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 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.     

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.     

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.     

Explaining the price-volume relationship: The difference between price changes and changing prices

Trading on the stock market increases when there are large changes in price levels, and falls when these changes are small. An experimental test revealed strong support for the hypothesis that large price changes cause heavy trading. Trading patterns, profit data, and memory measures revealed that the vast majority of the subjects employed a tracking strategy; that is, they bought when the price fell and sold when it rose. To test whether the use of this strategy was due to a selective application of the representativeness heuristic on the price stimuli, a second experiment was conducted in which subjects were presented either with only price information or with only price change information. Results supported the representativeness hypothesis, with subjects in the price change condition tracking poorly and earning less profit. The results are discussed with regard to their implications for the stock market and the psychology of prediction.     

Fehldiagnose Aufmerksamkeitsdefizit- und Hyperaktivit?tssyndrom?

Although it is assumed both by healthcare professionals as well as by public opinion that attention deficit hyperactivity disorder (ADHD) is widely overdiagnosed, so far there is little empirical evidence to support this presumption. However, the presented study shows clear evidence for an overdiagnosis of ADHD. Furthermore, the data demonstrate that based on identical symptoms, boys more often receive a diagnosis for ADHD than girls. A false ADHD diagnosis also correlates with a recommendation for medical and psychotherapeutic treatment. One explanation for misdiagnosis is the fact that therapists in the course of diagnosis, as with other everyday decision-making processes, are influenced by heuristics. The most common heuristics that can lead to misdiagnosis are the representativeness heuristic and the availability heuristic. Such mistakes could be avoided by clearly following diagnostic criteria and the use of structural interviews.     

Two Faces of Representativeness: The Effects of Response Format on Beliefs about Random Sampling

Two beliefs that act in concert have been proposed as the basis for the representativeness heuristic in general, and judgments about random sampling in particular: samples resemble their parent populations (resemblance), and random sampling is a self-correcting process (balancing). Based on the results of a preliminary experiment, we proposed the ‘rule-cuing’ hypothesis, which is that different aspects of sampling problems can invoke these two beliefs separately. We found that when response formats required subjects to estimate themean of a sample, subjects’ responses reflected resemblance beliefs, whereas when subjects estimated the total score in a sample, balancing beliefs were elicited. In additional experiments we eliminated two rival hypotheses: theproblem difficulty hypothesis, and thearithmetic inconsistency hypothesis. Results suggest that beliefs, as well as preferences, may be constructed on-line in response to task characteristics.     

More about linda or conjunctions in context

Abstract

Tversky and Kahneman (1982; 1983) reported that subjects rated the con junction of two events as more likely than one of the component events. This “conjunction effect” is an error in terms of formal probability, where the probability of more happening is always smaller than the probability of less. They explained this effect in terms of a “representativeness” heuristic. This paper focuses on the context of the problem and the suggestions implied by the questions in the task. The three studies reported here provide evidence that context effects and implicit suggestions alter subjects' judgements. Tvenky and Kahneman's models take no account of such factors. Two studies show that when implicit suggestions are reduced, subjects are much less prone to the conjunction “effect”. Subjects take being asked the question “Is person X a Y?”, as providing evidence that X may be Y.     

From recognition to decisions: Extending and testing recognition-based models for multialternative inference

The recognition heuristic is a noncompensatory strategy for inferring which of two alternatives, one recognized and the other not, scores higher on a criterion. According to it, such inferences are based solely on recognition. We generalize this heuristic to tasks with multiple alternatives, proposing a model of how people identify the consideration sets from which they make their final decisions. In doing so, we address concerns about the heuristic’s adequacy as a model of behavior: Past experiments have led several authors to conclude that there is no evidence for a noncompensatory use of recognition but clear evidence that recognition is integrated with other information. Surprisingly, however, in no study was this competing hypothesis—the compensatory integration of recognition—formally specified as a computational model. In four studies, we specify five competing models, conducting eight model comparisons. In these model comparisons, the recognition heuristic emerges as the best predictor of people’s inferences.     

Exploring the conjunction fallacy within a category learning framework

The literature presents two major theories on the cause of the conjunction fallacy. The first attributes the conjunction fallacy to the representativeness heuristic. The second suggests that the conjunction fallacy is caused by people combining p(A) and p(B) into p(A&B) in an inappropriate manner. These two theories were contrasted in two category‐learning experiments. As predicted by the latter theory, data showed that participants that could assess p(A&B) directly made fewer conjunction fallacies than participants who had to compute p(A) and p(B) separately and then combine them into p(A&B). Least conjunction fallacies were observed in the cases where the representativeness heuristic was applicable. Overall, data showed that an inability to appropriately combine probabilities is one of the key cognitive mechanisms behind the conjunction fallacy. Copyright © 2008 John Wiley & Sons, Ltd.     

The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness?

The representativeness heuristic has been invoked to explain two opposing expectations--that random sequences will exhibit positive recency (the hot hand fallacy) and that they will exhibit negative recency (the gambler's fallacy). We propose alternative accounts for these two expectations: (1) The hot hand fallacy arises from the experience of characteristic positive recency in serial fluctuations in human performance. (2) The gambler's fallacy results from the experience of characteristic negative recency in sequences of natural events, akin to sampling without replacement. Experiment 1 demonstrates negative recency in subjects' expectations for random binary outcomes from a roulette game, simultaneously with positive recency in expectations for another statistically identical sequence-the successes and failures of their predictions for the random outcomes. These findings fit our proposal but are problematic for the representativeness account. Experiment 2 demonstrates that sequence recency influences attributions that human performance or chance generated the sequence.     

Contingent approaches to making likelihood judgments about polychotomous cases: the influence of task factors

Two experiments tested the influence of three task factors on respondents' tendency to use normative, heuristic, and random approaches to making likelihood judgments about polychotomous cases (i.e., cases in which there is more than one alternative to a focal hypothesis). Participants estimated their likelihood of winning hypothetical raffles in which they and other players held various numbers of tickets. Responding on non‐numeric scales (vs. numeric ones) and responding under time pressure (vs. self‐paced) increased participants' use of a comparison‐heuristic approach, resulting in non‐normative judgment patterns. A manipulation of evidence representation (whether ticket quantities were represented by numbers or more graphically by bars) did not have reliably detectable effects on processing approaches to likelihood judgment. The authors discuss the implications of these findings for the further development of likelihood judgment theories, and they discuss parallels between contingent processing in choice and contingent processing in likelihood judgment. Copyright © 2005 John Wiley & Sons, Ltd.     

Representativeness reasoning and the search for the origins of stuttering: A return to basic observations

In this paper, we present our views on theories of the distal and proximal causes of stuttering. We suggest that the search for the etiology of stuttering has been hampered by the inappropriate use of the representativeness heuristic, a method of reasoning which proposes that the effects of a disorder reflect its causes. We encourage a return to the ideas of Froeschels and Bluemel so that the representativeness heuristic might properly be employed in investigations into the proximal, mechanical causes of stuttering and into the etiological implications of the repetitions of early stuttering.     

The cognitive substrate of subjective probability

The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as prototype similarity, relative likelihood, or evidential support accumulation (ESAM; D. J. Koehler, C. M. White, & R. Grondin, 2003); cue-based relative frequency; and exemplar memory, implemented by probabilities from exemplars (PROBEX; P. Juslin & M. Persson, 2002). Three experiments with different task structures consistently demonstrate that exemplar memory is the best account of the data whereas the results are inconsistent with extant formulations of the representativeness heuristic and cue-based relative frequency.     

How does acoustic similarity influence short-term memory?

This study attempts to discover why items which are similar in sound are hard to recall in a short-term memory situation. The input, storage, and retrieval stages of the memory system are examined separately. Experiments I, II and III use a modification of the Peterson and Peterson technique to plot short-term forgetting curves for sequences of acoustically similar and control words. If acoustically similar sequences are stored less efficiently, they should be forgotten more rapidly. All three experiments show a parallel rate of forgetting for acoustically similar and control sequences, suggesting that the acoustic similarity effect does not occur during storage. Two input hypotheses are then examined, one involving a simple sensory trace, the other an overloading of a system which must both discriminate and memorize at the same time. Both predict that short-term memory for spoken word sequences should deteriorate when the level of background noise is increased. Subjects performed both a listening test and a memory test in which they attempted to recall sequences of five words. Noise impaired performance on the listening test but had no significant effect on retention, thus supporting neither of the input hypotheses. The final experiments studied two retrieval hypotheses. The first of these, Wickelgren's phonemic-associative hypotheses attributes the acoustic similarity effect to inter-item associations. It predicts that, when sequences comprising a mixture of similar and dissimilar items are recalled, errors should follow acoustically similar items. The second hypothesis attributes the effect to the overloading of retrieval cues which consequently do not discriminate adequately among available responses. It predicts maximum error rate on, not following, similar items. Two experiments were performed, one involving recall of visually presented letter sequences, the other of auditorily presented word sequences. Both showed a marked tendency for errors to coincide with acoustically similar items, as the second hypothesis would predict. It is suggested that the acoustic similarity effect occurs at retrieval and is due to the overloading of retrieval cues.     

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.     

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.     

Cognitive Biases in Playing the Lottery: Estimating the Odds and Choosing the Numbers

Three experiments were conducted to examine the operation of the representativeness and anchoring and adjustment heuristics in lottery play. Subjects in Experiments 1 and 2 indicated their chances of winning a lottery with an objective probability of 1 in 10. Consistent with the anchoring and adjustment heuristic, subjects (in both experiments) perceived their chances of winning to be greater when the lottery was based on a single event than when it was based on a disjunctive event. Subjects in these two experiments also selected numbers to play in a pick-3 (Experiment 1) or pick-4 (Experiment 2) lottery. Consistent with the representativeness heuristic, subjects in Experiment 2 demonstrated a preference for numbers without repeating digits. This also occurred in Experiment 3 wherein the numbers actually played in the Indiana daily Pick-3 lottery were examined.     

The test taker's fallacy: How students guess answers on multiple‐choice tests

Many students and applicants take multiple‐choice tests to demonstrate their competence and achievement. When they are unsure, they guess the most likely answer to maximize their score. Despite the impact of guessing on test reliability and individual performance, studies have not examined how patterns of answer sequences in multiple‐choice tests affect guessing. This research presents the test taker's fallacy, which refers to an individual's tendency to expect a different answer to appear for the next question given a run of the same answer choices. The test taker's fallacy exhibits negative recency, similar to the gambler's fallacy. However, extending the sequential judgment literature, the test taker's fallacy shows that negative recency arises even when sequences may or may not be randomly generated. In three studies, including a survey and experiments, the test taker's fallacy is robustly observed. The test taker's fallacy is consistent with the operation of the representativeness heuristic. This research explains what and how test takers guess given a streak of answers and extends judgment under uncertainty to the test‐taking context.