Directional verbal probabilities: inconsistencies between preferential judgments and numerical meanings

Verbal probability expressions (e.g., it is possible or doubtful) convey not only vague numerical meanings (i.e., probability) but also semantic functions, called directionality. We performed two experiments to examine whether preferential judgments are consistent with numerical meanings of verbal probabilities regardless of directionality. The results showed that because of the effects of directionality, perceived degrees of certainty for verbal probabilities differed between a binary choice and a numerical translation (Experiment 1), and decisions based on a verbal probability do not correspond to those based on a numerical translation for verbal probabilities (Experiment 2). These findings suggest that directionality of verbal probabilities is an independent feature from numerical meanings; hence numerical meanings of verbal probability alone remain insufficient to explain the effects of directionality on preferential judgments.     

A possible basis for conservatism in signal detection and probabilistic categorization tasks

It is commonly claimed that conservative placement of the criterion in signal detection is due to the form of the utility function of money, to conservatism in the estimation of prior probabilities, or to probability matching tendencies. This article shows how conservatism could be caused by a systematic misconception of the shape of the underlying distributions. An experiment is described in which subjects were asked to make posterior probability judgments after performing numerical analogues of signal detection. The posterior probability judgments were radical, i.e., high posterior probabilities were overestimated and low posterior probabilities were underestimated; if this pattern of radical probability estimation reflects the subjects’ understanding of the underlying distributions, it would account for conservative criterion placement.     

The Influence of Positive Affect on the Decision Rule in Risk Situations: Focus on Outcome (and Especially Avoidance of Loss) Rather Than Probability

Two experiments examined the influence of positive affect on probability estimation and choice. Participants in whom positive affect had been induced, as well as no-manipulation controls, were asked to make both numerical evaluations of verbal probabilities in three-outcome gambles and actual betting decisions about similar gambles. Results from Experiment 1 showed the phenomenon labeledcautious optimism:Positive affect participants significantly overestimated the probabilities associated with phrases for winning relative to their estimates of probability of losing for the same phrases (optimism), while participants in a control condition did not; yet, in actual gambling situations, affect condition participants were much less likely to gamble than were controls when a real loss was possible (caution). Results of the betting task from Experiment 2 further indicated that affect participants used a betting-decision rule that was different from that of controls: They bet less than controls in gambles where potential losses were large, even though probability of loss was small, and they bet more than controls in gambles where the amount of the potential loss was small, even though the probability of loss was moderate or large. These findings suggest that positive affect can promote an overt shift from a decision rule focusing primarily on probabilities to one focusing on utilities or outcome values, especially for losses. Taken together, the results are compatible with an interpretation of the influence of positive affect in terms of an elaboration of positive cognitive material, and purposive behavior in decisions, rather than in terms of mere response bias.     

The mere exposure effect is sensitive to color information: evidence for color effects in a perceptual implicit memory test

Priming effects in perceptual tests of implicit memory are assumed to be perceptually specific. Surprisingly, changing object colors from study to test did not diminish priming in most previous studies. However, these studies used implicit tests that are based on object identification, which mainly depends on the analysis of the object shape and therefore operates color-independently. The present study shows that color effects can be found in perceptual implicit tests when the test task requires the processing of color information. In Experiment 1, reliable color priming was found in a mere exposure design (preference test). In Experiment 2, the preference test was contrasted with a conceptually driven color-choice test. Altering the shape of object from study to test resulted in significant priming in the color-choice test but eliminated priming in the preference test. Preference judgments thus largely depend on perceptual processes. In Experiment 3, the preference and the color-choice test were studied under explicit test instructions. Differences in reaction times between the implicit and the explicit test suggest that the implicit test results were not an artifact of explicit retrieval attempts. In contrast with previous assumptions, it is therefore concluded that color is part of the representation that mediates perceptual priming.     

Subjective probabilities and moral judgments

The two experiments reported here examined the relationship between subjective probability estimates and moral judgments (credit and blame assignment, trait attributions, and behavior evaluations). Subjects read about situations that varied in outcome valence (moral or immoral); in addition, the nature of situational demands (Experiment 1) or behavior frequency (Experiment 2) was varied. In the first experiment, subjective probabilities were related to judgments of immoral behaviors (but not moral behaviors), whereas the situational demands only had an impact on judgments of moral behaviors. Experiment 2 included a wider range of behavioral situations, and the probability estimates and moral judgments were assessed independently. In contrast to the first experiment, subjective probabilities were related to trait and behavior ratings of both moral and immoral acts. Consistent with the first experiment, however, subjective probabilities predicted blame but not credit. Across both studies, the prior expectancies were more strongly related to evaluations of immoral acts than moral acts. Implications for understanding the determinants of judgments of moral and immoral acts are discussed.     

Blushing-fearful individuals overestimate the costs and probability of their blushing

It has been proposed that blushing-fearful individuals overestimate both the probability and the interpersonal costs of blushing. To study these judgmental biases, we presented a treatment-seeking sample of blushing-fearful individuals a series of vignettes describing social events and tested whether this clinical sample would overestimate the costs and probability of blushing compared to non-fearful controls. To test if blushing-fearfuls overestimate and/or low-fearful individuals underestimate the cost of displaying a blush, a second experiment examined the effects of blushing in these situations on observers' judgments. Experiment 1 showed that blushing-fearfuls indeed have judgmental biases for the probability and costs of blushing. Experiment 2 showed that the observers' judgments were very similar to the judgments anticipated by the low-fear group in Experiment 1. Thus the judgmental biases that were evident in the high-fearfuls can be best interpreted as an overestimation of the social costs of displaying a blush. These findings help improving our understanding of the mechanisms that may drive blushing phobia and also point to the clinical implication that it might be worthwhile to challenge blushing-fearfuls' judgmental biases.     

The conscious, the unconscious, and familiarity

This article examines the role of subjective familiarity in the implicit and explicit learning of artificial grammars. Experiment 1 found that objective measures of similarity (including fragment frequency and repetition structure) predicted ratings of familiarity, that familiarity ratings predicted grammaticality judgments, and that the extremity of familiarity ratings predicted confidence. Familiarity was further shown to predict judgments in the absence of confidence, hence contributing to above-chance guessing. Experiment 2 found that confidence developed as participants refined their knowledge of the distribution of familiarity and that differences in familiarity could be exploited prior to confidence developing. Experiment 3 found that familiarity was consciously exploited to make grammaticality judgments including those made without confidence and that familiarity could in some instances influence participants' grammaticality judgments apparently without their awareness. All 3 experiments found that knowledge distinct from familiarity was derived only under deliberate learning conditions. The results provide decisive evidence that familiarity is the essential source of knowledge in artificial grammar learning while also supporting a dual-process model of implicit and explicit learning.     

Contrasting stochastic and support theory accounts of subadditivity

Numerous studies have found that likelihood judgment typically exhibits subadditivity in which judged probabilities of events are less than the sum of judged probabilities of constituent events. Whereas traditional accounts of subadditivity attribute this phenomenon to deterministic sources, this paper demonstrates both formally and empirically that subadditivity is systematically influenced by the stochastic variability of judged probabilities. First, making rather weak assumptions, we prove that regressive error (or variability) in mapping covert probability judgments to overt responses is sufficient to produce subadditive judgments. Experiments follow in which participants provided repeated probability estimates. The results support our model assumption that stochastic variability is regressive in probability estimation tasks and show the contribution of such variability to subadditivity. The theorems and the experiments focus on within-respondent variability, but most studies use between-respondent designs. Numerical simulations extend the work to contrast within- and between-respondent measures of subadditivity. Methodological implications of all the results are discussed, emphasizing the importance of taking stochastic variability into account when estimating the role of other factors (such as the availability bias) in producing subadditive judgments.     

A theory of belief

A theory of belief is presented in which uncertainty has two dimensions. The two dimensions have a variety of interpretations. The article focusses on two of these interpretations.The first is that one dimension corresponds to probability and the other to “definiteness,” which itself has a variety of interpretations. One interpretation of definiteness is as the ordinal inverse of an aspect of uncertainty called “ambiguity” that is often considered important in the decision theory literature. (Greater ambiguity produces less definiteness and vice versa.) Another interpretation of definiteness is as a factor that measures the distortion of an individual's probability judgments that is due to specific factors involved in the cognitive processing leading to judgments. This interpretation is used to provide a new foundation for support theories of probability judgments and a new formulation of the “Unpacking Principle” of Tversky and Koehler.The second interpretation of the two dimensions of uncertainty is that one dimension of an event A corresponds to a function that measures the probabilistic strength of A as the focal event in conditional events of the form A|B, and the other dimension corresponds to a function that measures the probabilistic strength of A as the context or conditioning event in conditional events of the form C|A. The second interpretation is used to provide an account of experimental results in which for disjoint events A and B, the judge probabilities of A|(A∪B) and B|(A∪B) do not sum to 1.The theory of belief is axiomatized qualitatively in terms of a primitive binary relation ? on conditional events. (A|B?C|D is interpreted as “the degree of belief of A|B is greater than the degree of belief of C|D.”) It is shown that the axiomatization is a generalization of conditional probability in which a principle of conditional probability that has been repeatedly criticized on normative grounds may fail.Representation and uniqueness theorems for the axiomatization demonstrate that the resulting generalization is comparable in mathematical richness to finitely additive probability theory.     

Effects of context on recollection and familiarity experiences are task dependent

The influence of test context on reports of recollection and familiarity depends on how these subjective recognition experiences are conceptualized and measured. Bodner and Lindsay (2003) found that critical items elicited more remember judgments but fewer know judgments in a less (vs. more) memorable context. In contrast, Tousignant and Bodner (2012) found that independent ratings of recollection and familiarity were both higher in a less memorable context. We replicated the dissociative pattern with judgments using recollect/familiar labels (Experiment 1), and in a novel R/F/B task that added a “both” option to eliminate the mutual exclusivity between the recollect and familiar options (Experiment 2). Adding a “guess” option eliminated these context effects (Experiment 3), however whether allowing guesses “cleans up” or “desensitizes” recollection and familiarity judgments remains unclear. Determining which task variants provide appropriate measures of subjective recognition experiences will require an examination of additional dissociations and triangulation with other measures.     

Understanding conjunction effects in probability judgments: the role of implicit mental models

Subjective probability judgments often violate a normative principle in that the conjunction of two events is judged to be more likely than the probability of either of the two events occurring separately. Most previous explanations of these conjunction effects have assumed that probability judgments depend on some psychological relation (e.g. representativeness) between the constituents mentioned explicitly in the stimulus information. In contrast, the present approach highlights the fundamental role of implicitly inferred information. Participants are assumed to transform the explicit stimulus information into implicit mental models in their attempt to make sense of the experimental task. Probability judgments should then reflect the degree of activation of such a mental model in memory given a set of propositions, rather than the quantitative fit or likelihood of the propositions themselves. Two studies are reported which provide converging evidence for the proposed mental model approach. In the first study, using graded conjunctions of one to five propositions, probability judgments are shown to vary as a function of the activation of a mental model rather than the likelihood of the component events. In a second study, a priming procedure is employed to activate mental models that either fit an event conjunction or do not, leading to an increase or decrease of conjunction effects in probability judgment. Copyright © 1999 John Wiley & Sons, Ltd.     

A cognitive‐emotional account of the shape of the probability weighting function

Research has shown a tendency of decision makers to overweight small probabilities and to underweight moderate and large probabilities. In standard treatments this is graphically modeled by an inverse S‐shaped probability weighting function. We suggest that emotions play a significant role in the shaping of the probability weighting function. In particular, the weighting function is proposed to be some function of objective probability, expected elation, and expected disappointment. The overweighting of small probabilities results from the anticipated elation after having won, given that winning was very unlikely. The underweighting of large probabilities results from anticipated disappointment after having failed to win, given that winning was very likely. Hence, probability is assumed to influence utility. Three experiments investigate these hypotheses. Experiments 1 and 2 show that a convex function relates probability to surprise. Experiment 3 elicits choice data and further supports the proposed hypotheses. The model adds to the understanding of the cognitive and emotional processes underlying the shape of the probability weighting function. Copyright © 2002 John Wiley & Sons, Ltd.     

Felt dispensability in groups of coactors: The effects of shared responsibility and explicit anonymity on cognitive effort

The study reported here tests the effects of explicit anonymity and shared responsibility on cognitive effort. In Experiment 1, ninety-nine undergraduate students participated in a multiattribute judgment task, and math models of their judgments were constructed. Results showed that students who believed the responsibility for the judgment task was shared by 15 others used less complex judgment strategies than single judges or judges working in pairs. Results also showed that the effect of explicit anonymity on cognitive effort was quite small. In Experiment 2, students performed the job evaluation task and responded to questionnaire items measuring attitudes toward the task. Responses to these items showed that students who shared responsibility for the judgment task with 15 others felt more dispensable than students working alone or students working in pairs. Together these data show that feelings of dispensability can be the primary cause of social loafing in some situations and that feeling necessary can motivate effort in spite of anonymity.     

Knowledge activation after information encoding: Implications of trait priming on person judgment

It is widely assumed that traits primed after the encoding of person information do not lead to assimilation effects on the judgment of that person. The authors challenge this view by providing evidence that post-encoding trait primes can result in assimilative person judgments under certain conditions. In Experiments 1 and 2, we identify the conditions under which these assimilation effects occur. Experiment 1 shows the importance of participants’ goals during person information encoding: assimilation is observed when person information is encoded as part of a memorization goal (as opposed to an impression formation goal). The findings of Experiment 2 further reveal that the encoded person information should imply trait concepts rather than being merely vague with respect to the primed trait category. Finally, the results of Experiment 3 suggest that the obtained assimilation effect is driven by differential accessibility for prime-congruent person information.     

Likelihood judgment based on previously observed outcomes: the alternative-outcomes effect in a learning paradigm

Previous research has demonstrated that intuitive perceptions of certainty regarding a focal outcome are sensitive to variations in how evidence supporting nonfocal alternatives is distributed, even when such variations have no bearing on objective probability. We investigated this alternative-outcomes effect in a learning paradigm in which participants made likelihood judgments on the basis of their memory for past observations of relevant outcomes. In Experiment 1, a manipulation of evidence (observed frequencies) across alternative outcomes influenced not only intuitive certainty estimates about a focal outcome but also numeric subjective probabilities. Experiment 2 ruled out the possibility that these effects were attributable to the influence of information loss on frequency estimations. The findings were consistent with the heuristic comparison account, which suggests that the judged likelihood of a focal outcome will be disproportionately influenced by the strength (frequency) of the strongest alternative outcome.     

A sampling approach to biases in conditional probability judgments: beyond base rate neglect and statistical format

Conditional probability judgments of rare events are often inflated. Early accounts assumed a general deficit in using statistical base rates. More recent approaches predict improvement when problems are presented in frequency format or refer to natural categories. The present theory focuses on sampling processes. Experiment 1 showed that a seeming advantage of frequency over probability formats is due to a confounded factor, the need to mentally transform stimulus samples. An information search paradigm was used in Experiment 2. When sampling by the predictor, the probability to be estimated, p(criterion/predictor), was conserved in the samples and judgments were quite accurate. However, when sampling by the criterion, the low base-rate event was strongly overrepresented, accounting for the entire bias. Judgments were quite sensitive to the sampled data, but failed to take sampling constraints into account, as shown in Experiments 3 and 4.     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.     

The effect of polar projection on the perception of euclidean structure from motion

The aim of the present study was to examine whether euclidean structure could be recovered from apparent motion sequences under polar projection. In Experiment 1, length judgments of two sides of a simulated triangle rotating in depth did not reveal effects of type of projection, polar or parallel, on the perception of euclidean structure. However, there was a significant correlation between simulated and produced slants. The results also indicated that absolute depth judgments could not be accounted for by a random mechanism suggested by Todd and Bressan (1990). Experiments 2 and 3, in which a continuous dot surface was substituted for the triangle, showed that polar projection information from a relatively large visual angle, 17.40°, as compared with a small visual angle, 4.35°, facilitated discrimination of depth. Produced height:width ratios were consistently related to simulated shape, although the depth dimension was underestimated. Finally, Experiment 4 showed significant correlations between simulated and produced height:width ratios that could be accounted for only by an analysis in whichX andY velocities were treated independently. As in previous experiments, the variation in the depth dimension was underestimated. It was concluded that the visual system utilizes the additional information that is available in polar projection when recovering structure from motion, but that for different reasons the perceived structure does not become euclidean. These reasons are discussed briefly.