The tension between what Jones & Love (J&L) refer to as “fundamentalist” and “enlightened” Bayesian approaches to cognition is well illustrated in the field of human reasoning. Historically, Bayesian models have played an important role in trying to answer an intriguing but difficult problem in inductive reasoning: how people make predictions about objects whose category membership is uncertain. This problem can be illustrated by the example of a person hiking through a forest who hears a rustling in the scrub near her feet and wishes to predict whether they are in danger. Although the hiker knows of many animals (e.g., snakes, small mammals, birds) that could produce the noise, she cannot be certain about the actual source. The main question is to what extent does she consider the various category alternatives when making a prediction about the likelihood of danger?

One influential approach to this problem is Anderson's (1991b) Rational Model (for a more recent instantiation, see Sanborn et al. Reference Sanborn, Griffiths and Navarro2010a). This Bayesian model assumes that “categorization reflects the derivation of optimal estimates of the probability of unseen features of objects” (Anderson Reference Anderson1991b, p. 409). In the case of inductive prediction with uncertain categories, the model assumes that predictions will be based on a normative consideration of multiple candidate animal categories and the conditional probability of a target feature (e.g., whether or not the animal is likely to cause injury) within each category.

One of the appeals of the model is that it can account for cases of inductive prediction where category membership of the target object is uncertain, as well as cases where the object's category membership has been established with certainty. In contrast, most non-Bayesian accounts of induction (e.g., Osherson et al. Reference Osherson, Smith, Wilkie, Lopez and Shafir1990; Sloman Reference Sloman1993) only deal with the latter case.

Despite this promise, the Rational Model suffers from many of the shortcomings that J&L attribute to “fundamentalist” Bayesian approaches. These include the following:

1. 1. Lack of attention to psychological processes such as selective attention. A considerable body of empirical evidence shows that, contrary to the Bayesian account, people do not consider all relevant category alternatives when making feature predictions (for a review, see Murphy & Ross Reference Murphy, Ross, Feeney and Heit2007). Instead, they generally make predictions based only on the category that a target object is most likely to belong to. In other words, in most cases of uncertain induction people ignore the uncertainty and selectively attend to the most likely category alternative. Although this leads to non-normative predictions, it may be a useful heuristic, leading to predictions that are approximately correct while avoiding much of the complex computation involved in integrating probabilities across categories (Ross & Murphy Reference Ross and Murphy1996).

2. 2. Implausible or incorrect assumptions about representation. Like many other Bayesian accounts, the Rational Model makes assumptions about feature and category representation that are not well-grounded in psychological theory and data. The model assumes that people treat features as conditionally independent when making inductive predictions. This means that the target object's known features (e.g., the rustling sound) are only used to identify the categories to which it might belong. These features are then ignored in the final stage of feature prediction. This assumption ignores a wealth of evidence that people are sensitive to correlations between features in natural categories and that such feature correlations influence categorization (Malt & Smith Reference Malt and Smith1984; Murphy & Ross Reference Murphy and Ross2010; Rosch & Mervis Reference Rosch and Mervis1975). Moreover, we have shown that people frequently base their inductive predictions on such feature correlations (Griffiths et al., in press; Newell et al. Reference Newell, Paton, Hayes and Griffiths2010; Papadopoulos et al. Reference Papadopoulos, Hayes and Newell2011).

3. 3. Failure to consider the impact of learner's goals and intent. The extent to which inductive prediction conforms to Bayesian prescriptions often reflects the goals of the reasoner. The same individual can show more or less consideration of category alternatives when making an inductive prediction, depending on a variety of task-specific factors such as the degree of association between category alternatives and the to-be-predicted feature and the cost of ignoring less likely alternatives (Hayes & Newell Reference Hayes and Newell2009; Ross & Murphy Reference Ross and Murphy1996). When people do factor category alternatives into their predictions, it is not necessarily because they are following Bayesian prescriptions but because of changes in what J&L refer to as “mechanistic considerations” such as changes in the relative salience of the categories (Griffiths et al., in press; Hayes & Newell Reference Hayes and Newell2009).

4. 4. Disconnect between representation and decision processes. Bayesian algorithms like those proposed by Anderson (Reference Anderson1991b) are best interpreted as models of the decision process. As such, they often make assumptions about (rather than examine) how people represent the category structures involved in induction. In the case of uncertain induction this is a problem because the neglect of less probable category alternatives may occur prior to the final decision, when people are still encoding evidence from the candidate categories (Griffiths et al., in press; Hayes et al. Reference Hayes, Kurniawan and Newell2011). It remains an open question whether Bayesian models of induction can capture such biases in evidence-sampling and representation (e.g., through the appropriate adjustment of priors).

In sum, the Rational Model has not fared well as an account of induction under category uncertainty. Many of the model's shortcomings reviewed here are common to other Bayesian models of cognition. These shortcomings do not necessarily mean that we should abandon Bayesian approaches. But progress in fields like inductive inference is more likely to be achieved if Bayesian models are more grounded in psychological reality.