The kinematics of belief and desire

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. This paper is one of a pair dedicated to Richard Jeffrey and prepared for a workshop held in his memory at the 26th International Wittgenstein Symposium. My thanks to the organisers of, and the participants in, this workshop and to two anonymous referees for their comments.     

Intra‐sentential context effects on the interpretation of logical metonymy⋆

Verbs such as enjoy in the student enjoyed the book exhibit logical metonymy: enjoy is interpreted as enjoy reading. Theoreticalwork [Computational Linguistics 17 (4) (1991) 409; The Generative Lexicon, MIT Press, Cambridge, MA, 1995] predicts that this interpretation can be influenced by intra‐sentential context, e.g., by the subject of enjoy. In this article, we test this prediction using a completion experiment and find that the interpretation of a metonymic verb is influenced by the semantic role of its subject. We present a Bayesian model that accounts for the interpretation of logical metonymy and achieves a good fit on our experimental data. We show that the parameters of the model can be estimated from completion data or from corpus data.     

Bayes modal estimation in item response models

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.This research was supported by a grant from the Spencer Foundation, Chicago, IL. Comments and suggestions on earlier drafts by Charles Lewis, Frederic Lord, Rosenbaum, James Ramsey, Hiroshi Watanabe, the editor, and two anonymous referees are gratefully acknowledged.     

Measuring misinformation in repeat trial pick 1 of 2 tests

An extension is described to a product testing model to account for misinformation among subjects. A misinformed subject is one who associates the taste of product A with product B and vice-versa; thus, the subject would tend to perform incorrectly on pick 1 of 2 tests. A likelihood ratio test for the presence of misinformation is described. The model is applied to a data set, and misinformation is found to exist. Biases due to model misspecificationand other implications for product testing are discussed.The first author is currently on leave from Carnegie Mellon University.     

MODIFYING LETTER AND NUMBER REVERSALS IN ELEMENTARY SCHOOL CHILDREN1

Children from regular and special-education classes were exposed to tutoring procedures designed to modify letter and number reversals. In Experiment I, two students showed reversals during letter-naming (e.g., saying p for q) and two-digit number (e.g., writing 31 for 13) exercises. In Experiment II, one subject made two-digit reversals, while the other child reversed single-digit numbers (e.g., 9 written with circle on right side of stem). The subject in Experiment III emitted letter reversals under naming, dictation, and copying exercises. The child in Experiment IV showed written letter reversals on both sides of the “body midline” under dictation procedures. Basic treatment procedures during all experiments involved modelling of correct and incorrect symbol formation, and differential experimenter feedback following student responses. During Experiments I and II, subjects were praised for each correct response, and informed when a reversal occurred. Experiment III included a Modelling Only Phase before these feedback procedures. Besides praise, treatment conditions in Experiment IV consisted of additional feedback following correct responses (e.g., charting correct responses), and temporal delays imposed between dictated letters and student responses. Except for occasional letter-naming reversals of one subject (Experiment I), and letter dictation errors of another (Experiment IV), reversals were eliminated when all experiments terminated. The Modelling Only Phase in Experiment III also reduced reversals to a low level. These findings suggest that a variety of reversal problems may be effectively assessed and remediated via simple modelling and reinforcement procedures. In addition, postcheck observations indicated that the effects were enduring. The present procedures should be easily implemented by school personnel.     

TEACHING COIN SUMMATION TO THE MENTALLY RETARDED1

A procedure to teach four mild and moderately retarded persons to sum the value of coin combinations was tested. Subjects were first taught to count a single target coin, and then to sum that coin in combination with coins previously trained. Five American coins and various combinations were trained. Modelling, modelling with subject participation, and independent counting by the subject constituted the training sequence. The subjects improved from a mean pretest score of 29% to 92% correct at posttest. A four-week followup score showed a mean of 79% correct. A multiple-baseline design suggested that improvement in coin-counting performance occurred only after the coin was trained. The results indicate that this procedure has potential for teaching the retarded to sum combinations of coins in 5 to 6 hr of instruction.     

Correspondence between saying and doing: teaching children to share and praise

Five small groups of preschool children were taught to share and praise by the modelling of these behaviors and reinforcement of their reports of sharing and praising. Experiment I demonstrated that modelling and reinforcement of any (true or untrue) reports of sharing, and then of praising, promptly increased reports of the corresponding behaviors. Modelling and reinforcement for true reports of each behavior increased both reporting and actual behavior. Experiment II showed that both reported and actual sharing and praising may be increased by modelling and reinforcement for true reports of the target behavior, without previous reinforcement for any (true or untrue) reports of those behaviors. Sharing, but not praising, generalized to a second setting. Experiment III replicated the results of Experiment II for sharing and praising, and demonstrated similar success in increasing a third behavior, specific praising. In general, these experiments show that developing correspondence between children's reports of behavior and actual behavior may be an efficient means of increasing prosocial responses.     

Statistics as psychometrics

In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.1980 Psychometric Society presidential address.I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.     

Learning from exemplars: emulation,character formation and the complexities of ordinary life

In the field of character education role-modelling is advocated as an important pedagogical strategy. It is supposed that students learn from ‘significant others’ who exemplify important virtues and values. However, in these strategies it is not clear what and how students precisely can and should learn from exemplars and how the following of exemplars relates to the educational aim of ‘becoming a self.’ In this article, it is argued that modelling is only a relevant pedagogical strategy if moral exemplars are somehow related to life in its full extent, including its moral complexities and ambiguities. Understanding moral exemplarity demands not only the reappropriation of an Aristotelian conception of emulation but also an understanding of the typical modern relocation of moral exemplarity in the fullness of life, importantly originating from what Charles Taylor calls the Protestant ‘affirmation of ordinary life.’ In addition, a distinction is introduced between ‘role exemplarity’ and ‘existential exemplarity.’ Based on this distinction it is argued that emulation should not be limited to learning from role models, but should also include something that runs deeper, to the depth of our own subjectivity or self.