Although we agree that the two-system nested set account provides a better fit to the data reviewed in the target article than the alternative frequency-format accounts, we believe that the nested set account is an overly narrow lens through which to view base-rate use and its relation to probability and frequency judgments. In particular, manipulations making nested set representations more transparent may not be sufficient to improve base-rate use and such manipulations are not necessary to improve base-rate use. In terms of the dual systems model, base-rate use is not improved solely by rule-based processes, nor is base-rate neglect always driven by associative processes. By focusing only on areas where frequency formats increase base-rate use, the target article oversells the value of frequency formats – and rule-based or System 2 processes more generally – in improving intuitive judgment.

A case-based judgment account built on Kahneman and Tversky's early theorizing (e.g., Kahneman & Tversky Reference Kahneman and Frederick1973) provides a perspective on intuitive judgment that is compatible with yet broader than the nested set account. The case-based account provides a parsimonious explanation of patterns of base-rate use and neglect across both probability reasoning tasks and experience-based probability judgments, and also provides a more realistic view of the debiasing value of frequency formats. According to the case-based account, intuitive judgments focus on assessing the strength of evidence relevant to the current case at hand (Brenner et al. Reference Brenner, Griffin and Koehler2005; Griffin & Tversky Reference Griffin and Tversky1992). Strength of evidence is commonly evaluated by associative processes such as similarity or fluency, but can also be evaluated by rule-based processes. However, to the extent that both associative and rule-based processes focus on the strength of impression favoring a particular hypothesis about the current case, background evidence about class or extensional relations is not included when the strength of evidence is mapped onto a probability (or related) scale. This produces neglect of base rates, as well as neglect of cue validity in intuitive judgments.

According to the case-based account, any evidence that influences the strength of impression regarding the case at hand will affect probability judgment. This explains why base rates that can be interpreted (associatively, via System 1 processes) as a propensity of the single case are highly influential. Racial or gender stereotypes, for example, can be interpreted as base rates but also can yield a strong expectation about a particular individual. Similarly, the win-loss record of a sports team can yield an impression of the strength of that team (Gigerenzer et al. Reference Gigerenzer, Hell and Blank1988). The debate about “causal” base rates can also be interpreted in this way (Tversky & Kahneman Reference Tversky, Kahneman and Fishbein1980). When provided with a statistical summary of the number of blue versus green cabs in a city, people rely on the testimony of a fallible accident witness and disregard the base rate; however, when base rates are given a causal significance by describing the differential likelihood of accidents for the cabs, both the witness's testimony and the accident-proneness of cabs contribute to the strength of impression for this particular accident. In these contexts, the use of base rates per se does not indicate a System 2 rule-based process.

Furthermore, improved judgment resulting from a diagram or other aid to viewing a problem in terms of nested sets does not necessarily implicate rule-based reasoning. Diagrams prompting an immediate comparison of the size of circles may allow a low-level perceptual computation to solve the problem. If wording or outcome formats allow a judge to represent such relationships visually or symbolically, the line between associative and rule-based solutions becomes blurred. From the perspective of the case-based account, such manipulations may operate through their impact on the case-specific impression of evidence strength. The results of the Girotto and Gonzalez (Reference Girotto and Gonzalez2001) study described in the target article could be interpreted in this manner.

According to the evolutionary frequency module account, “our hunter-gatherer ancestors were awash in statistical information in the form of the encountered frequencies of real events: in contrast, the probability of a single event was inherently unobservable to them” (Cosmides & Tooby Reference Cosmides and Tooby1994, p. 330). In several recent studies (Brenner et al. Reference Brenner, Griffin and Koehler2005; Reference Brenner, Griffin and Koehler2006), we have examined probability judgment in a learning paradigm similar to the Gluck and Bower (Reference Gluck and Bower1988) study described in the target article. In this simulated stock market study, case-specific evidence is provided in terms of a company's sales and costs. A participant's task is to estimate the probability that the stock price will increase, given the financial information and experience in the market which provide evidence about the base rate of stock increases and the validity of financial cues. Notably, participants were extremely accurate in estimating the base rates that they had experienced. However, despite this – and despite being awash in encountered frequencies – participants' probability judgments were largely unaffected by base rates or cue validity. When juxtaposed with case-specific information, apparently, such extensional considerations can be readily available, yet be viewed as largely irrelevant to the judgment. A more evolutionarily grounded outcome measure would assess the resources that an individual is willing to commit to a decision based on uncertain evidence. A natural measure is thus the price one is willing to pay for a stock certificate for a particular company. When price is used as an outcome measure in our learning paradigm, however, the neglect of base rate and cue validity remains.

Barbey & Sloman (B&S) offer a helpful reappraisal of the impact of frequency representations on base-rate use in probability reasoning tasks. We agree that the evidence clearly does not support the strong claim that frequency formulations yield effortless Bayesian reasoning. The view that base-rate use proceeds only or primarily through application of rules of set inclusion, however, may also be too strong. On the one hand, Bayesian solution rates are far from perfect when set relations are explicitly highlighted (see Table 4 of the target article). On the other hand, under the right circumstances, base rates may be used effortlessly, if they are captured in the immediate impression of the strength of evidence regarding the case at hand.