The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals.

The conclusions of Barbey & Sloman (B&S) crucially depend on evidence for different representations of statistical information. Unfortunately, a muddled distinction made among these representations calls into question the authors' conclusions. We clarify some notions of statistical representations which are often confused in the literature. These clarifications, combined with new empirical evidence, do not support a dual-process model of judgment.

The tendency to neglect base-rates in judgment under uncertainty may be “notorious,” as Barbey & Sloman (B&S) suggest, but it is neither inevitable (as they document; see also Koehler 1996) nor unique. Here we would like to point out another line of evidence connecting ecological rationality to dual processes, the failure of individuals to appropriately judge cumulative probability.

Barbey & Sloman's (B&S's) base-rate respect model is anticipated by Reyna's denominator neglect model. There are parallels at three levels: (a) explanations are grounded in a general cognitive theory (rather than in domain-specific ideas); (b) problem structure is treated as a key source of reasoning errors; and most importantly, (c) nested set relations are seen as the cause of base-rate neglect.

Both the theoretical frameworks that organize the first part of Barbey & Sloman's (B&S's) target article and the empirical evidence marshaled in the second part are marked by distinctions that should not exist (i.e., false dichotomies), conflations where distinctions should be made, and selective omissions of empirical results – within the very studies discussed – that create illusions of theoretical and empirical favor.

Research in mathematical cognition has shown that rates, and other interpretations of x/y, are hard to learn and understand. On the other hand, there is extensive evidence that the brain is endowed with a specialized mechanism for representing and manipulating the numerosities of sets – that is, frequencies. Hence, base-rates are neglected precisely because they are rates, whereas frequencies are indeed natural.

Barbey & Sloman (B&S) claim that frequency formats and other task manipulations induce people to substitute associative thinking for rule-based thinking about nested sets. My critique focuses on the substitution assumption. B&S demonstrate that nested sets are important to solve base-rate problems but they do not show that thinking about these nested sets relies on a different type of reasoning.

We agree that current evolutionary accounts of base-rate neglect are unparsimonious, but we dispute the authors' account of the effect in terms of parallel associative and rule-based processes. We also question their assumption that cueing of nested set relations facilitates performance due to recruitment of explicit reasoning processes. In our account, such reasoning is always involved, but usually unsuccessful.

We present evidence supporting the target article's assertion that while the presentation of base-rate information in a natural frequency format can be helpful in enhancing sensitivity to base rates, method of presentation is not a panacea. Indeed, we review studies demonstrating that when subjects directly experience base rates as natural frequencies in a trial-by-trial setting, they evince large base-rate neglect.

The general principle behind the effects of nested sets on the use of base rates, we believe, is that the mind is prepared to take in “ecologically structured information.” Without any need to assume two cognitive systems, this principle explains how the proper use of base rates can be facilitated and also accounts for occasions when base rates are overused.

The terms nested sets, partitive frequencies, inside-outside view, and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999). The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis – it uses exactly the same numbers as natural frequencies. We show that non-Bayesian reasoning in children, laypeople, and physicians follows multiple rules rather than a general-purpose associative process in a vaguely specified “System 1.” It is unclear what the theory in “dual process theory” is: Unless the two processes are defined, this distinction can account post hoc for almost everything. In contrast, an ecological view of cognition helps to explain how insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures.

Barbey & Sloman (B&S) conclude that natural frequency theorists have raised a fundamental question: What are the conditions that compel individuals to reason extensionally? We argue that word problems asking for a numerical judgment used by these theorists cannot answer this question. We present evidence that nonverbal tasks can elicit correct intuitions of posterior probability even in preschoolers.

Manipulations that draw attention to extensional or set-based considerations are neither sufficient nor necessary for enhanced use of base rates in intuitive judgments. Frequency formats are only one part of the puzzle of base-rate use and neglect. The conditions under which these and other manipulations promote base-rate use may be more parsimoniously organized under the broader notion of case-based judgment.

Barbey & Sloman (B&S) advocate a dual-process (two-system) approach by comparing it with an alternative perspective (ecological rationality), claiming that the latter is unwarranted. Rejecting this alternative approach cannot serve as sufficient evidence for the viability of the former.

The hypothesis that structural properties and not frequencies per se improve base-rate sensitivity is supported from the perspective of natural sampling. Natural sampling uses a special frequency format that makes base-rates redundant. Unfortunately, however, it does not allow us to empirically investigate human understanding of essential properties of uncertainty – most importantly, the understanding of conditional probabilities in Bayes' Theorem.

Barbey & Sloman (B&S) attribute all instances of normative base-rate usage to a rule-based system, and all instances of neglect to an associative system. As it stands, this argument is too simplistic, and indeed fails to explain either good or bad performance on the classic Medical Diagnosis problem.

Human responses to probabilities can be studied through gambling and through experiments presenting biased sequences of stimuli. In both cases, participants are sensitive to base rates. They adjust automatically to changes in base rate; such adjustment is incompatible with conformity to Bayes' Theorem. ”Base-rate neglect” is therefore specific to the exercises in mental arithmetic reviewed in the target article.

The formulation of the conditional probability in classical tasks does not guarantee the effective transmission of the independence of the hit rate from the base rate. In these kinds of tasks, data are all available, but subjects are able to understand them in the specific meanings proper to a specialized language only if these are adequately transmitted. From this perspective, the partitive formulation should not be considered a facilitation, but rather, a way of effectively transmitting the conditional probability.

Consistent with Barbey & Sloman (B&S), it is proposed that performance on Bayesian inference tasks is well explained by nested sets theory (NST). However, contrary to those authors' view, it is proposed that NST does better by dispelling with dual-systems assumptions. This article examines why, and sketches out a series of NST's core principles, which were not previously defined.

The article by Barbey & Sloman (B&S) provides a valuable framework for integrating research on base-rate neglect and respect. The theoretical arguments and data supporting the nested set model are persuasive. But we found the dual-process account to be under-specified and less compelling. Our concerns are based on (a) inconsistencies within the literature cited by B&S, and (b) studies of base-rate neglect in categorization.