Pragmatic Aspects of the Base-rate Fallacy

Abstract

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

“…Furthermore, this explanation conflicts with the sample-space account because Macchi's suggestion that participants' interpretations [i.e., formulation (2)] rely on the sample space defined by feature D. Yet, according to the sample-space explanation, this is an unnatural and unlikely basis for probabilityjudgments. Finally, even though our formulation of the diagnostic information was in line with Macchi's (1995) recommendations for reducing the inverse fallacy, we still found that 51% of participants made almost all their judgments in accordance with the inverse fallacy.…”

“…This tendency has been alternatively labeled the conversion error (Wolfe, 1995), the confusion hypothesis (Macchi, 1995), the Fisherian algorithm (Gigerenzer & Hoffrage, 1995), and the inverse fallacy (Koehler, 1996a). In the present article, we adopt Koehler's term to refer to the tendency for judges to confuse any of participants can use when they estimate posterior probabilities (see, e.g., Gigerenzer & Hoffrage, 1995), the inverse fallacy is often the most frequent error observed.…”

“…Alternatively, Macchi (1995Macchi ( , 2000 proposed that the formulation of diagnostic information plays a key role in the interpretation of the data. Consider the following formulations: (1) The percentage of elements presenting the feature D is three times higher among H elements than among ,H elements.…”

“…(3) The feature D is present in x% of H elements, the feature D is present in y% of ,H elements, and x is three times higher than y. Macchi (1995) proposed that a formulation such as (1) is as is demonstrated by the diagrams presented in Figure 1. Furthermore, this explanation conflicts with the sample-space account because Macchi's suggestion that participants' interpretations [i.e., formulation (2)] rely on the sample space defined by feature D. Yet, according to the sample-space explanation, this is an unnatural and unlikely basis for probabilityjudgments.…”

Use of base rates and case cue information in making likelihood estimates

“…It would appear that the natural frequency format makes directly available to participants the information they need to make likelihood estimates, rather than forcing them to derive the information from base rates and rates of witness accuracy. Similarly Macchi (1995Macchi ( , 2000 has argued that making transparent the conditional probabilities inherent in base rate problems and the links among the pieces of information presented in problems may minimize base rate neglect. Certainly, it is desirable to present information in the most transparent and usable manner possible; however, much of the statistical information to which people are exposed in daily life is in the form of probabilities.…”