In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). This belief violates the conjunction rule in probability theory. Tversky and Kahneman called this phenomenon the “conjunction fallacy”. Since the discovery of the phenomenon in 1983, researchers in psychology and philosophy (...) have engaged in important controversies around the conjunction fallacy. The goal of this paper is to explore the most important of these controversies, namely, the controversy about the nature of the conjunction fallacy. Is the conjunction fallacy mainly due to a misunderstanding of the problem by participants (misunderstanding hypothesis) or is it mainly due to a genuine reasoning bias (reasoning bias hypothesis)? A substantial portion of research on the topic has been directed to test the misunderstanding hypothesis. I review this literature and argue that a stronger case can be made against the misunderstanding hypothesis. Thus, I indirectly provide support for the reasoning bias hypothesis. (shrink)

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.

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.

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.

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.

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.”.

This paper addresses the problems of justifying and explaining beliefs about facts in the context of civil trials. The first section contains some remarks about the nature of adjudicative fact-finding and highlights the communicative features of deciding about facts in judicial context. In Sect. 2, some difficulties and the incompleteness presented by Bayesian and coherentist frameworks, which are taken as methods suitable to solve the above-mentioned problems, are pointed out. In the third section, the purely epistemic approach to the justification (...) and the explanation of beliefs about facts is abandoned and focus is given to the dialectical nature of civil procedure, where the parties and, particularly, the judge have to make their reasoning clear enough to allow a fruitful and efficient debate about facts. For this purpose, a communication/argumentation system is put forward, consisting of fourteen intertwined rules of discourse. The system embodies the fundamental epistemic principle according to which belief is updated given new evidence, is tailored for abductive inferences and is structured on fundamental concepts of civil procedural law. The fourth section presents an empirical application of the system to a real case. (shrink)

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.

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.

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.

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.

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 (...) in tasks where base rates are implicitly learned or can be represented in frequentist terms. Base rates are also used more when they are reliable and relatively more diagnostic than available individuating information. At the normative level, the base rate fallacy should be rejected because few tasks map unambiguously into the narrow framework that is held up as the standard of good decision making. Mechanical applications of Bayes's theorem to identify performance errors are inappropriate when (1) key assumptions of the model are either unchecked or grossly violated, and (2) no attempt is made to identify the decision maker's goals, values, and task assumptions. Methodologically, the current approach is criticized for its failure to consider how the ambiguous, unreliable, and unstable base rates of the real world are and should be used. Where decision makers' assumptions and goals vary, and where performance criteria are complex, the traditional Bayesian standard is insufficient. Even where predictive accuracy is the goal in commonly defined problems, there may be situations (e.g., informationally redundant environments) in which base rates can be ignored with impunity. A more ecologically valid research program is called for. This program should emphasize the development of prescriptive theory in rich, realistic decision environments. (shrink)

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 (...) and normative/prescriptive) are best answered through empirical studies that use real-world performance standards. (shrink)

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.

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.

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.

Judges and jurors must make decisions in an environment of ignoranceand uncertainty for example by hearing statements of possibly unreliable ordishonest witnesses, assessing possibly doubtful or irrelevantevidence, and enduring attempts by the opponents to manipulate thejudge''s and the jurors'' perceptions and feelings. Three importantaspects of decision making in this environment are the quantificationof sufficient proof, the weighing of pieces of evidence, and therelevancy of evidence. This paper proposes a mathematical frameworkfor dealing with the two first aspects, namely the quantification ofproof (...) and weighing of evidence. Our approach is based on subjectivelogic, which is an extension of standard logic and probability theory,in which the notion of probability is extended by including degrees ofuncertainty. Subjective Logic is a framework for modelling humanreasoning and we show how it can be applied to legalreasoning. (shrink)

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 (...) the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)