Making probability judgments of future product failures: The role of mental unpacking

When consumers mentally unpack (i.e., imagine) the reasons for product failure, their probability judgments of future product failures are higher than when no mental unpacking is undertaken. However, increasing the level of mental unpacking does not lead to monotonically increasing effects on probability judgments but results in inverted U-shaped relationships. Using a two-factor structure, we propose that when consumers undertake mental unpacking, there will be two conflicting processes; while imagining causes for an event will lead to greater perceived probability, the greater difficulty in generating reasons for an event will lead to lower perceived probability.     

时间分解效应及其对跨期决策的影响

本文基于经典的分解效应, 提出并证实了一种影响人们判断与决策中时间知觉的新因素--时间分解效应。共包括两个研究, 分别在“时间够用”判断与跨期决策中检验了该效应的存在性与稳固性。实验结果表明：(1)相比未分解条件, 分解条件下的被试判断给定时间内完成某项任务的时间更够用, 即时间知觉更长。该效应受到任务难度的调节, 在较简单的任务中时间分解效应更显著; (2)在跨期决策中, 分解操纵增大了人们对较大较远的收益(larger & later, LL)选项中时间延迟的知觉, 证实了时间分解效应。此外, 还发现时间分解效应会导致人们在跨期决策中更偏好较小较近的收益(smaller & sooner, SS)选项, 对时间延迟的知觉中介了这一过程。总之, 本研究不仅在理论上提出了一种新的分解效应, 同时对现实生活中的决策(如计划制定等)有重要的应用价值。     

决策与判断中的分解效应

分解效应是人类主观判断中的一种较稳固的行为偏差,并且判断结果会对随后的决策产生重要影响,因此,对该领域研究成果的全面梳理具有重要的理论意义和实际价值。本文主要介绍了支持理论中的分解效应,总结梳理了概率判断与时间判断中分解效应的研究,综述了其他社会判断中的分解效应研究成果,展望了决策与判断中的分解效应的未来研究方向。通过上述内容的阐述,希望能为该领域研究者提供新的思路,推动国内相关领域研究的发展。     

A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors, including the anchoring and adjustment model for probability judgments. In the quantum model, a new fundamental concept in cognition is advanced--the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. We conclude that quantum information-processing principles provide a viable and promising new way to understand human judgment and reasoning.     

Unpacking unpacking: greater detail can reduce perceived likelihood

Past research suggests that a categorical event is perceived to be more likely if its subcases are explicitly delineated or "unpacked." In 6 studies, we find that unpacking can often make an event seem less likely, especially when the details being unpacked are already highly accessible. Process evidence shows that the provision of greater detail accompanying unpacking reduces the simplicity of an event and that this dysfluency is used as a negative cue for likelihood. This work establishes processing fluency as a mechanism that opposes the other effects of unpacking, such as enhanced accessibility.     

Subadditivity in Memory for Personal Events

Abstract—People's subjective probability judgments of external events are often subadditive (i.e., the probability estimates of component parts of a single event sum to greater than one)—a clear violation of the extensional nature of probability theory. We show that people's frequency judgments of personal events can also be subadditive. We found subadditivity even when component events made up a proper subset of a wider composite event. Our findings imply that the somewhat arbitrary choice of the specificity with which questions are asked can produce widely different reports for the same composite events.     

Analyzing the accuracy of probability judgments for multiple events: An extension of the covariance decomposition

The probability score (PS) can be used to measure the overall accuracy of probability judgments for a single event, e.g., “Rain falls,” or “This patient has cancer.” It has been shown previously how a “covariance decomposition” of the mean of PS over many occasions indexes several distinct aspects of judgment performance (J. F. Yates, Organizational Behavior and Human Performance, 30, 132–156 (1982)). There are many situations in which probability judgments are reported for sample space partitions containing more than one event and its complement, e.g., medical situations in which a patient might suffer from Disease X, Disease Y, or Disease Z, or testing situations in which the correct answer to an item might be any one of alternatives (a) through (e). The probability score for multiple events (PSM) serves as a measure of the overall accuracy of probability judgments for the events in partitions of any size. The present article describes and interprets an extension of the covariance decomposition to the mean of PSM. The decomposition is illustrated with data from two contexts, medicine and education.     

Thanks, but I'm used to better: a relative rank model of gratitude

We argue that more help does not necessarily lead to more gratitude. Rather, gratitude depends on how a given instance of help compares with the help that a person is used to receiving. Participants read vignettes detailing an event in which 11 different friends either lent them varying amounts of money or spent varying amounts of time providing help. The amount of gratitude elicited by a given amount of help (e.g., a loan of ￡36 [about $56] or 49 min help) differed substantially depending on how this amount ranked among the help they were getting from their other friends. Comparison across four experimental conditions suggested that these judgments operated via the same general cognitive mechanisms used to judge other social events and psychophysical stimuli (as outlined by range frequency theory). Although more help does lead to more gratitude, people appear to be sensitive to how that help compares with what others are providing, and experienced gratitude depends on these relative judgments.     

Representativeness and fallacies of probability judgment

Representativeness is the name given to the heuristic people often employ when they judge the probability of a sample by how well it represents certain salient features of the population from which it was drawn. The representativeness heuristic has also been used to account for how people judge the probability that a given population is the source of some sample. The latter probability, however, depends on other factors (e.g., the population's prior probability) as well as on the sample characteristics. A review of existing evidence suggests that the ignoring of such factors, a central finding of the heuristics approach to judgment under uncertainty, is a phenomenon which is conceptually distinct from the representativeness heuristic. These factors (base rates, sample size, and predictability) do not always exert the proper influence on people's first-order probability judgments, but they are not ignored when people make second-order (i.e., confidence) judgments. Other fallacies and biases in subjective evaluations of probability are, however, direct causal results of the employment of representativeness. For example, representativeness may be applied to the wrong features. Most devastating, perhaps, is that subjective probability judgments obey a logic of representativeness judgments, even though probability ought to obey an altogether different logic. Yet although the role of representativeness judgments in probability estimation leaves a lot to be desired, it is hard to envision prediction and inference completely unaided by representativeness.     

Ambiguity and rationality

Recently, several theories of decision making and probability judgment have been proposed that take into account ambiguity (Einhorn and Hogarth, 1985; Gardenfors and Sahlin, 1982). However, none of these theories explains exactly what the psychological causes of ambiguity are or addresses the issue of whether ambiguity effects are rational. In this paper, we define ambiguity as the subjective experience of missing information relevant to a prediction. We show how this definition can explain why ambiguity affects decisions in the ways it does. We argue that there are a variety of rational reasons ambiguity affects probability judgments and choices in the ways it does. However, we argue that the ambiguity effect does not cast doubt on the claim that utility theory is a standard of rational choice. Rather, we suggest that the effect of ambiguity on decisions highlights the fact that utility theory, like any normative model of decision making only prescribes the optimal decision, given what one knows.     

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.     

A theory of perceived risk and attractiveness

People judged both the attractiveness and risk of lotteries to win or lose money. The lotteries were designed to test whether risk and attractiveness judgments show systematic deviations from the simple sum of probability-by-utility-products analogous to (S)EU theory. Our results led to an alternative combination rule for probability and outcome information, with a relative weight averaging component and a configural (i.e., sign- or rank-dependent) probability weighting component. Ratings of risk and attractiveness were negatively correlated, but the two tasks showed systematic differences in the rank order of judgments. Both judgments could be fit by the same configural relative weight averaging model, but with different parameters (especially the sign-dependent probability weighting functions). Risk judgments were more sensitive to the probability of losses and zero outcomes compared to attractiveness judgments, which were more sensitive to the probability of gains. There were individual differences on the extent of this difference in probability weights between risk and attractiveness judgments.