Probability and Choice in the Selection Task

A Bayesian view of covariation assessment

When participants assess the relationship between two variables, each with levels of presence and absence, the two most robust phenomena are that: (a) observing the joint presence of the variables has the largest impact on judgment and observing joint absence has the smallest impact, and (b) participants' prior beliefs about the variables' relationship influence judgment. Both phenomena represent departures from the traditional normative model (the phi coefficient or related measures) and have therefore been interpreted as systematic errors. However, both phenomena are consistent with a Bayesian approach to the task. From a Bayesian perspective: (a) joint presence is normatively more informative than joint absence if the presence of variables is rarer than their absence, and (b) failing to incorporate prior beliefs is a normative error. Empirical evidence is reported showing that joint absence is seen as more informative than joint presence when it is clear that absence of the variables, rather than their presence, is rare.

Optimal data selection: revision, review, and reevaluation

Since it first appeared, there has been much research and critical discussion on the theory of optimal data selection as an explanation of Wason's (1966,1968) selection task (Oaksford & Chater, 1994). In this paper, this literature is reviewed, and the theory of optimal data selection is reevaluated in its light. The information gain model is first located in the current theoretical debate in the psychology of reasoning concerning dual processes in human reasoning. A model comparison exercise is then presented that compares a revised version of the model with its theoretical competitors. Tests of the novel predictions of the model are then reviewed. This section also reviews experiments claimed not to be consistent with optimal data selection. Finally, theoretical criticisms of optimal data selection are discussed. It is argued either that the revised model accounts for them or that they do not stand up under analysis. It is concluded that some version of the optimal data selection model still provides the best account of the selection task. Consequently, the conclusion of Oaksford and Chater's (1994) original rational analysis (Anderson, 1990), that people's hypothesis-testing behavior on this task is rational and well adapted to the environment, still stands.

Data selection and natural sampling: probabilities do matter

Probabilistic accounts of Wason's selection task (Oaksford & Chater, 1994, 1996) are controversial, with some researchers failing to replicate the predicted effects of probability manipulations. This paper reports a single experiment in which participants sampled the data naturally-that is, sequentially. The proportions of possible data types (i.e., cards in the selection task) also reflected the probability manipulation. Other than this procedural difference, the materials were the same as those in Oberauer, Wilhelm, and Rosas-Diaz's (1999) Experiment 3, which failed to show probabilistic effects. Significant probabilistic effects were observed. Moreover, in a comparative model-fitting exercise, a revised version of the information gain model (Hattori, 1999, 2002; Oaksford & Chater, in press-b) was shown to provide better fits to these data than did competing explanations.

Logic and human reasoning: an assessment of the deduction paradigm

The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases.

Conditionals: a theory of meaning, pragmatics, and inference

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals.

A quantitative model of optimal data selection in Wason's selection task

The optimal data selection model proposed by Oaksford and Chater (1994) successfully formalized Wason's selection task (Wason, 1966). The model, however, involved some questionable assumptions and was also not sufficient as a model of the task because it could not provide quantitative predictions of the card selection frequencies. In this paper, the model was revised to provide quantitative fits to the data. The model can predict the selection frequencies of cards based on a selection tendency function (STF), or conversely, it enables the estimation of subjective probabilities from data. Past experimental data were first re-analysed based on the model. In Experiment 1, the superiority of the revised model was shown. However, when the relationship between antecedent and consequent was forced to deviate from the biconditional form, the model was not supported. In Experiment 2, it was shown that sufficient emphasis on probabilistic information can affect participants' performance. A detailed experimental method to sort participants by probabilistic strategies was introduced. Here, the model was supported by a subgroup of participants who used the probabilistic strategy. Finally, the results were discussed from the viewpoint of adaptive rationality.

Ten years of the rational analysis of cognition

Rational analysis is an empirical program that attempts to explain the function and purpose of cognitive processes. This article looks back on a decade of research outlining the rational analysis methodology and how the approach relates to other work in cognitive science. We illustrate rational analysis by considering how it has been applied to memory and reasoning. From the perspective of traditional cognitive science, the cognitive system can appear to be a rather arbitrary assortment of mechanisms with equally arbitrary limitations. In contrast, rational analysis views cognition as intricately adapted to its environment and to the problems it faces.

DEDUCTIVE REASONING

This chapter describes the main accounts of deductive competence, which explain what is computed in carrying out deductions. It argues that people have a modicum of competence, which is useful in daily life and a prerequisite for acquiring logical expertise. It outlines the three main sorts of theory of deductive performance, which explain how people make deductions: They rely on factual knowledge, formal rules, or mental models. It reviews recent experimental studies of deductive reasoning in order to help readers to assess these theories of performance.