Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni [Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and we observe lower performance levels than those in the original article.     

Walking through doorways causes forgetting: environmental effects

Previous work has shown a decline in memory for objects carried through a doorway versus across a room. The aim of the current study is to extend this work to understand how variations in perceptual experience during these event shifts influence this finding. First a change in procedure to reduce memory load to a single item was assessed. Next we explored whether performance is influenced by spatial distance versus spatial categories, the ability to perceptually preview the next location, and changes in the colour and texture of the walls. The location updating effect was consistently observed for all manipulations, suggesting that such event transformations have a robust influence on human memory. This suggests that event cognition is driven more by the use of perceptual information to infer or impose a categorical shift from one event to another rather than by the nature of perceptual information available at the time.     

Mature Ego Development: A Gateway to Ego Transcendence?

This paper explores whether the highest stage in ego development is indicative of ego-transcendence as I initially surmised. Overall, I will explore some of the similarities and differences between rational awareness of the limits of representational thought and genuine postsymbolic knowing. I will present the research territory with a linear and a non-linear model of human development. Both models can accommodate both Eastern and Western self theories including ego development theory and Alexander's levels of mind. Next, I will outline an alternative developmental trajectory based on Alexander's notion of the shifts in the dominant mode of processing from personal–verbal–discursive to transpersonal–postsymbolic. Then, I will present ego development theory as I conceive of it now and outline the important characteristics of the highest stage (Cook-Greuter, 1999). Finally, I will consider the question of whether and in what way the Unitive ego stage is related to higher consciousness and introduce two testable propositions to clarify the issue.     

Extending Standard Models of ZFC to Models of Nonstandard Set Theories

We study those models of ZFCwhich are embeddable, as the class of all standard sets, in a model of internal set theory >ISTor models of some other nonstandard set theories. This revised version was published online in June 2006 with corrections to the Cover Date.     

A multitrait-multimethod model with minimal assumptions

A new model of confirmatory factor analysis (CFA) for multitrait-multimethod (MTMM) data sets is presented. It is shown that this model can be defined by only three assumptions in the framework of classical psychometric test theory (CTT). All other properties of the model, particularly the uncorrelated-ness of the trait with the method factors are logical consequences of the definition of the model. In the model proposed there are as many trait factors as different traits considered, but the number of method factors is one fewer than the number of methods included in an MTMM study. The covariance structure implied by this model is derived, and it is shown that this model is identified even under conditions under which other CFA-MTMM models are not. The model is illustrated by two empirical applications. Furthermore, its advantages and limitations are discussed with respect to previously developed CFA models for MTMM data.     

The Failure to Use Gender Information in Parsing: A Comment on van Berkum, Brown, and Hagoort (1999)

We critically review the empirical evidence published by van Berkum, Brown, and Hagoort (1999a, b) against syntax-first models of sentence parsing. According to van Berkum et al., discourse factors and word gender information are used instantaneously to guide the parser. First, we note that the density of the experimental trials (relative to fillers) and the slow presentation rate of the van Berkum et al. design seem likely to have elicited the use of tactics involving rapid reanalysis of the material. Second, we present new data from a questionnaire study showing that the grammatical gender information of a relative pronoun in Dutch is often completely ignored, even during the wrap-up phase at the end of the sentence.     

Decomposition,Interdependence and Precision in Multiattribute Utility Measurements

Traditionally, parameters of multiattribute utility models, representing a decision maker's preference judgements, are treated deterministically. This may be unrealistic, because assessment of such parameters is potentially fraught with imprecisions and errors. We thus treat such parameters as stochastic and investigate how their associated imprecision/errors are propagated in an additive multiattribute utility function in terms of the aggregate variance. Both a no information and a rank order case regarding the attribute weights are considered, assuming a uniform distribution over the feasible region of attribute weights constrained by the respective information assumption. In general, as the number of attributes increases, the variance of the aggregate utility in both cases decreases and approaches the same limit, which depends only on the variances as well as the correlations among the single-attribute utilities. However, the marginal change in aggregate utility variance decreases rather rapidly and hence decomposition as a variance reduction mechanism is generally useful but becomes relatively ineffective if the number of attributes exceed about 10. Moreover, it was found that utilities which are positively correlated increase the aggregate utility variance, hence every effort should be made to avoid positive correlations between the single-attribute utilities. We also provide guidelines for determining under what condition and to what extent a decision maker should decompose to obtain an aggregate utility variance that is smaller than that of holistic assessments. Extensions of the current model and empirical research to support some of our behavioural assumptions are discussed. © 1997 John Wiley & Sons, Ltd.     

Information matrix estimation procedures for cognitive diagnostic models

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance.     

Is imagery better than reality? Performance in imagined dart throwing

We investigated whether deviations from optimal performance are predicted in motor imagery. In Experiment 1, novices and experts imagined and executed dart throws. In imagination, they reported the final position of the dart. Experts performed better than novices in execution and imagination. Distance to the target and bias were smaller in imagination than in execution. In Experiment 2, we dissociated the roles of feedback from proximal and distal action elements for predictions. Three groups of novices estimated the dart’s final position in imagination, in execution without visual feedback, or in execution with delayed visual feedback. Estimates did not differ significantly between groups, indicating that (the lack of) feedback did not influence predictions. Deviations from optimal performance were lower in estimated than in actual performance. In conclusion, although predictive mechanisms may be similar in imagination and execution, the full extent of deviation from optimal performance is not predicted.