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Switch to: References
Citations of:
Should Bayesians sometimes neglect base rates?
Behavioral and Brain Sciences 4 (3):342-343 (1981)
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The standard of proof applied in civil trials is the preponderance of evidence, often said to be met when a proposition is shown to be more than 50% likely to be true. A number of theorists have argued that this 50%+ standard is too weak – there are circumstances in which a court should find that the defendant is not liable, even though the evidence presented makes it more than 50% likely that the plaintiff’s claim is true. In this paper, (...) |
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According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...) |
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This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) |
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Two distinct issues are sometimes confused in the base rate literature: Why do people make logical mistakes in the assessment of probabilities? and why do subjects not use base rates the way experimenters do? The latter problem may often reflect differences in an implicit reference class rather than a disinclination to update a base rate by Bayes' theorem. Also important are considerations concerning the interaction of several potentially relevant base rates. |
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Koehler's target article attempts a balanced view of the relevance of knowledge of base rates to judgments of subjective or credal probability, but he is not sensitive enough to the difference between requiring and permitting the equation of probability judgments with base rates, the interaction between precision of base rate and reference class information, and the possibility of indeterminate probability judgment. |
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Koehler is right to argue for more nuanced interpretation of base rate anomalies. These anomalies are best understood in relation to a broader class of cognitive anomalies, which are important for theory and practice. Recognizing a need for more nuanced analysis should not be taken as a license for treating the effects as “explained away.”. |
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Koehler's summary and critique of research on the base rate fallacy is cogent and persuasive. However, he may have overstated the case, and his suggestions for future research may be too restrictive. We agree that methodological approaches to this topic should be broadened, but we argue that experimental laboratory research and the Bayesian normative standard are useful and should not be abandoned. |
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Setting the two hypotheses of complete neglect and full use of base rates against each other is inappropriate. The proper question concerns the degree to which base rates are used (or neglected), and under what conditions. We outline alternative approaches and recommend regression analysis. Koehler's conclusion that we have been oversold on the base rate fallacy seems to be premature. |
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There is a familiar risk of antinomy if fromxisEand p(xisH/xisE) =rit is permissible to infer p(xisH) =r, and what Carnap (1950) called “The requirement of total evidence” will not prevent such antinomies satisfactorily. What is needed instead is a properly developed theory of evidential weight. |
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Commentators agree that simple conclusions about a general base rate fallacy are not appropriate. It is more constructive to identify conditions under which base rates are differentially weighted. Commentators also agree that improving the ecological validity of the research is desirable, although this is less important to those interested exclusively in psychological processes. The philosophers and ecologists among the commentators offer a kinder perspective on base rate reasoning than the psychologists. My own perspective is that the interesting questions (both psychological (...) |
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Any instance (i.e., event, behavior, trait) belongs to infinitely many reference classes, hence there are infinitely many base rates from which to choose. People clearly do not entertain all possible reference classes, however, so something must be limiting the search space. We suggest some possible mechanisms that determine which reference class is evoked for the purpose of judgment and decision. |
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A recent study showed physicians' reasoning about a realistic case to be ignorant of base rate. It also showed physicians interpreting information pertinent to base rate differently, depending on whether it was presented early or late in the case. Although these adult reasoners might do better if given hints through talk of relative frequencies, this would not prove that they had no problem of base rate neglect. |
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Koehler's call for a reanalysis of the base rate fallacy is particularly important in the applied domain of accounting, since base rate data appear to be an important input for many accounting tasks. In this commentary I discuss the use of base rates in accounting and explain why more flexible standards of performance are important when judging the use of base rates. |
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The underutilization of base rates is a consistent finding. The strong claim that base rates are ignored has been rejected and this needs no further emphasis. Following the path of “normal science,” research examines the conditions predicting changes in the degree of underutilization. A scientific revolution that might dethrone the heuristics and biases paradigm is not in sight. |
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As illustrated by research Koehler himself cites (Dawes et al. 1993), the purpose of experiments is to choose between contrasting explanations of past observations – rather than to seek statistical generalizations about the prevalence of effects. True external validity results not from sampling various problems that are representative of “real world” decision making, but from reproducing an effect in the laboratory with minimal contamination (including from real world factors). |
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Does the most common response given by participants presented with Tversky and Kahneman’s famous taxi cab problem amount to a violation of Bayes’ theorem? In other words, do they fall victim to so-called base-rate fallacy? In the present paper, following an earlier suggestion by Crupi and Girotto, we will identify the logical arguments underlying both the original diagnosis of irrationality in this reasoning task under uncertainty and a number of objections that have been raised against such a diagnosis. This will (...) |
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Cognitive algebra strongly disproved the representativeness heuristic almost before it was published; and therewith it also disproved the base rate fallacy. Cognitive algebra provides a theoretical foundation for judgment-decision theory through its joint solution to the two fundamental problems – true measurement of subjective values, and cognitive rules for integration of multiple determinants. |
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This commentary presents a self-assessment inventory that will allow readers to determine their own attitude toward the base rate fallacy and its literature. The inventory is scientifically valid but not Medicare/Medicaid reimbursable. |
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Normative ethics usually presupposes background accounts of human agency, and although different ethical theorists might have different pictures of human agency in mind, there is still something like a standard account that most of mainstream normative ethics can be understood to rest on. Ethical theorists tend to have Rational Man, or at least some close relative to him, in mind when constructing normative theories. It will be argued here that empirical findings raise doubts about the accuracy of this kind of (...) |
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Failure to consider base rate is regarded as potentially hazardous, mainly because its consideration is assumed to be determined solely by P(H/D), the probability of the individuating data if the hypothesis is true, and not at all by P(D/˜H), the probability if the hypothesis is false. However, when P(D/˜H) is unconfounded from P(D/H), it turns out to be the stronger determinant of base rate consideration. |
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The fallacy beneath the base rate fallacy is that we know what a base rate is. We talk as if base rates and individuating information were two different kinds of information. From a Bayesian perspective, however, the only difference between base rate and individuating information is – which comes first. |
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When base rates are learned and used in an experiential manner subjects show better base rate use, perhaps because the implicit learning system is engaged. A causal framework in which base rates are relevant might also be necessary. Humans might thus perform better on more ecologically valid tasks, which are likely to contain those three components. |
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Abstract(1) The miscitations of seminal experiments in the base rate literature adds to the existing database of systematic miscitations of wellknown psychological experiments. These miscitations may be caused by a process of reconstructive remembering. (2) Representative design should be the methodological core of Koehler's call for ecologically valid research. This approach can benefit both basic and applied research. |
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This commentary discusses three points: (1) The implications of the fact that it is rational to ignore base rates if probabilities are estimated by frequencies from samples without missing data (natural sampling); (2) second order probabilities distributions are a plausible way to model imprecise probabilities; and (3) Bayesian networks represent a normative reference for multi-cue models of probabilistic inference. |
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We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. At the empirical level, a thorough examination of the base rate literature (including the famous lawyer–engineer problem) does not support the conventional wisdom that people routinely ignore base rates. Quite the contrary, the literature shows that base rates are almost always used and that their degree of use depends on task structure and representation. Specifically, base rates play a relatively larger role (...) |
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This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that (...) |
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Base rates are vital in predicting violent criminal recidivism. However, both lay people given simulated prediction tasks and professionals milking real life predictions appear insensitive to variations in the base rate of violent recidivism. Although there are techniques to help decision makers attend to base rates, increased decision accuracy is better sought in improved actuarial models as opposed to improved clinicians. |
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The base rate fallacy is directly dependent on a particular judgment paradigm in which information may be unambiguously designated as either “base rate” or “individuating,” and in which subjects make two-stage sequential judgments. The paradigm may be a poor match for real world settings, and the fallacy may thus be undefined for natural ecologies of judgment. |
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Abstract(1) There is enough contradictory evidence regarding the role of base rates in category learning to confirm the nonexistence of biases in such learning. (2) It is not always possible to activate statistical reasoning through frequentist representation. (3) It is necessary to use the concept of systematic processing in reconsidering the published work on biases. |
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The environment in which humans evolved is strongly and positively autocorrelated in space and time. Probabilistic judgments based on the assumption of independence may not yield evolutionarily adaptive behavior. A number of “faults” of human reasoning are not faulty under fuzzy arithmetic, a nonprobabilistic calculus of reasoning under uncertainty that may be closer to that underlying human decision making. |
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Base rates have no necessary relation to judgments that are not themselves probabilities. There is no logical imperative, for instance, that behavioral base rates must affect causal attributions or that base rate information should affect judgments of legal liability. Decision theorists should be cautious in arguing that base rates place normative constraints on judgments of anything other than posterior probabilities. |
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Koehler's work will assist the effort to understand legal fact finding. It leaves two questions somewhat open: (i) the extent to which empirical research can measure correctness of fact-finding, a function that involves the resolution of normative questions and (ii) the standards judges should use in the absence of the research he advocates. |
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The base rate literature has an opposite twin in the social psychological literature on stereotypes, which concludes that people use their preexisting beliefs about probabilistic category attributes too much, rather than not enough. This ironic discrepancy arises because beliefs about category attributes enhance accuracy when the beliefs are accurate and diminish accuracy when they are not. To determine the accuracy of base rate/stereotype beliefs requires research that addresses specific content. |
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Consistent with Koehler's position, we propose a generalization of the base rate fallacy and earlier conservatism literatures. In studies using both traditional tasks and new tasks based on ecologically valid base rates, our subjects typically underweight individuating information at least as much as they underweight base rates. The implications of cue consistency for averaging heuristics are discussed. |
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Koehler is right that base rate information is used, to various degrees, both in laboratory tasks and in everyday life. However, it is not time to turn our backs on laboratory tasks and focus solely on ecologically valid decision making. Tightly controlled experimental data are still needed to understandhowbase rate information is used, and how this varies among groups. |
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In contrast to traditional research on base-rate neglect, an ecologically-oriented research program would analyze the correspondence between cognitive algorithms and the nature of information in the environment. Bayesian computations turn out to be simpler when information is represented in frequency formats as opposed to the probability formats used in previous research. Frequency formats often enable even uninstructed subjects to perform Bayesian reasoning. |
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The important question is how people process probabilistic information, not whether they process it in accordance with a normative model that we never should have expected them to be capable of following. Experience is not the cure, as widely thought, to problems with utilizing base rate information. |
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