The base-rate fallacy in the context of sequential categories

Three experiments assessed base-rate utilization in a paradigm in which the relevant categories of the population were trials in sequences of variable length. In one version of stimulus materials, for example, a trial was represented by a toss of a coin, and a sequence was a series of coin tosses. Since each described sequence was to end upon the scoring of a “hit” in any trial, the likelihood of a trial’s being attempted was a decreasing function of its position in the sequence. Subjects who estimated the particular trial upon which the hit in a sequence was most likely to occur showed a significant tendency to ignore the probable higher prevalence—the greater base rate— of early trials in the overall population of atttempts, typically estimating that the hit in the sequence was equally likely on any trial. This tendency, however, was modified by the specific problem context. In all experiments, significantly more normatively correct estimates were made in the coin context, in which the disparity between base rates of early trials and later trials was most pronounced. Although subjects in the third experiment who had previously taken a statistics course displayed superior performance on the coin problem, there was no evidence of transfer of this superiority to another context. These results are interpreted within the theoretical framework of the base-rate fallacy. In particular, the article discusses implications of the finding that general base rates may be ignored even in the absence of specific diagnostic indicators.     

Social stereotypes and judgments of individuals: An instance of the base-rate fallacy

Social stereotypes may be defined as beliefs that various traits or acts are characteristic of particular social groups. As such, stereotypic beliefs represent subjective estimates of the frequencies of attributes within social groups, and so should be expected to “behave like” base-rate information within the context of judgments of individuals: specifically, individuating target case information should induce subjects to disregard their own stereotypic beliefs. Although the results of previous research are consisten with this prediction, no studies have permitted normative evaluation of stereotypic judgments. Because the hypothesis equates base rates and stereotypes, normative evaluation is essential for demonstrating equivalence between the base-rate fallacy and neglect of stereotypes in the presence of individuating case information. Two experiments were conducted, allowing for normative evaluation of effects of stereotypes on judgments of individuals. The results confirmed the hypothesis and established the generalizability of the effect across controversial and uncontroversial, socially desirable and socially underirable stereotypic beliefs. More generally, an examination of the differences between intuitive and normative statistical models of the judgment task suggest that the base-rate fallacy is but one instance of a general characteristic of intuitive judgment processes: namely, the failure to appropriately adjust evaluations of any one cue in the light of concurrent evaluations of other cues.     

Asymmetric attributions for compliance: Reward vs punishment

It was proposed that people attribute an individual's behavior more to internal factors when that individual's actions are influenced by reward than when those actions are influenced by punishment. Previous research has failed to control for the power of reward versus punishment which, in effect, creates a confounding of behavioral base rates (consensus) with the reward-punishment manipulation. The current research created reward and punishment contingencies that were equal in their base rates for producing a compliant response. In Experiment 1, subjects (n = 63) who produced the base-rate data also made attributions regarding a compliant target person. The results supported the reward-punishment attributional asymmetry hypothesis in that the target person was held more responsible for his actions in the reward than in the punishment conditions. A second experiment (n = 72) provided some attributors with information regarding base rates for compliance and measured perceived base rates for compliance. Knowledge of the base rates for compliance eliminated the reward-punishment attributional asymmetry phenomenon. Subjects not provided with such knowledge erroneously assumed different base rates for reward and punishment and maintained the perception of reward-punishment attributional asymmetry. Using subjects' estimates of base rate for compliance as a covariate eliminated the attributional asymmetry effect. It is suggested that erroneous base-rate assumptions mediate the attributional asymmetry phenomenon.     

Individual differences in causal learning and decision making

In judgment and decision making tasks, people tend to neglect the overall frequency of base-rates when they estimate the probability of an event; this is known as the base-rate fallacy. In causal learning, despite people's accuracy at judging causal strength according to one or other normative model (i.e., Power PC, DeltaP), they tend to misperceive base-rate information (e.g., the cause density effect). The present study investigates the relationship between causal learning and decision making by asking whether people weight base-rate information in the same way when estimating causal strength and when making judgments or inferences about the likelihood of an event. The results suggest that people differ according to the weight they place on base-rate information, but the way individuals do this is consistent across causal and decision making tasks. We interpret the results as reflecting a tendency to differentially weight base-rate information which generalizes to a variety of tasks. Additionally, this study provides evidence that causal learning and decision making share some component processes.     

The illusion of replacement in research into the development of thinking biases: the case of the conjunction fallacy

The conjunction fallacy is a violation of a very basic rule of probability. Interestingly, although committing the fallacy seems irrational, adults are no less susceptible to the fallacy than young children. In Experiment 1, by employing tasks where the conjunctive response option involved two non-representative items, we found a large reduction in fallacy rates as compared to traditional conjunction fallacy problems. Nevertheless, fallacy rates remained relatively high in both adolescents and adults, although adults showed more consistency in their normative responses. In Experiment 2, we demonstrated that children’s relatively good performance on the task was not the consequence of their missing knowledge of social stereotypes. Additionally, children were more strongly affected by explicitly presented frequency information than adults. Indeed, adults only took frequency information into account when frequencies were made relevant by a training in probabilistic reasoning. Overall, the results suggest that whereas the potential for normative reasoning increases with development, this potential is often overshadowed by a pervasive tendency in adolescence and adulthood to rely on contextual information, knowledge, and beliefs, even when conflicting information is available. By contrast, children are more strongly influenced by explicitly presented information than relevant knowledge cued by the tasks.     

Diagnosticity and the base-rate effect

A common judgmental task involves predicting the category membership of an individual on the basis of information specific to that individual and background information regarding the base rate of different categories. According to statistical theory, predictions may deviate from base rates only to the extent that the individuating information is diagnostic. Previous research has demonstrated that diagnosticity is often judged by “representativeness,” the degree to which the individuating information is differentially suggestive of the different possible categories. Thus, information with high differential representativeness will swamp base-rate information even if it is almost worthless (e.g., because its source is unreliable). The present studies varied differential representativeness by manipulating the prediction categories’ similarity to one another vis-a-vis the individuating information. It was found that the effect of the base rate increased systematically as differential representativeness decreased. Representativeness was measured independently by several converging techniques. These measures predicted the magnitude of the base-rate effect, supporting the hypothesis that neutral stimuli are assigned to categories in proportion to the base rates.     

Partitive Formulation of Information in Probabilistic Problems: Beyond Heuristics and Frequency Format Explanations

I propose a simple theory on the use of base rate according to which neither heuristic nor frequentist factors underlie demonstrations of the occurrence or the elimination of the base-rate fallacy. According to this view, what is crucial for the occurrence or elimination of the base-rate fallacy is the absence or presence, respectively, of what can be called a partitive formulation (Macchi, 1995) of the conditional likelihood datum. A partitive formulation defines the set of which the numerical datum is a part (in terms of percentages or frequencies) by referring to the likelihood datum relative to the base rate information. The predictive power of this hypothesis is shown by comparing responses to different versions of problems containing the same implied natural heuristic principles and supplied data, but which differ in the way the information is presented (partitive vs nonpartitive). Whether probabilistic or frequentist, the partitive versions lead to an almost complete elimination of the bias which remains when nonpartitive versions are used. On the basis of these experimental results, the paper includes a critical discussion of heuristic, frequentist, and mental models theories.     

Accentuation of information processes and biases in group judgments integrating base-rate and case-specific information

This article investigates differences in the ways that groups and individuals apply information-processing strategies and fall prey to biases in their judgments. Judgments were made on probabilistic inference problems that involved base-rate and case-specific information. Consistent with hypotheses, when individuals neglect base-rate information in their probability judgments, groups accentuate this tendency. Moreover, when the source of case-specific information is inaccurate, individuals neglect the case-specific information, and groups accentuate this tendency with the base-rate information dominating their probability judgments. In addition, groups accentuate the strategies used by individuals to integrate the base-rate and case-specific information. These results provide strong support for a group accentuation tendency for the application of information-processing biases and the strategies used to integrate information. Discussion reflects upon the relationship of the results of this experiment with other research on base-rate neglect and group judgment. Underlying mechanisms and potential moderators of the group accentuation pattern are also discussed.     

Another look at sex stereotypes and social judgments: an analysis of the social perceiver's use of subjective probabilities

Locksley, Borgida, Brekke, and Hepburn (1980) assert that subjects fall prey to the base-rate fallacy when they make stereotype-related trait judgments. They found that subjects ignored their stereotypes when trait judgments were made in the presence of trait-related behavioral information. The present article reexamines those findings with respect to two issues: (a) the use of a normative criterion in comparison with subjects' judgments and (b) the level of analysis (group vs. individual) of subjects' judgments. We conducted a replication of the Locksley et al. (1980) Study 2, and the results were examined with respect to these two issues. We found no support for the base-rate fallacy. When a Bayesian normative criterion was constructed for each subject based on the subject's own stereotype judgments and was compared with assertiveness judgments made in the presence of individuating information, there was no evidence that subjects ignored or underused their stereotypes as the base-rate fallacy predicts.     

Some effects of task relevance and friendship on helping: You don't always help the one you like

It was hypothesized that being outperformed on a task that is relevant to one's self-definition is threatening to self-esteem, and that this threat is greater when one is outperformed by a friend rather than by a stranger. When another's performance threatens self-esteem, persons will be less likely to help the other by making the task easy. To test these hypotheses, 52 friendship pairs participated with strangers in a word identification task described either as a measure of important skills (high relevance) or as a game (low relevance). Participants chose clues for both a friend and a stranger to use in identifying target words. As predicted, they gave harder clues under high-relevance than under low-relevance conditions. Moreover, they gave harder clues to strangers than to friends under low-relevance conditions, but gave harder clues to friends than to strangers under high-relevance conditions.     

Pragmatic Aspects of the Base-rate Fallacy

An investigation was made of the role played by verbal structure in the problems used to study the base-rate fallacy, which has traditionally been attributed to the role of heuristics (e.g. causality, specificity). It was hypothesized that elements of the verbal form of text problems led to a misunderstanding of the question or the specific information, rendering obscure the independence of the sets of data (specific information is obtained independently from the base rate). Nine texts were presented to various groups of subjects: four were taken from Tversky and Kahneman (1980) and used as controls; five were obtained by modifying the verbal form of the original in order to reveal or conceal the links between the sets of data. The percentage of base-rate fallacies was greatly reduced with texts in which the independence of the data was clear, regardless of the causality and specificity of the information they contained (which was not changed). This result suggests that there is a need to consider the rules of natural language in order to move towards a better understanding of observed phenomena.     

The impacts of task relevance and cognitive load on adults’ decision information search

ABSTRACT

Higher relevance may increase older adults’ engagement in cognitively demanding activities; however, whether this effect will maintain when available cognitive resources are limited? Consequently, we investigated the joint impact of task relevance and cognitive load on older and younger adults’ decision search behaviors. We adopted a 2 (age: young/old) × 2 (cognitive load: without load/with load) × 2 (task relevance: high/low) mixed design. Sixty-one younger and 63 older adults completed high-relevance and low-relevance decisions. Our results revealed that older (vs. younger) adults took more time and more alternative-based search before decision-making. Both age groups sampled less information with an additional memory task. Additionally, they spent more time and effort to sample more information on high-relevance (vs. low-relevance) decisions; however, such differences disappeared when with an additional memory task. Task relevance promoted both age groups' search engagement, but this effect was subjected to their available cognitive resources.     

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

In judging posterior probabilities, people often answer with the inverse conditional probability--a tendency named the inverse fallacy. Participants (N = 45) were given a series of probability problems that entailed estimating both p(H / D) and p(approximately H / D). The findings revealed that deviations of participants' estimates from Bayesian calculations and from the additivity principle could be predicted by the corresponding deviations of the inverse probabilities from these relevant normative benchmarks. Methodological and theoretical implications of the distinction between inverse fallacy and base-rate neglect and the generalization of the study of additivity to conditional probabilities are discussed.     

Base rates versus sample accuracy: competition for control in human matching to sample

People often place undue weight on specific sources of information (case cues) and insufficient weight on more global sources (base rates) even when the latter are highly predictive, a phenomenon termed base-rate neglect. This phenomenon was first demonstrated with paper-and-pencil tasks, and also occurs in a matching-to-sample procedure in which subjects directly experience case sample (cue) accuracy and base rates, and in which discrete, nonverbal choices are made. In two nonverbal experiments, subjects were exposed to hundreds of trials in which they chose between two response options that were both probabilistically reinforced. In Experiment 1, following one of two possible samples (the unpredictive sample), either response was reinforced with a .5 probability. The other sample (predictive) provided reinforcement for matching on 80% of the trials in one condition but in only 20% of the trials in another condition. Subjects' choices following the unpredictive sample were determined primarily by the contingencies in effect for the predictive sample: If matching was reinforced following the predictive sample, subjects tended to match the unpredictive sample as well; if countermatching the predictive sample was generally reinforced, subjects tended to countermatch the unpredictive sample. These results demonstrate only weak control by base rates. In Experiment 2, base rates and sample accuracy were simultaneously varied in opposite directions to keep one set of conditional probabilities constant. Subjects' choices were determined primarily by the overall accuracy of the sample, again demonstrating only weak control by base rates. The same pattern of choice occurred whether this pattern increased or decreased rate of reinforcement. Together, the results of the two experiments provide a clear empirical demonstration of base-rate neglect.     

Waiting for the bus: when base-rates refuse to be neglected

The paper reports the results from 16 versions of a simple probability estimation task, where probability estimates derived from base-rate information have to be modified by case knowledge. In the bus problem [adapted from Falk, R., Lipson, A., & Konold, C. (1994). The ups and downs of the hope function in a fruitless search. In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 353-377). Chichester, UK: Wiley], a passenger waits for a bus that departs before schedule in 10% of the cases, and is more than 10 min delayed in another 10%. What are Fred's chances of catching the bus on a day when he arrives on time and waits for 10 min? Most respondents think his probability is 10%, or 90%, instead of 50%, which is the correct answer. The experiments demonstrate the difficulties people have in replacing the original three-category 1/8/1 partitioning with a normalized, binary partitioning, where the middle category is discarded. In contrast with typical studies of "base-rate neglect", or under-weighing of base-rates, this task demonstrates a reversed base-rate fallacy, where frequentistic information is overextended and case information ignored. Possible explanations for this robust phenomenon are briefly discussed.     

I know the rule,but I'll just go with my gut: is there a rational use of intuition?

ABSTRACT

Research has established that human thinking is often biased by intuitive judgement. The base-rate neglect effect provides such an example, so named because people often support their decisions in stereotypical individuating information, neglecting base-rates. Here, we test the hypothesis that reasoners acknowledge information provided by base-rates and may use individuating information in support of a “rational” decision process. Results from four experiments show that “base-rate neglecting” occurs when participants acknowledge sample distributions; participants who prefer individuating over base-rate information perceive base-rates as less diagnostic and are more confident in their individuating-based responses; and that posterior probabilities (assigned after all relevant information is considered) predict more individuating-based responses for individuating-preference participants (suggesting a rational process). However, data also show a deeper form of base-rate neglect: even when some participants report to prefer base-rate information, define individuating information as non-diagnostic, and their posterior probabilities suggest otherwise, they still provide individuating-based responses.     

Using statistical risk information to assess oral contraceptive safety

The effect of variations in the presentation of oral contraceptive risk information on perceived safety was investigated. Four tests of the hypothesis that consumers focus on the absolute value of the numbers presented when assessing risk probabilities were performed with the following results: (1) when base rates are given, risks are perceived as less likely than when base rates are not given; (2) risks seem smaller when the information provided focuses on the number that will not die than when the number of expected deaths is presented; (3) contrary to our expectation, respondents do not focus on foreground numbers when risk was represented in an ‘X out of Y occurrences’ format; (4) respondents judged a risk of ‘4.15 times greater’ as less likely than when the information was presented as ‘415% greater risk’. We concluded that consumers convert statistical risk information into judgements about the magnitude of the number presented (small or large number) and utilize this more meaningful information when making risk judgements.     

心理距离对基线比例忽略的影响

基线比例忽略是指在不确定情境中, 个体进行判断和决策时不能充分利用或者忽略基线比例的现象。本研究通过系列情境实验探索了三种不同维度的心理距离, 即时间距离、空间距离和社会距离对基线比例忽略的影响。结果发现, 三种心理距离均能够对基线比例忽略产生影响：当时间距离、空间距离和社会距离较近时, 个体更容易表现出基线比例忽略现象; 而当时间距离、空间距离和社会距离较远时, 个体的基线比例忽略倾向减弱。     

Problem structure and the use of base-rate information from experience

This article is concerned with the use of base-rate information that is derived from experience in classifying examples of a category. The basic task involved simulated medical decision making in which participants learned to diagnose hypothetical diseases on the basis of symptom information. Alternative diseases differed in their relative frequency or base rates of occurrence. In five experiments initial learning was followed by a series of transfer tests designed to index the use of base-rate information. On these tests, patterns of symptoms were presented that suggested more than one disease and were therefore ambiguous. The alternative or candidate diseases on such tests could differ in their relative frequency of occurrence during learning. For example, a symptom might be presented that had appeared with both a relatively common and a relatively rare disease. If participants are using base-rate information appropriately (according to Bayes' theorem), then they should be more likely to predict that the common disease is present than that the rare disease is present on such ambiguous tests. Current classification models differ in their predictions concerning the use of base-rate information. For example, most prototype models imply an insensitivity to base-rate information, whereas many exemplar-based classification models predict appropriate use of base-rate information. The results reveal a consistent but complex pattern. Depending on the category structure and the nature of the ambiguous tests, participants use base-rate information appropriately, ignore base-rate information, or use base-rate information inappropriately (predict that the rare disease is more likely to be present). To our knowledge, no current categorization model predicts this pattern of results. To account for these results, a new model is described incorporating the ideas of property or symptom competition and context-sensitive retrieval.