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ABSTRACTLearning the probabilities of multiple events from the environment is an important core competency of any organism. In our within‐participant experiment, participants experienced samples from two distributions, or prospects, each comprised of two to four events, and were required to provide simultaneous, rather than sequential, judgment of the likelihood of the complete set of observed events. Empirical calibration curves that map experienced probabilities to subjective probabilities reveal that the degree of underextremity (overestimation of low likelihood events and underestimation of high likelihood events) is strongly conditional on the number of judged events. We uncover two regularities conditional on the number of events that modify (a) the crossover points of the calibration curves with the identity line and (b) the gradient or sensitivity of probability judgments. We present a process model of elicited (subjective) probabilities that captures these empirical regularities. Experienced events recalled from memory may be erroneously attributed to the wrong events based on the similarity of event outcomes. We conclude that the observed miscalibration of probability judgments can be attributed to the noisy retrieval component of a rational process‐based decision model. We discuss the implications of our model for the conflicting empirical findings of overweighting and underweighting in the decisions from experience literature. Finally, we show that reliance on small samples can be an ecologically rational strategy for a bounded rational decision‐maker (subject to noisy recall), as aggregated subjective probabilities are closer to the ecological probabilities than the experienced (or sampled) probabilities are.

This paper examines the sensitivity of probability judgments pertaining to real-world events (e.g., the chance of getting a speeding ticket) to the events' time horizon (e.g., 1, 2, or 8 weeks) and performer characteristics (e.g., 1, 2, and 8 drivers). Using the participants' multiple responses to different time horizons and number of performers, we assessed the degree of deviance from the normative prescription and potential explanations for such deviance. In Study 1, two questionnaires were administered to a sample of 120 students. In the first questionnaire, in violation of the normative disjunctive model, most participants did not adjust probabilities sufficiently for various time horizons. This pattern cannot be attributed merely to regression to the mean with a fixed error term (Erev et al. 1994). In the second questionnaire, the same bias was replicated in scenarios featuring different numbers of individuals, indicating no time-specific contributing factors. In Study 2, a sample of 140 students responded to a computerized questionnaire in which the items preceding target questions were controlled. The direction of the deviance did not change as a function of previous items. The results are attributed to the "extension neglect" tendency (Kahneman 2003).

The Value of Studying Subjective Evaluations of Probability -- The True Subjective Probability Problem -- Subjective Probability: A Judgment of Representativeness -- The Psychological Concept of Subjective Probability: A Measurement-Theoretic View -- Are Subjective Probabilities Probabilities? -- On the Generalizability of Experimental Results -- Statistical Analysis: Theory Versus Practice -- A Selected Bibliography -- Author Index.

A one-of-a-kind resource on identifying and dealing with bias in statistical research on causal effects. Do cell phones cause cancer? Can a new curriculum increase student achievement? Determining what the real causes of such problems are, and how powerful their effects may be, are central issues in research across various fields of study. Some researchers are highly skeptical of drawing causal conclusions except in tightly controlled randomized experiments, while others discount the threats posed by different sources of bias, even in less rigorous observational studies. Bias and Causation pre

The RISK of an event generally relates to its expected severity and the perceived probability of its occurrence. In RISK research, however, there is no standard measure for subjective probability estimates. In this study, we compared five commonly used measurement formats—two rating scales, a visual analog scale, and two numeric measures—in terms of their ability to assess subjective probability judgments when objective probabilities are available. We varied the probabilities (low vs. moderate) and severity (low vs. high) of the events to be judged as well as the presentation mode of objective probabilities (sequential presentation of singular events vs. graphical presentation of aggregated information). We employed two complementary goodness‐of‐fit criteria: the correlation between objective and subjective probabilities (sensitivity), and the root mean square deviations of subjective probabilities from objective values (accuracy). The numeric formats generally outperformed all other measures. The severity of events had no effect on the performance. Generally, a rise in probability led to decreases in performance. This effect, however, depended on how the objective probabilities were encoded: pictographs ensured perfect information, which improved goodness of fit for all formats and diminished this negative effect on the performance. Differences in performance between scales are thus caused only in part by characteristics of the scales themselves—they also depend on the process of encoding. Consequently, researchers should take the source of probability information into account before selecting a measure.

AbstractIn cultivation research, differentiation is made between first- and second-order cultivation questions. However, their definition and relation remain unclear. This paper proposes a differentiation that focuses on the type of judgment underlying the respective cultivation questions. The former are frequency and probability judgments, while the latter are evaluative and address attitudes or values. Current theory in the field of cultivation research argues that these types of judgments are tied to on-line (second-order) and memory-based (first-order) processing. Based on psychological literature and a study on the cultivation of crime-related perceptions representative for the German population, we demonstrate that second-order judgments can also be built memory-based. Furthermore, we argue that the interrelation of first- and second-order judgments depends on whether judgments are built on-line or memory-based (especially in the case of second-order judgments). This may account for divergent empirical evidence in the field.

Persuasion (Aristotle) -- A truth resembling truth -- Probability or necessity -- Logos, topos, stoikheion -- Reflection (Heidegger) -- Breaking with the primacy of the theoretical -- The genesis of the theoretical -- Beyond theory: theoria, or watching over what is still to come -- Judgment (Arendt) -- The space of appearance -- The wind of thought -- A sense of the world

Substantiation can have an important effect on what interventions are pursued for children investigated for maltreatment, but researchers lack knowledge about how the decision to substantiate is made. Using information from 4,515 children from a national probability study of children investigated for maltreatment, this study examined how caseworker judgments of harm, risk, and evidence predicted substantiation. The substantiation rate was 29.9%, but the majority of cases were substantiated when caseworkers reported at least moderate harm, at least moderate risk, and/or probably to clearly sufficient evidence. Each judgment variable significantly predicted substantiation in a multivariable model, with evidence the strongest predictor. Child gender and age were significant predictors beyond harm, risk, and evidence, suggesting that other judgments also influence substantiation. In 9 of 100 cases, reports were not substantiated despite moderate to severe harm. Thus, substantiation is generally based on judgments of harm, risk, and evidence but not exclusively. The findings underline previous researchers' conclusions that substantiation is a flawed measure of child maltreatment and suggest that policy and practice related to substantiation are due for a fresh appraisal by state child welfare service agencies.

This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination process in practice. The role of experts is important because their judgments can provide valuable information, particularly in view of the limited availability of "hard data" regarding many important uncertainties in risk analysis. Because uncertainties are represented in terms of probability distributions in probabilistic risk analysis (PRA), we consider expert information in terms of probability distributions. The motivation for the use of multiple experts is simply the desire to obtain as much information as possible. Combining experts' probability distributions summarizes the accumulated information for risk analysts and decision‐makers. Procedures for combining probability distributions are often compartmentalized as mathematical aggregation methods or behavioral approaches, and we discuss both categories. However, an overall aggregation process could involve both mathematical and behavioral aspects, and no single process is best in all circumstances. An understanding of the pros and cons of different methods and the key issues to consider is valuable in the design of acombination process for a specific PRA. The output, a "combined probabilitydistribution," can ideally be viewed as representing a summary of the current state of expert opinion regarding the uncertainty of interest.