Judgment dissociation theory: An analysis of differences in causal, counterfactual and covariational reasoning.

Research suggests that causal judgment is influenced primarily by counterfactual or covariational reasoning. In contrast, the author of this article develops judgment dissociation theory (JDT), which predicts that these types of reasoning differ in function and can lead to divergent judgments. The actuality principle proposes that causal selections focus on antecedents that are sufficient to generate the actual outcome. The substitution principle proposes that ad hoc categorization plays a key role in counterfactual and covariational reasoning such that counterfactual selections focus on antecedents that would have been sufficient to prevent the outcome or something like it and covariational selections focus on antecedents that yield the largest increase in the probability of the outcome or something like it. The findings of 4 experiments support JDT but not the competing counterfactual and covariational accounts. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A quantum theoretical explanation for probability judgment errors.

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors, including the anchoring and adjustment model for probability judgments. In the quantum model, a new fundamental concept in cognition is advanced—the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. We conclude that quantum information-processing principles provide a viable and promising new way to understand human judgment and reasoning. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

On the probability of making Type I errors.

A statistical test leads to a Type I error whenever it leads to the rejection of a null hypothesis that is in fact true. The probability of making a Type I error can be characterized in the following 3 ways: the conditional prior probability, the overall prior probability, and the conditional posterior probability. In this article, we show (a) that the alpha level can be equated with the 1st of these and (b) that it provides an upper bound for the second but (c) that it does not provide an estimate of the third, although it is commonly assumed to do so. We trace the source of this erroneous assumption first to statistical texts used by psychologists, which are generally ambiguous about which of the 3 interpretations is intended at any point in their discussions of Type I errors and which typically confound the conditional prior and posterior probabilities. Underlying this, however, is a more general fallacy in reasoning about probabilities, and we suggest that this may be the result of erroneous inferences about probabilistic conditional statements. Finally, we consider the possibility of estimating the (posterior) probability of a Type I error in situations in which the null hypothesis is rejected and, hence, the proportion of statistically significant results that may be Type I errors. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Inferred values and the reverse-incentive effect in induced compliance.

It is proposed that when Ss are offered a large payment for engaging in an activity, they infer that the activity must be difficult, tedious, risky, or unpleasant in some way. This inference can produce the familiar reverse-incentive effect in induced compliance situations. Unlike other explanations, this analysis predicts that the reverse-incentive effect will occur even when Ss do not engage in the activity and when they have no choice about engaging in it. The results of 4 studies support these predictions. It is suggested that the same analysis in terms of inferred values can explain other reverse-incentive effects, particularly certain instances of the overjustification effect. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

True or false: Do 5-year-olds understand belief?

In 3 studies (N = 188) we tested the hypothesis that children use a perceptual access approach to reason about mental states before they understand beliefs. The perceptual access hypothesis predicts a U-shaped developmental pattern of performance in true belief tasks, in which 3-year-olds who reason about reality should succeed, 4- to 5-year-olds who use perceptual access reasoning should fail, and older children who use belief reasoning should succeed. The results of Study 1 revealed the predicted pattern in 2 different true belief tasks. The results of Study 2 disconfirmed several alternate explanations based on possible pragmatic and inhibitory demands of the true belief tasks. In Study 3, we compared 2 methods of classifying individuals according to which 1 of the 3 reasoning strategies (reality reasoning, perceptual access reasoning, belief reasoning) they used. The 2 methods gave converging results. Both methods indicated that the majority of children used the same approach across tasks and that it was not until after 6 years of age that most children reasoned about beliefs. We conclude that because most prior studies have failed to detect young children's use of perceptual access reasoning, they have overestimated their understanding of false beliefs. We outline several theoretical implications that follow from the perceptual access hypothesis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Reasoning From Inconsistency to Consistency.

This article presents a theory of how individuals reason from inconsistency to consistency. The theory is based on 3 main principles. First, individuals try to construct a single mental model of a possibility that satisfies a current set of propositions, and if the task is impossible, they infer that the set is inconsistent. Second, when an inconsistency arises from an incontrovertible fact, they retract any singularly dubious proposition or any proposition that is inconsistent with the fact; otherwise, they retract whichever proposition mismatches the fact. A mismatch can arise from a proposition that has only mental models that conflict with the fact or fail to represent it. Third, individuals use their causal knowledge-in the form of models of possibilities-to create explanations of what led to the inconsistency. A computer program implements the theory, and experimental results support each of its principles. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Ecological and evolutionary validity: Comments on Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni's (1999) mental-model theory of extensional reasoning.

The mental-model account of naive probabilistic reasoning by P. N. Johnson-Laird, P. Legrenzi, V. Girotto, A. S. Legrenzi, and J.-P. Caverni (1999) provides an opportunity to clarify several similarities and differences between it and ecological rationality (frequentist) accounts. First, ambiguities in the meaning of Bayesian reasoning can lead to disagreements and inappropriate arguments. Second, 2 conflated effects of using natural frequencies are noticed but not actually tested separately because of an artificial dissociation of frequency representations and natural sampling. Third, similarities are noted between the subset principle and the principle of natural sampling. Finally, some potentially misleading portrayals of the role of evolutionary factors in psychology are corrected. Mental-model theory, rather than better explaining probabilistic reasoning, may be able to use frequency representations as a key element in clarifying its own ambiguous constructs. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Geotechnical Engineering Reliability: How Well Do We Know What We Are Doing?

Uncertainty and risk are central features of geotechnical and geological engineering. Engineers can deal with uncertainty by ignoring it, by being conservative, by using the observational method, or by quantifying it. In recent years, reliability analysis and probabilistic methods have found wide application in geotechnical engineering and related fields. The tools are well known, including methods of reliability analysis and decision trees. Analytical models for deterministic geotechnical applications are also widely available, even if their underlying reliability is sometimes suspect. The major issues involve input and output. In order to develop appropriate input, the engineer must understand the nature of uncertainty and probability. Most geotechnical uncertainty reflects lack of knowledge, and probability based on the engineer’s degree of belief comes closest to the profession’s practical approach. Bayesian approaches are especially powerful because they provide probabilities on the state of nature rather than on the observations. The first point in developing a model from geotechnical data is that the distinction between the trend or systematic error and the spatial error is a modeling choice, not a property of nature. Second, properties estimated from small samples may be seriously in error, whether they are used probabilistically or deterministically. Third, experts generally estimate mean trends well but tend to underestimate uncertainty and to be overconfident in their estimates. In this context, engineering judgment should be based on a demonstrable chain of reasoning and not on speculation. One difficulty in interpreting results is that most people, including engineers, have difficulty establishing an allowable probability of failure or dealing with low values of probability. The F–N plot is one useful vehicle for comparing calculated probabilities with observed frequencies of failure of comparable facilities. In any comparison it must be noted that a calculated probability is a lower bound because it must fail to incorporate the factors that are ignored in the analysis. It is useful to compare probabilities of failure for alternative designs, and the reliability methods reveal the contributions of different components to the uncertainty in the probability of failure. Probability is not a property of the world but a state of mind; geotechnical uncertainty is primarily epistemic, Bayesian, and belief based. The current challenges to the profession are to make use of probabilistic methods in practice and to sharpen our investigations and analyses so that each additional data point provides maximal information.     

Propositional reasoning by model.

Describes a new theory of propositional reasoning, that is, deductions depending on if, or, and, and not. The theory proposes that reasoning is a semantic process based on mental models. It assumes that people are able to maintain models of only a limited number of alternative states of affairs, and they accordingly use models representing as much information as possible in an implicit way. They represent a disjunctive proposition, such as "There is a circle or there is a triangle," by imagining initially 2 alternative possibilities: one in which there is a circle and the other in which there is a triangle. This representation can, if necessary, be fleshed out to yield an explicit representation of an exclusive or an inclusive disjunction. The theory elucidates all the robust phenomena of propositional reasoning. It also makes several novel predictions, which were corroborated by the results of 4 experiments. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Predicting intermediate and multiple conclusions in propositional logic inference problems: Further evidence for a mental logic.

This article examines whether a particular mental logic introduced by M. D. S. Braine, B. J. Reiser, and B. Rumain (1984) is a reasonably accurate model of people's logical routines for propositional reasoning. Participants are presented with reasoning problems; to make their reasoning steps explicit, they write down, in order, everything they infer. The inferences predicted by the model are compared with participants' output. Three quarters of participants' responses were predicted, and 85%–90% of the time the output of the model's core inference rules was written down. To predict equally well, L. J. Rips's (1994) mental logic model would need to adopt some of our model's features. The data indicate several problems in the mental models theory and cannot be explained by pragmatic reasoning schemas. Arguments against a mental logic are questioned. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Distributional versus singular approaches to probability and errors in probabilistic reasoning.

Four experiments examined differences in probabilistic reasoning as a function of whether problems were presented in a frequentist or case-specific form. The experiments demonstrated that these different forms influence the likelihood of Ss committing the conjunction and disjunction fallacies. The authors contend that these 2 forms elicit different approaches to probability. Frequency problems, it is argued, elicit a distributional approach in which probabilities are equated with relative frequencies, whereas case-specific problems elicit a singular approach in which probabilities are equated with the propensities or causal forces operating in an individual case. According to this account, distributional and singular approaches evoke different kinds of inferential rules and heuristic procedures, some of which are more closely aligned with extensional principles than others. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The primacy of thinking about possibilities in the development of reasoning.

One of the main tenets of the mental model theory is that when individuals reason, they think about possibilities. According to this theory, reasoning on what is possible from the truth of a sentence would be psychologically basic, whereas reasoning the other way round, on the truth or falsity of a sentence from a given state of affairs, would require some meta-ability. The present study tested the developmental corollary of this theory, which is that reasoning about possibilities should develop first, whereas the development of reasoning about truth-value should be delayed. For this purpose, 3rd, 6th, and 9th graders as well as adults were presented with tasks requiring them to evaluate either the possibilities compatible with conditional sentences or the truth-value of these sentences from these same possibilities. The results revealed 2 phenomena. First, the same developmental trend was observed in both tasks with 3 successive interpretational levels: conjunctive, biconditional, and then conditional. Second, there was a developmental lag between the 2 forms of reasoning—with developmental transitions from one level to the next occurring about 3 years later when reasoning about truth-value. The implications of these results for theories of cognitive development and of reasoning are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

A policy-capturing investigation of the role of expectancies in decisions to pursue job alternatives.

Two methodological approaches, policy capturing and narrative self-reports, were used to examine how individuals combine information about job characteristics and probabilities of receiving job offers (expectancies) in decisions to pursue job vacancies. 10 college students evaluated 24 hypothetical job alternatives at 3 expectancy levels in terms of overall attractiveness and whether they would apply for a job interview. A variety of within-S analyses were used to infer how probabilities of receiving a job offer affect peoples' propensities to apply for jobs. Results indicate that there was wide individual variability in the way expectancies influenced job-search patterns. Low probabilities of receiving job offers acted as much stronger search deterrrants for some Ss than for others. Results are discussed in terms of (a) possible sources of individual differences in expectancy usage, (b) the value of using multiple methodologies to investigate decision processes, and (c) the desirability of broadening the types of questions typically asked about the role of expectancies in job search and choice. (35 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Deduction as verbal reasoning.

Most theories of deduction have assumed that linguistic processes transduce from language into an internal representation and back again, and that non-linguistic processes are central to deduction itself. In this article it is proposed that for deduction tasks for which the necessary information is provided verbally, the heart of deduction for untrained participants involves repeatedly reencoding the problem, a type of behavior referred to here as verbal reasoning. It is shown that model theory accounts of behavior on most deduction tasks are consistent with verbal reasoning and that verbal reasoning can account for detailed behavior in a single task; a computational model of syllogistic reasoning—VR—based on linguistic mechanisms is presented. VR models all of the standard phenomena, makes a number of accurate novel predictions, and fits the behavior of individual participants with an accuracy that rivals their own test–retest reliability. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Can any ostrich fly?: some new data on belief bias in syllogistic reasoning

According to one version of the mental models theory (Oakhill, J.V., Johnson-Laird, P.N., Garnham, A., 1989. Believability and syllogistic reasoning. Cognition 31, 117-140) beliefs exert their influence on reasoning in three ways. First they can affect the interpretation of the premises, for example by conversion. Second, they can curtail the search for alternative models of the premises, if an initial model supports a believable conclusion. Third, they can act as a filter on any conclusion that is eventually generated. This last influence is important in explaining the effects of belief bias in one-model syllogisms with no convertible premises, since such syllogisms, by definition, have no alternative models. However, the most natural interpretation of such a filter is that it filters out conclusions and leads to the response 'no valid conclusion'. The present study, which was conducted with groups of both British and Italian subjects, looked at the effect of prior knowledge on syllogistic reasoning, and showed that: (1) invalid conclusions for such one model syllogisms, either thematic or abstract, are typically not of the type 'no valid conclusion', but state invalid relations between the end terms; (2) belief-bias is completely suppressed when previous knowledge is incompatible with the premises, and therefore the premises themselves are always considered. The results are compatible with a version of the mental models theory in which a representation of prior knowledge precedes modelling of the premises, which are then incorporated into the representation of this knowledge. The relation between this theory and other accounts of belief bias in syllogistic reasoning, and the implications of these findings for reasoning more generally, are considered.     

In defense of reasoning: A reply to Greene (1992).

Responds to S. B. Greene's (see record 1992-15270-001) argument that assertions of the form "None of the A are in the same place as some of the C" are difficult for Ss to generate and that this explains the results of multiply quantified reasoning without having to invoke mental models or deductive reasoning by P. N. Johnson-Laird et al (see record 1990-03501-001). This article shows (1) that the phenomenon fails to explain most of the principal results; (2) that, far from undermining the theory of mental models, it can actually be explained by the theory; and (3) that the best available account of the results is that Ss both reason and rely on mental models to do so. (PsycINFO Database Record (c) 2010 APA, all rights reserved)