The probability—outcome correspondence principle: A dispositional view of the interpretation of probability statements (original) (raw)
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Individual differences in the perception of probability
PLOS Computational Biology, 2021
In recent studies of humans estimating non-stationary probabilities, estimates appear to be unbiased on average, across the full range of probability values to be estimated. This finding is surprising given that experiments measuring probability estimation in other contexts have often identified conservatism: individuals tend to overestimate low probability events and underestimate high probability events. In other contexts, repulsive biases have also been documented, with individuals producing judgments that tend toward extreme values instead. Using extensive data from a probability estimation task that produces unbiased performance on average, we find substantial biases at the individual level; we document the coexistence of both conservative and repulsive biases in the same experimental context. Individual biases persist despite extensive experience with the task, and are also correlated with other behavioral differences, such as individual variation in response speed and adjustment rates. We conclude that the rich computational demands of our task give rise to a variety of behavioral patterns, and that the apparent unbiasedness of the pooled data is an artifact of the aggregation of heterogeneous biases.
Affective and Cognitive Factors Influencing Sensitivity to Probabilistic Information
Risk Analysis, 2011
In study 1 different groups of female students were randomly assigned to one of four probabilistic information formats. Five different levels of probability of a genetic disease in an unborn child were presented to participants (within-subject factor). After the presentation of the probability level, participants were requested to indicate the acceptable level of pain they would tolerate to avoid the disease (in their unborn child), their subjective evaluation of the disease risk, and their subjective evaluation of being worried by this risk. The results of study 1 confirmed the hypothesis that an experience-based probability format decreases the subjective sense of worry about the disease, thus, presumably, weakening the tendency to overrate the probability of rare events. Study 2 showed that for the emotionally laden stimuli, the experience-based probability format resulted in higher sensitivity to probability variations than other formats of probabilistic information. These advantages of the experience-based probability format are interpreted in terms of two systems of information processing: the rational deliberative versus the affective experiential and the principle of stimulus-response compatibility.
Conceptions of probability: reality between a rock and a hard place
1983
How do people's theories of uncertainty differ from formal theories of probability? As an introduction to an investigation of this question, brief reviews were provided of a) various schools of thought within the science of probability, and b) research which has tried to determine how consistent people ' s behavior is with that prescribed by formal theories. While much of the research has suggested that, in many respects, people are poor intuitive statisticians, little has been said of how people actually arrive at probabilistic judgments. More recent research which has attempted to describe the strategies or heuristics that are used in reasoning about uncertainty have inferred reasoning processes from group performance on questionnaire items. This investigation employed a more direct methodology: Sixteen undergraduates were interviewed and instructed to "think aloud" as they solved several word problems which required probabilistic judgments. Videotapes of the interviews were analyzed, and a model of probabilistic reasoning was developed and described as an "outcome approach" to uncertainty. According to the outcome approach, the goal in questions of uncertainty is to predict the outcome of an event. Since the primary focus is on an individual trial (as opposed to a sample), predictions take the form of yes or no decisions of whether an outcome will occur on a particular trial. These predictions are then evaluated, after-the-fact, as having been either right or wrong. Moreover, rather than employing a chance or "black-box" model of uncertainty, outcome-oriented individuals often arrive at predictions by identifying factors that are believed to cause or inhibit certain outcomes The validity of the outcome approach was supported with correlational evidence based on coded portions of the interviews and with reportage of interview segments. In addition, predictions were made of how outcome-oriented subjects would respond to a different set of questions. These predictions were verified in a second set of interviews with 12 of the original subjects. While the outcome approach was described as being inconsistent in several respects with formal theories of probability, it was portrayed as being internally consistent and valid in the context of everyday decision-making. vii
Dispositions, 1978
The propensity interpretation poses an intriguing alternative to the frequency definition for the explication of probability as a physical magnitude. It is intended to provide an explicitly dispositional account of this concept within the context of statistical laws. First systematically advocated by Karl Popper, it has been endorsed-in one form or another-by Ian Hacking and D. H. Mellor, among others. The purpose of this paper is, first, to distinguish two rather different formulations of the propensity construct (which we shall refer to as the 'Iong run' and 'single case' concepts); second, to explain away some oftheobjections that, primafacie, might be thought to undermine an explication of this kind; and, third, to analyze the inadequacies of a single case dispositional account that fails to take seriously the concept of probability as a statistical disposition. According to Karl Popper, probabilities are "unobservable dispositional properties ofthe physical world."l These properties are envisioned as belonging to specifiable sets of conditions, which may be referred to as 'experimental arrangements' or as 'chance set-ups'. They are dispositional in the sense of being tendencies to display particular patterns of response under appropriate test conditions. As Popper explains it, Every experimental arrangement is liable to prodace, if we repeat the experiment very often, a sequence with frequencies which depend upon this partictilar experimental arrangement. These virtual frequencies (themselves) may be caIled probabilities. But since these probabilities turn out to depend upon the experimental arrangement, they may be looked upon as properties 01 this arrtlllgement. '11Iey cluJracterize the disposltlo", or the propenslty, of the experimental arrangement to give rise to certain characteristic frequencies when the experiment Is olte" repeated. I This passage thus suggests that probabilities should be conceived as dispositional tendencies for experimental arrangements to generate certain outcomes with characteristic relative frequencies during long runs of experiments.
Judging the likelihood of future events: The role of anticipated affect
The desirability bias explains that desirable events are judged as more likely to occur. Lench (2009) paired positive affect to a white car image and found higher likelihood ratings for the white car, supporting the desirability bias. In this study, participants (N=90) anticipated watching a valenced video (positive, negative, or neutral), viewed a series of neutral images (including a white car image), then rated the likelihood of owning a white car. The “buffer hypothesis” suggests that anticipation of a negative event (i.e., a negative video) would infuse current experiences (owning a white car) with positive affect so that these experiences would be rated as more likely to occur, supporting the desirability bias. Although this effect was not found, significant correlations reveal a positive relationship between feelings towards white cars and likelihood of owning a white car. It is suggested that anticipation decreased congruency between these variables.
Organizational Behavior and Human Decision Processes, 1999
Verbal phrases denoting uncertainty are of two kinds: positive, suggesting the occurrence of a target outcome, and negative, drawing attention to its nonoccurrence (Teigen & Brun, 1995). This directionality is correlated with, but not identical to, high and low p values. Choice of phrase will in turn influence predictions and decisions. A treatment described as having "some possibility" of success will be recommended, as opposed to when it is described as "quite uncertain," even if the probability of cure referred to by these two expressions is judged to be the same (Experiment 1). Individuals who formulate their chances of achieving a successful outcome in positive terms are supposed to make different decisions than individuals who use equivalent, but negatively formulated, phrases . Finally, negative phrases lead to fewer conjunction errors in probabilistic reasoning than do positive phrases (Experiment 4). For instance, a combination of 2 "uncertain" outcomes is readily seen to be "very uncertain." But positive phrases lead to fewer disjunction errors than do negative phrases. Thus verbal probabilistic phrases differ from numerical probabilities not primarily by being more "vague," but by suggesting more clearly the kind of inferences that should be drawn. ᭧
Psychonomic Bulletin & Review, 2001
What do people regard as an informative and valuable probability statement? This article reports four experiments that show participants to have a clear preference for more extreme and higher probabilities over less extreme and lower ones. This pattern emerged in Experiment 1, in which no context was provided, and was further explored in Experiment 2 within a positive and a negative context. The findings were further confirmed in Experiment 3, which employed a Bayesian framework with revisions of opinions. Finally, Experiment 4 showed how preference for high probabilities can lead people to prefer an overconfident to a more well-calibrated (accurate) forecaster. The results are interpreted as manifestations of a search for definitive predictions principle, which asserts that high probabilities are preferred to medium ones and often favored over the corresponding complementary low probabilities on the basis of their capacity to predict the occurrence of single outcomes.
Journal of Behavioral …, 1997
demonstrated that over-and undercon®dence can be observed simultaneously in judgment studies, as a function of the method used to analyze the data. They proposed a general model to account for this apparent paradox, which assumes that overt responses represent true judgments perturbed by random error. To illustrate that the model reproduces the pattern of results, they assumed perfectly calibrated true opinions and a particular form (log-odds plus normally distributed error) of the model to simulate data from the full-range paradigm. In this paper we generalize these results by showing that they can be obtained with other instantiations of the same general model (using the binomial error distribution), and that they apply to the half-range paradigm as well. These results illustrate the robustness and generality of the model. They emphasize the need for new methodological approaches to determine whether observed patterns of over-or undercon®dence represent real eects or are primarily statistical artifacts.