In the target article, Barbey & Sloman (B&S) argue against various versions of the popular natural frequency heuristic and claim that the best account of the data should be framed in terms of a dual-process model of judgment. Base-rate neglect with the standard problem format is attributed to the pervasiveness of the associative system. Frequency versions and other reviewed task manipulations are argued to boost performance because they would induce people to substitute associative thinking for rule-based thinking. Although I am sympathetic to the basic rationale behind the B&S framework, I want to point out that it lacks support for the crucial substitution assumption. The authors nicely clarify that representations in terms of nested sets reduce base-rate neglect but they do not show that thinking about these nested sets relies on a different type of reasoning. Such a claim requires an examination of the processing characteristics of the two postulated modes of thinking.

One of the core characteristics of rule-based reasoning is that it draws on executive, working-memory resources, whereas associative thinking is more automatic in nature (e.g., Stanovich & West Reference Stanovich2000). If the good performance on the frequency versions is due to a switch to rule-based reasoning, one would at least need to show that people recruit executive resources when they solve the frequency versions. This would demonstrate that the kind of thinking that is triggered by the frequency format exhibits the hallmark of rule-based thinking.

The good news is that B&S's model leads to some clear-cut, testable predictions. It is not hard to see, for example, how the substitution claim could be directly tested in a dual-task study (e.g., see De Neys Reference De Neys2006a; Reference De Neys2006b, for a related approach). B&S argue that in the vast majority of cases people rely on automatic, associative thinking to solve the standard probability format problems. Hence, burdening peoples' working-memory resources while they solve the probability versions should hardly affect their responses any further. However, if the frequency versions indeed trigger executive-demanding, rule-based processing, then the good performance on Bayesian inference problems with frequency formats should decrease under concurrent working-memory load (i.e., show a larger decrease than with standard probability formats). Note that the natural frequency accounts make the exact opposite prediction because they attribute the good performance on the modified versions to the recruitment of an automatically operating, module-based reasoning process. Hence, if the natural frequency theorists are right and people rely on an automatic module to solve the frequency versions, burdening peoples' working-memory resources should not hamper performance.

In theory, studies that look at the correlation between cognitive capacity and use of base rates may also help to test the substitution claim. If people recruit resource-demanding, rule-based thinking to solve the frequency versions, one expects that individual differences in working-memory capacity (or general intelligence) will mediate performance. The more resources that are available, the more likely that the correct response will be computed. The operation of an automatic, encapsulated module, on the other hand, should not depend on the size of a general cognitive resource pool. Unfortunately, the little correlational data we have is not conclusive. In their extensive research program, Stanovich and West included two Bayesian inference problems (i.e., so-called noncausal base-rate problems) with a standard probability format (i.e., the notorious “Cab” and “Aids” problems based on Casscells et al. Reference Casscells, Schoenberger and Graboys1978 and on Bar-Hillel Reference Bar-Hillel1980). In contrast to the bulk of their findings with other reasoning tasks, Stanovich and West did not find any systematic correlations with cognitive capacity measures.Footnote ¹ However, they did not look at correlations between cognitive capacity and performance on the crucial frequency format versions. Brase et al. (Reference Brase, Fiddick and Harries2006) did observe that students in top-tier universities solved frequency versions better than students in lower-ranked universities. If we simply assume that students in higher-ranked universities have a higher working memory capacity, the Brase et al. findings might present support for B&S's position. However, this conclusion remains tentative since Brase et al. did not explicitly test their participants on a standardized cognitive capacity measure.

In summary, B&S present an innovative model that highlights the central role of the set structure of a problem in the base-rate neglect phenomenon. I have tried to show that the model leads to some clear-cut predictions that might help to validate the framework in future studies. Unfortunately, the bad news is that in the absence of such processing validation, the central substitution claim of B&S's dual-system account remains questionable. Based on the available evidence, one needs to refrain from strong claims about the involvement of a rule-based reasoning system as the key mediator of base-rate “respect.”