In Experiment 1, a sample of Italian children was presented with the natural frequency version of five Bayesian inference problems employed by Zhu and Gigerenzer (2006), but only a tiny minority of them were able to produce correct responses. In Experiment 2, we found that the children's accuracy, as well as the coherence between their probability judgments, depended on the type of question but not on the format (natural frequency vs. chance) in which information was presented. We conclude that children's competence in drawing quantitative Bayesian inferences is lower than suggested by Zhu and Gigerenzer (2006) and, similarly to what happens with adults, it relies more on a problem representation that fosters an extensional evaluation of possibilities than on a specific numerical format.

Another chance for good reasoning.

Disagreement on the "probability status" of chances casts doubt on Girotto and Gonzalez's (2001) conclusion that the human mind can make sound Bayesian inferences involving single-event probabilities. The main objection raised has been that chances are de facto natural frequencies disguised as probabilities. In the present study, we empirically demonstrated that numbers of chances are perceived as being distinct from natural frequencies and that they have a facilitatory effect on Bayesian inference tasks that is completely independent from their (minor) frequentist readings. Overall, therefore, our results strongly disconfirm the hypothesis that natural frequencies are a privileged cognitive representational format for Bayesian inferences and suggest that a significant portion of laypeople adequately handle genuine single-event probability problems once these are rendered computationally more accessible by using numbers of chances.

Judging the Probability of Hypotheses Versus the Impact of Evidence: Which Form of Inductive Inference Is More Accurate and Time-Consistent?

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability.

Noisy probability judgment, the conjunction fallacy, and rationality: Comment on Costello and Watts (2014).

According to Costello and Watts (2014), probability theory can account for key findings in human judgment research provided that random noise is embedded in the model. We concur with a number of Costello and Watts's remarks, but challenge the empirical adequacy of their model in one of their key illustrations (the conjunction fallacy) on the basis of recent experimental findings. We also discuss how our argument bears on heuristic and rational thinking.

Corpus-based estimates of word association predict biases in judgment of word co-occurrence likelihood.

This paper draws a connection between statistical word association measures used in linguistics and confirmation measures from epistemology. Having theoretically established the connection, we replicate, in the new context of the judgments of word co-occurrence, an intriguing finding from the psychology of reasoning, namely that confirmation values affect intuitions about likelihood. We show that the effect, despite being based in this case on very subtle statistical insights about thousands of words, is stable across three different experimental settings. Our theoretical and empirical results suggest that factors affecting traditional reasoning tasks are also at play when linguistic knowledge is probed, and they provide further evidence for the importance of confirmation in a new domain.

Why quantum probability does not explain the conjunction fallacy.

We agree with Pothos & Busemeyer (P&B) that formal tools can be fruitfully employed to model human judgment under uncertainty, including well-known departures from principles of classical probability. However, existing findings either contradict P&B's quantum probability approach or support it to a limited extent. The conjunction fallacy serves as a key illustration of both kinds of problems.

On the determinants of the conjunction fallacy: probability versus inductive confirmation.

Major recent interpretations of the conjunction fallacy postulate that people assess the probability of a conjunction according to (non-normative) averaging rules as applied to the constituents' probabilities or represent the conjunction fallacy as an effect of random error in the judgment process. In the present contribution, we contrast such accounts with a different reading of the phenomenon based on the notion of inductive confirmation as defined by contemporary Bayesian theorists. Averaging rule hypotheses along with the random error model and many other existing proposals are shown to all imply that conjunction fallacy rates would rise as the perceived probability of the added conjunct does. By contrast, our account predicts that the conjunction fallacy depends on the added conjunct being perceived as inductively confirmed. Four studies are reported in which the judged probability versus confirmation of the added conjunct have been systematically manipulated and dissociated. The results consistently favor a confirmation-theoretic account of the conjunction fallacy against competing views. Our proposal is also discussed in connection with related issues in the study of human inductive reasoning.

Updating: learning versus supposing.

Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event A after learning B should equal the conditional probability of A given B prior to learning B. We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial differences between the conditional probability of an event A supposing an event B compared to the probability of A after having learned B. Specifically, supposing B appears to have less impact on the credibility of A than learning that B is true.