Science presents occasional examples of parallel development of the same ideas to explain the same findings. I comment here on such an example found in the psychology of judgment and decision making: the dual-process model of base-rate neglect proposed in the target article by Barbey & Sloman (B&S) and a dual-process model of base-rate neglect that was developed in the 1990s by Reyna (Reference Reyna1991; Reyna & Brainerd Reference Reyna, Brainerd, Davies and Logie1993; Reference Reyna, Brainerd, Wright and Ayton1994; Reference Reyna and Brainerd1995).

The key properties of the Barbey-Sloman model are its assumptions that (a) an explanation of base-rate neglect must be grounded in a general cognitive theory (not domain-specific ideas), (b) structural features of base-rate problems are what cause errors, and (c) set nesting is the structural feature that is directly responsible for errors. These are also properties of Reyna's dual-process denominator neglect model. The research program that led to Reyna's theory was the first to develop a process model for Tversky and Kahneman's (Reference Tversky and Kahneman1983) suggestion that set nesting produces errors in the conjunction fallacy, and was the first to elucidate specific cognitive difficulties that nested sets foment in reasoners.

Concerning assumption (a), the aim of Reyna's research program was to identify cognitive mechanisms that cause various classes of reasoning illusions. From the beginning, the guiding principles were that models of reasoning illusions, such as base-rate neglect, should be grounded in a general cognitive theory and that domain-specific accounts are at best unparsimonious and at worst untestable. This work produced a general framework, known as fuzzy-trace theory (FTT), that explains reasoning illusions by focusing on relations between memory processes and reasoning operations. FTT's level of generality is such that it has been widely used to explain basic memory processes (e.g., FTT's models of recognition and recall) as well as reasoning illusions.

Concerning assumption (b), FTT explains reasoning illusions by isolating structural properties of reasoning problems that interfere with three general stages of cognitive processing: (1) storing the correct problem representation (its “gist”), (2) retrieving that representation and the appropriate processing operations on reasoning problems, and (3) executing the steps that are required for the processing operations to deliver solutions. This approach is exemplified in FTT's explanations of many types of reasoning failures, such as arithmetic errors (Brainerd & Reyna Reference Brainerd and Reyna1988) and transitive inference errors (Reyna & Brainerd Reference Reyna and Brainerd1990).

Concerning assumption (c), extensive research was conducted on the cognitive mechanisms that cause errors in the family of illusions to which base-rate neglect belongs: inclusion illusions. Much of that work involved a prototypical task that produces such errors: Piaget's class-inclusion problem. The mechanisms that were identified were then generalized to base-rate problems, conjunction problems, probability problems, expected-value problems, and other tasks in the inclusion illusions family. Class-inclusion problems are structurally simple but cognitively impenetrable: Children are presented with an array of objects, subdivided into two (or more) familiar sets, such as 7 cows and 3 horses, that belong to a common superordinate set (10 animals), and are asked “Are there more animals or more cows?” Young children consistently respond: “more cows.” This error persists for many years, with the error rate at age 10 still being 50% (Winer Reference Winer1980), and adults routinely make the error on slightly more complex versions of the problem (Reyna Reference Reyna1991). Why are such problems so difficult?

The answer that emerged, following many experiments (e.g., Brainerd & Reyna Reference Brainerd and Reyna1990; Reference Brainerd and Reyna1995), is that nested sets interfere massively with the aforementioned processing stages. Reyna (Reference Reyna1991) summarized the cognitive effects as follows: “processing focuses on the subset mentioned in the question, the superordinate set recedes, and the question appears to involve nothing more than … a subset-subset comparison” (p. 325). These effects were found to be rooted in the fact that problems in the inclusion illusions family have two-dimensional structures, with one dimension (the subset-subset) being salient and easy to process and the other (the subset-superordinate set), which is crucial to solution, being obscure. The obscurity is caused by the containment relation, which creates “mental booking” problems in which subsets disappear whenever the mind focuses on the superordinate set and the superordinate set disappears whenever the mind focuses on the subsets. Yet, correct reasoning demands subset-superordinate set comparisons. Reyna went on to formulate the denominator neglect model, wherein this difficulty was posited as the cause of base-rate neglect, the conjunction fallacy, and other errors that arise from comparing numerical parts to numerical wholes. The term “denominator” referred to the fact that denominator information is ignored because denominators are obscure wholes of part–whole relations.

A last point that illustrates the deep parallels between the Reyna and the Barbey-Sloman models is the centrality of formatting manipulations in tests of the models. These are manipulations that make problem structure more transparent and, crucially, enhance the salience of subset-superordinate set relations. Reyna noted that her model predicts that such manipulations reduce the mental bookkeeping problem and, therefore, should significantly reduce errors. A formatting manipulation called tagging provided dramatic confirmation. Young children, who failed problems such as the animal example across the board, performed nearly perfectly when simple tags (e.g., a hat on each animal's head, a bow on each animal's tail) were affixed to all the members of each subset, so that the superordinate set was just as salient as the subsets. Likewise, B&S stress the importance of presentation formats that allow “accurate representation in terms of nested sets of individuals” (target article, Abstract) in base-rate problems. With respect to the most effective presentation formats that they discuss, these formats, too, are ones that ought to reduce the mental bookkeeping problem of nested sets.

Although the Barbey-Sloman model is anticipated to a remarkable degree by the Reyna model, the dual-process frameworks that lie behind the models are different. The Barbey-Sloman framework is the traditional System 1/System 2 approach, which treats intuition as a primitive form of thinking that cognitive development and expertise evolve away from. The Reyna framework is FTT, which treats intuition as an advanced mode of thinking that cognitive development and expertise evolve towards. That intuition is advanced by virtue of memory considerations, though different ones than those which figure in the Barbey-Sloman model (see Table 1).