What do you think I think you think?: Strategic reasoning in matrix games

In reasoning about strategic interpersonal situations, such as in playing games, an individual's representation of the situation often includes not only information about the goals and rules of the game, but also a mental model of other minds. Often such mental models involve a hierarchy of reflexive reasoning commonly employed in social situations ("What do you think I think you think..."), and may be related to the developmental notion of 'theory of mind'. In two experiments, the authors formally investigate such interpersonal recursive reasoning in college-age adults within the context of matrix games. Participants are asked to predict the moves of another player (experimenter's confederate) in a two-choice, sequential-move game that may terminate at various stages with different payoffs for each player. Participants are also asked to decide optimally on their own moves based on the prediction made. Errors concerning the prediction, or translation of those predictions into decisions about one's action, were recorded. Results demonstrate the existence of a "default" mental model about the other player in the game context that is dynamically modified as new evidence is accumulated. Predictions about this other player's behavior are, in general, used consistently in decision-making, though the opponent tends to be modeled, by default, to behave in a myopic fashion not anticipating the participant's own action.     

Development of rules and strategies: balancing the old and the new

The experiments described in the lead articles replicate findings from previous studies of development of knowledge about balance scales, add several new findings, and raise four key questions: (a) How can rule use best be assessed? (b) How can we reconcile systematic use of rules with variable use of strategies? (c) When do children begin to use rules? and (d) How do children generate new rules? In this Reflection, we summarize current understanding of development of knowledge about balance scales and consider each of the four questions.     

Developmental and content effects in reasoning with causal conditionals

Two predictions derived from Markovits and Barrouillet's (2001) developmental model of conditional reasoning were tested in a study in which 72 twelve-year-olds, 80 fifteen-year-olds, and 104 adults received a paper-and-pencil test of conditional reasoning with causal premises ("if cause P then effect Q"). First, we predicted that conditional premises would induce more correct uncertainty responses to the Affirmation of the consequent and Denial of the antecedent forms when the antecedent term is weakly associated to the consequent than when the two are strongly associated and that this effect would decrease with age. Second, uncertainty responding to the Denial of the antecedent form ("P is not true") should be easier when the formulation of the minor premise invites retrieval of alternate antecedents ("if something other than P is true"). The results were consistent with the hypotheses and indicate the importance of retrieval processes in understanding developmental patterns in conditional reasoning with familiar premises.     

Molecular analyses of the principal components of response strength

Killeen and Hall (2001) showed that a common factor called strength underlies the key dependent variables of response probability, latency, and rate, and that overall response rate is a good predictor of strength. In a search for the mechanisms that underlie those correlations, this article shows that (a) the probability of responding on a trial is a two-state Markov process; (b) latency and rate of responding can be described in terms of the probability and period of stochastic machines called clocked Bernoulli modules, and (c) one such machine, the refractory Poisson process, provides a functional relation between the probability of observing a response during any epoch and the rate of responding. This relation is one of proportionality at low rates and curvilinearity at higher rates.     

On normal theory based inference for multilevel models with distributional violations

Data in social and behavioral sciences are often hierarchically organized though seldom normal, yet normal theory based inference procedures are routinely used for analyzing multilevel models. Based on this observation, simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions. For characterizing the distribution of parameter estimates, sandwich-type covariance matrices are derived. Standard errors based on these covariance matrices remain consistent under distributional violations. Implications of various covariance estimators are also discussed. For evaluating the quality of a multilevel model, a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model. The rescaled statistic, improving the likelihood ratio statistic by estimating one extra parameter, approaches the same mean as its reference distribution. A simulation study with a 2-level factor model implies that the rescaled statistic is preferable.This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.     

Interval length and time-use by children with AD/HD: a comparison of four models

Predictions made by 4 competing models of time use by children with AD/HD were tested using a computerized version of the Matching Familiar Figures Test in 2 studies. In Study 1 teacher-identified AD/HD children (N = 10) and non-AD/HD controls (N = 10) completed the task under 3 different trial duration conditions (5, 10, and 15 s). In Study 2 the same task was completed by a group of children with a diagnosis of Hyperkinetic Disorder (N = 12) and controls (N = 12). In both studies AD/HD children performed poorly on trials of both 5- and 15-s duration but as well as controls on the 10-s trials. This quadratic function provided support for the State Regulation Deficit model of time use in AD/HD. The value of tailoring the temporal features of learning contexts to the conceptual style of AD/HD children is discussed.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

中小学生认知能力发展水平测验的研究

以皮亚杰的认知发展理论为基础,采用皮亚杰及其学生研究认知发展时的任务为测验题目,编制成测量中小学生认知能力发展水平的测验.通过对2240名中小学生施测,结果表明本测验不仅具有很好的信度和效度,而且也具有适中的难度.然后以一所中学特长班学生为被试,通过对他们进行测量,并将测验结果与同年级普通班学生的认知成绩进行比较,结果存在很明显的差异.最后对中小学生认知能力发展水平测量问题进行了探讨.     

Infants' formation and use of categories to segregate objects

Four- and-a-half-month-old infants' (N = 100) category formation and use was studied in a series of five experiments. For each experiment, the test events featured a display composed of a cylinder and a box. Previous research showed that this display is not clearly parsed as a single unit or as two separate units by infants of this age. Immediately prior to testing, infants were shown a set of category exemplars. Knowledge about this category could help infants disambiguate the test display, which contained a novel exemplar of this category. Clear interpretation of the test display as composed of two separate units (as indicated by infants' longer looking at the move-together than at the move-apart test event) was taken as evidence of category formation and use. In Experiments 1 and 5, infants' prior experience with a set of three different boxes that were similar to the test box facilitated their segregation of the test display. Experiment 2 showed that three different exemplars are necessary: prior experience with any two of the three boxes used in Experiment 1 did not facilitate infants' segregation of the test display. Experiment 3 showed that variability in the exemplar set is necessary: prior experience with three identical boxes did not facilitate infants' segregation of the test display. Experiment 4 showed that under these conditions of very brief prior exposure, similarity between the exemplar set and test box is necessary: prior experience with three different boxes that were not very similar to the test box did not facilitate infants' segregation of the test display. Together, these findings suggest that: (a) number of exemplars, variability, and similarity in the exemplar set are important for infants' category formation, and (b) infants use their category knowledge to determine the boundaries of the objects in a display.     

Tailoring Cognitive Behavioral Therapy for Individuals Diagnosed with Bulimia Nervosa

There is a wealth of data indicating the effectiveness of cognitive behavioral therapy in the treatment of bulimia nervosa. However, the best evidence indicates a treatment success rate of 50%. The purpose of this paper is to briefly describe cognitive behavioral treatment of bulimia nervosa and to offer suggestions on how this therapy approach may be tailored to best serve the needs of individual clients. Such tailoring should ultimately lead to even greater treatment success.