Exemplars in the mist: the cognitive substrate of the representativeness heuristic

The idea that people often make probability judgments by a heuristic short-cut, the representativeness heuristic, has been widely influential, but also criticized for being vague. The empirical trademark of the heuristic is characteristic deviations between normative probabilities and judgments (e.g., the conjunction fallacy, base-rate neglect). In this article the authors contrast two hypotheses concerning the cognitive substrate of the representativeness heuristic, the prototype hypothesis (Kahneman & Frederick, 2002) and the exemplar hypothesis (Juslin & Persson, 2002), in a task especially designed to elicit representativeness effects. Computational modelling and an experiment reveal that representativeness effects are evident early in training and persist longer in a more complex task environment and that the data are best accounted for by a model implementing the exemplar hypothesis.     

Representativeness and conjoint probability

People commonly violate a basic rule of probability, judging a conjunction of events to be more probable than at least 1 of its component events. Many manifestations of this conjunction fallacy have been ascribed to people's reliance on the representativeness heuristic for judging probability. Some conjunction fallacies, however, have been ascribed to the incorrect rules people use to combine probabilities. In 2 experiments, representativeness was pitted against probability combination to determine the contributions of each to the fallacy. Even for exemplar representativeness problems, the fallacy stemmed primarily from the application of incorrect combination rules. Representativeness seemed to be involved only insofar as it influenced the probabilities of a conjunction's component events. Implications of these findings are discussed for the representativeness account of judgmental errors and the relation between similarity and probability.     

Suppressing natural heuristics by formal instruction: The case of the conjunction fallacy

A basic principle of probability is the conjunction rule, p(B) p(A&B). People violate this rule often, particularly when judgments of probability are based on intensional heuristics such as representativeness and availability. Though other probabilistic rules are obeyed with increasing frequency as people's levels of mathematical talent and training increase, the conjunction rule generally does not show such a correlation. We argue that this recalcitrance is not due to inescapable “natural assessments”; rather, it stems from the absence of generally useful problem-solving designs that bring extensional principles to bear on this class of problem. We predict that when helpful extensional strategies are made available, they should compete well with intensional heuristics. Two experiments were conducted, using as subjects adult women with little mathematical background. In Experiment 1, brief training on concepts of algebra of sets, with examples of their use in solving problems, reduced conjunction-rule violations substantially, compared with a control group. Evidence from similarity judgments suggested that use of the representativeness heuristic was reduced by the training. Experiment 2 confirmed these training effects and also tested the hypothesis that conjunction-rule violations are due to misunderstanding of “B” as “B and not A.” Changes in detailed wording of the propositions to be ranked produced substantial effects on judgment, but the pattern of these effects supported the hypothesis that, for the type of problem used here, most conjunction errors are due to use of representativeness or availability. We conclude that such intensional heuristics can be suppressed when alternative strategies are taught.     

判断与决策中的情感启发式

情感启发式是指在判断与决策的过程中,个体会有意识或无意识的利用自己对任务选项的主观情感反应来做出决策。具体来说,个体头脑中物体和事件的表征会激起不同水平的情感体验,这种不同的体验会对所有的表征做出积极或消极的标记,人们根据这些被标记的体验来做出判断和决策。情感启发式是个体在决策中常用的策略。目前,关于情感启发式心理机制的解释主要有情感启发式模型和双加工理论。此外,情感启发式的影响因素主要包括经验、时间压力、可评估性和计数能力等。未来的研究应主要集中在探究情感启发式的产生根源和进一步扩展情感启发式应用领域的研究。     

A foundation for support theory based on a non-Boolean event space

A new foundation is presented for the theory of subjective judgments of probability known in the psychological literature as “Support Theory”. It is based on new complementation operations that, unlike those of classical probability theory (set-theoretic complementation) and classical logic (negation), need not satisfy the principles of the Law of The Excluded Middle and the Law of Double Complementation. Interrelationships between the new complementation operations and the Kahneman and Tversky judgmental heuristic of availability are described.     

Racial Categorization and Stereotype-Based Judgments About Homeless People1

The present study uses a social-cognitive paradigm to examine the association between racial categorization and stereotype-based judgments about homeless people. The study uses data from a national White subsample (N= 1,221) surveyed about attitudes toward homeless/homeless mentally ill people. It was hypothesized that individual differences in perceptions of the representativeness of Blacks in the homeless population, as measured by subjective estimates of the percentage of Blacks, would be associated with the enhancement of racially relevant negative stereotypes about homeless people. A secondary hypothesis was that perceptions of the representativeness of Blacks would be more strongly associated with the stereotype of homeless people as dangerous than with the view of them as lazy. The results support these hypotheses.     

Representativeness in the Market for Bets on National Football League Games

In laboratory experiments the representativeness heuristic has been shown to affect participants' judgments. Finding representativeness in a real-world economic market would indicate that even decision makers who are highly experienced and motivated use the heuristic, and would, in addition, violate the efficient market hypotheses, i.e. the theory that market prices fully reflect all available information. Testing for representativeness in the market for bets on National Football Leagues games avoids complications that make tests of representativeness in a stock market difficult to interpret. Evidence for representativeness in the NFL betting market is found in a data set from an earlier study which failed to test for representativeness, and in the 1976– 9 market. Representativeness does not appear to exist in the contemporary market, however, perhaps because with the advent of the personal computer the market depends less on purely human judgment.     

Risk Perception: Using Conditional Versus General Base Rates for Risk Communication1

In general, people judge their chance of experiencing a health risk as being less than the general base rate because of their favorable status on risk factors (e.g., history of stroke). Presenting base rates for high and low risk groups (conditional base rates) were hypothesized to lessen people's tendency to adjust downward from the base rate because risk factors are included in conditional base rates (CBRs). Young (M= 19 years) and older women (M= 46 years) were presented with either a general base rate (GBR) or CBRs for high‐ and low‐risk groups for 5 health risks. The CBR groups were significantly less likely to adjust their probability judgments from the base rate for the risk group that they believed applied to them (e.g., smoker vs. nonsmoker). The CBR effect was replicated in a second experiment in which women (M = 19 years) were informed of either a GBR, a CBR for a high‐risk group, or a CBR for a low‐risk group. The findings suggest that people might estimate subjective probabilities by considering both the base rate for a health risk and self‐assessments on risk factors. Biases about one's status on risk factors, however, may limit people's identification with relevant risk groups and warrant further investigation.     

Linda问题：“齐当别”抉择模型的解释

大量有关人类归因判断的研究表明,人类经常违反理性概率公理。Tversky和Kahneman（1983）使用Linda问题等特定场景的研究发现,人们系统性地表现出违反理性推断标准,判断合取事件发生概率大于其组成事件发生概率,称之为合取谬误,并用人们使用代表性启发式判断概率来解释该现象产生的原因。然而使用启发式观点对合取谬误现象进行解释过于模糊不清。该文首先介绍了合取谬误现象及其解释模型,然后应用Li（1994,2004）提出的不确定情形下决策理论——“齐当别”抉择模型对Linda问题中合取谬误产生的原因进行了新的解释     

The similarity heuristic

Decision makers often make snap judgments using fast‐and‐frugal decision rules called cognitive heuristics. Research into cognitive heuristics has been divided into two camps. One camp has emphasized the limitations and biases produced by the heuristics; another has focused on the accuracy of heuristics and their ecological validity. In this paper we investigate a heuristic proposed by the first camp, using the methods of the second. We investigate a subset of the representativeness heuristic we call the “similarity” heuristic, whereby decision makers who use it judge the likelihood that an instance is a member of one category rather than another by the degree to which it is similar to others in that category. We provide a mathematical model of the heuristic and test it experimentally in a trinomial environment. In this environment, the similarity heuristic turns out to be a reliable and accurate choice rule and both choice and response time data suggest it is also how choices are made. We conclude with a theoretical discussion of how our work fits in the broader “fast‐and‐frugal” heuristics program, and of the boundary conditions for the similarity heuristic. Copyright © 2009 John Wiley & Sons, Ltd.     

The influence of hierarchy on probability judgment

Consider the task of predicting which soccer team will win the next World Cup. The bookmakers may judge Brazil to be the team most likely to win, but also judge it most likely that a European rather than a Latin American team will win. This is an example of a non-aligned hierarchy structure: the most probable event at the subordinate level (Brazil wins) appears to be inconsistent with the most probable event at the superordinate level (a European team wins). In this paper we exploit such structures to investigate how people make predictions based on uncertain hierarchical knowledge. We distinguish between aligned and non-aligned environments, and conjecture that people assume alignment. Participants were exposed to a non-aligned training set in which the most probable superordinate category predicted one outcome, whereas the most probable subordinate category predicted a different outcome. In the test phase participants allowed their initial probability judgments about category membership to shift their final ratings of the probability of the outcome, even though all judgments were made on the basis of the same statistical data. In effect people were primed to focus on the most likely path in an inference tree, and neglect alternative paths. These results highlight the importance of the level at which statistical data are represented, and suggest that when faced with hierarchical inference problems people adopt a simplifying heuristic that assumes alignment.     

Children's developing notions of (im)partiality

This research examines the development of children's understanding that people's judgments may be skewed by relationships, and that situational factors may make it difficult to be impartial. One hundred and seventy-one adults and children between kindergarten and eighth grade heard stories about judges in contests with objective or subjective criteria for winning. In Experiment 1, by fourth grade, children rated a judge with no personal connection (the "neutral judge") as being more likely to be objective than a judge with a personal connection (the "connected judge"). Younger children showed the opposite pattern. Experiment 2 replicated this finding for judges, and also found that children across development have similar ideas regarding the characteristics for being a good judge. Not until eighth grade, however, did children indicate that a connected judge was more problematic in subjective situations than in objective ones.     

Perceived Event Frequency and the Optimistic Bias: Evidence for a Two-Process Model of Personal Risk Judgments

People often judge themselves to be at lower risk for various negative life events than are their peers. The two empirical studies presented here show that the magnitude of this optimistic bias can be either negatively or positively related to the perceived frequency of the event, depending on whether people judge their own risk relative to that of an average peer (make comparative risk judgments) or judge their own and an average peer's risk separately (make absolute risk judgments). A new two-process model is presented to account for these results. The model combines a better-than-average heuristic with elements of the singular target-focused and singular- distributional models of Klar and colleagues (Klar & Giladi, 1997, 1999; Klar, Medding, & Sarel, 1996). The empirical results and model have many implications for the study of personal risk judgments, the optimistic bias, and risk-taking behavior.     

Natural sample spaces and uncertain belief.

This article proposes a novel framework for understanding judgments of probability. Both accurate and inaccurate judgments are conceptualized in terms of the sets of information, or sample spaces, on which they are based. When appropriate sample spaces are easily accessed from memory (e.g., when they correspond to natural cognitive categories), people will make relatively accurate judgments; otherwise, people may substitute more accessible but inappropriate sample spaces and make judgment errors. In 3 experiments, the sample space framework was applied to account for the base rate fallacy. Results showed that (a) people spontaneously access sample spaces that correspond to natural categories, (b) reliance on inappropriate sample spaces produces the base rate fallacy, and (c) highlighting appropriate sample spaces improves the sensitivity of people's judgments to base rates. Discussion extends the framework to explain accuracy and error in other judgment domains.     

Scientific discovery: The larger problem situation

Present discussion of scientific discovery is in transition from a psychological idiom which reduced it from an irrational quasi-magical process to a more methodological idiom regarding it as a rational heuristic, if not a logic. The greatest obstacle to the latter endeavor is found to be a Romantic genre of introspective and anecdotal psychology. A more fruitful conceptual source is to be found in the classic tradition of ars inveniendi and its development into modern versions such as Dewey's pragmatic logic of inquiry and Gadamer's hermeneutic dialectic of question and answer. On this basis, a research program is sketched out for understanding scientific discovery as a rational heuristic in its ontological, psychological and methodological dimensions and for coming to terms with this phenomenon in the present cultural situation.     

Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning

When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the conclusions (e.g., Evans, Newstead, Allen, & Pollard, 1994). However, logic effects in syllogistic reasoning emerge even when participants are unlikely to carry out a full logical analysis of the problems (e.g., Shynkaruk & Thompson, 2006). There is also evidence that people can implicitly detect the conflict between their beliefs and the validity of the problems, even if they are unable to consciously produce a logical response (e.g., De Neys, Moyens, & Vansteenwegen, 2010). In 4 experiments we demonstrate that people intuitively detect the logicality of syllogisms, and this effect emerges independently of participants' conscious mindset and their cognitive capacity. This logic effect is also unrelated to the superficial structure of the problems. Additionally, we provide evidence that the logicality of the syllogisms is detected through slight changes in participants' affective states. In fact, subliminal affective priming had an effect on participants' subjective evaluations of the problems. Finally, when participants misattributed their emotional reactions to background music, this significantly reduced the logic effect.     

Conflict Aversion: Preference for Ambiguity vs Conflict in Sources and Evidence

This research investigates preferences and judgments under ambiguous vs conflicting information. Three studies provided evidence for two major hypotheses: (1) Conflicting messages from two equally believable sources are dispreferred in general to two informatively equivalent, ambiguous, but agreeing messages from the same sources (i.e., conflict aversion); and (2) conflicting sources are perceived as less credible than ambiguous sources. Studies 2 and 3 yielded evidence for two framing effects. First, when the outcome was negative, subjects' preferences were nearly evenly split between conflict and ambiguity, whereas a positive outcome produced marked conflict aversion. Second, a high probability of a negative outcome or a low probability of a positive one induced conflict preference. However, no framing effects were found for source credibility judgments. Study 3 also investigated whether subject identification with a source might affect preferences or credibility judgments, but found no evi dence for such an effect. The findings suggest cognitive and moti vational explanations for conflict aversion as distinct from ambi guity aversion. The cognitive heuristic is that conflict raises suspicions about whether the sources are trustworthy or credi ble. The motivational explanation stems from that idea that if sources disagree, then the judge not only becomes uncertain but also must disagree with at least one of the sources, whereas if the sources agree then the judge may agree with them and only has to bear the uncertainty.     

Differential effects of shared attention on perception of heading and 3-D object motion

When a person moves in a straight line through a stationary environment, the images of object surfaces move in a radial pattern away from a single point. This point, known as thefocus of expansion (FOE), corresponds to the person’s direction of motion. People judge their heading from image motion quite well in this situation. They perform most accurately when they can see the region around the FOE, which contains the most useful information for this task. Furthermore, a large moving object in the scene has no effect on observer heading judgments unless it obscures the FOE. Therefore, observers may obtain the most accurate heading judgments by focusing their attention on the region around the FOE. However, in many situations (e.g., driving), the observer must pay attention to other moving objects in the scene (e.g., cars and pedestrians) to avoid collisions. These objects may be located far from the FOE in the visual field. We tested whether people can accurately judge their heading and the three-dimensional (3-D) motion of objects while paying attention to one or the other task. The results show that differential allocation of attention affects people’s ability to judge 3-D object motion much more than it affects their ability to judge heading. This suggests that heading judgments are computed globally, whereas judgments about object motion may require more focused attention.     

Making heads or tails of probability: An experiment with random generators

Background. The equiprobability bias is a tendency for individuals to think of probabilistic events as ‘equiprobable’ by nature, and to judge outcomes that occur with different probabilities as equally likely. The equiprobability bias has been repeatedly found to be related to formal education in statistics, and it is claimed to be based on a misunderstanding of the concept of randomness. Aims. The aim of the present study was to examine whether experimenting with random generators would decrease the equiprobability bias. Sample. The participants were 108 psychology students whose performance was measured either immediately after taking part in a training session (n= 55), or without doing any training exercises (n= 53). Method. The training session consisted of four activities. These included generating random sequences of events, and learning about the law of large numbers. Subsequently, the participants were tested on a series of equiprobability problems, and a number of other problems with similar structure and content. Results. The results indicated that the training successfully decreased the equiprobability bias. However, this effect was moderated by participants’ cognitive ability (i.e., higher ability participants benefitted from the training more than participants with lower cognitive ability). Finally, the training session had the unexpected side effect of increasing students’ susceptibility to the representativeness heuristic. Conclusions. Experimenting with random generators has a positive effect on students’ general understanding of probability, but the same time it might increase their susceptibility to certain biases (especially, to the representativeness heuristic). These findings have important implications for using training methods to improve probabilistic reasoning performance.     

An empirical examination of relative deprivation theory

Relative deprivation theory centers around the proposition that the negative affect associated with judgments of one's own status is not simply a function of one's objective status. Instead, resentment, anger, dissatisfaction and other deprivation-related emotions vary with the subjective assessment of one's status. In the present experiment, subjects read vignettes in which the hypothesized preconditions of felt deprivation were manipulated. They then indicated the degree of perceived resentment and related cognitive-emotional factors attributed to the story characters. Perceptions of deprivation become more prevalent when an individual who lacks a desired outcome (X) (a) compares with another who does possess X, (b) feels entitled to X, (c) feels it was once feasible to attain X, and (d) feels it is not feasible to attain X in the future. The results also suggest that certain preconditions, such as the presence of a comparison other and entitlement, act conjunctively in affecting judgments of felt deprivation. Finally, personal control over desired outcomes appears to be important for relative deprivation theory.