The case of Piaget's group INRC

What is it that distinguishes Piaget's transformations N, R, and C from the rest of the 16! transformations of the 16 binary propositional operations? Here Piaget's INRC is considered as a subgroup of the group $\text{M}$₂ of all automorphisms and dual automorphisms of the free Boolean algebra with two generators. This group is isomorphic to S₄ × C₂. Its elements are given explicitly. Many other psychologically relevant subgroups of $\text{M}$₂ play an important role. They are discussed and their connections shown. Particular attention is given to involutions, even if the view that they constitute the sole representation of reversibility is abandoned. Piaget's transformation R turns out not to be the inverse operation of relations. The group of automorphisms, dual automorphisms, anti-automorphisms of the algebra of binary relations on a finite set is found. A crystallographic presentation of these groups is given and related work by Bart (Journal of Mathematical Psychology, 1971, 5, 539–553), Leresche (Revue Européenne des Sciences Sociales, 1976, 14, 219–241), and Pólya (The Journal of Symbolic Logic, 1940, 5, 98–103) is discussed.     

Finite and infinite state confusion models

A confusion model is defined as a model that decomposes response probabilities in stimulus identification experiments into perceptual parameters and response parameters. Historically, confusion models fall into two groups. Models in Group I, which includes Townsend's (Perception and Psychophysics, 1971, 9, 40–50) overlap model, were developed on the basis of the notion that stimulus identification is mediated by a finite number of internal states. We call the general class of models that have this processing interpretation finite state confusion models. Models in Group II, which includes Luce's (R. O. Luce et al., Eds., Handbook of Mathematical Psychology (Vol. I), New York: Wiley, 1963) biased choice model, were not developed on the basis of an explicit processing interpretation. It is shown here that models in Group II are not finite state confusion models. We prove in addition that except for Falmagne's (Journal of Mathematical Psychology, 1972, 9, 206–224) simply biased model models in Group II belong to a certain class of infinite state confusion models, namely, models asserting that stimulus identification is mediated by a continuous space of vectors representing detector activation levels.     

An experimental and theoretical investigation of the constant-ratio rule and other models of visual letter confusion

The constant-ratio rule (CRR) and four interpretations of R. D. Luce's (In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1). New York: Wiley, 1963) similarity choice model (SCM) were tested using an alphabetic confusion paradigm. Four stimulus conditions were employed that varied in set size (three, four or five stimulus elements) and set constituency (block letters: A, E, X; F, H, X; A, E, F, H; A, E, F, H, X), and were presented to each subject in independent blocks. The four interpretations of the SCM were generated by constraining one, both, or neither of its similarity and bias parameter sets to be invariant in across-stimulus set model predictions. The strictest interpretation of the SCM (both the similarity and bias parameters constrained), shown to be a special case of the CRR, and the CRR produced nearly equivalent across-set predictions that provided a reasonable first approximation to the data. However, they proved inferior to the least strict SCM (neither the similarity nor bias parameters were constrained; the common interpretation of the SCM in visual confusion). Additionally, the least strict SCM was compared to J. T. Townsend's (Perception and Psychophysics, 1971, 9, 40–50, 449–454) overlap model, the all-or-none model (J. T. Townsend, Journal of Mathematical Psychology, 1978, 18, 25–38), and a modified version of L. H. Nakatani's (Journal of Mathematical Psychology, 1972, 9, 104–127) confusion-choice model. Both the least strict SCM and confusion-choice models produced nearly equivalent within stimulus set predictions that were superior to the overlap and all-or-none within-set predictions. Measurement conditions related to model structure and equivalence relations among the models, many of them new, were examined and compared with the statistical fit results of the investigation.     

Efficient sets,decision heuristics,and single-peaked preferences

The origins of single-peaked preferences in multiattribute choice behavior are analyzed. The starting point is (a), (b), 16, 261–266) theory which explains single-peakedness as the joint effect of task and behavior characteristics. Whereas the task conditions—so-called efficient sets—are retained, and their importance is even more stressed, it is argued that Coombs and Avrunin's behavioral assumptions—classical marginally decreasing preference functions—may not be representative of actually displayed choice behavior. Rather, the information processing approach to decision research has shown that multiattribute choices are often based on simplifying heuristic rules which, due to their possible intransitivity, are inconsistent with Coombs and Avrunin's behavioral requirements. Tversky's (Psychological Review, 1969, 76, 31–48) additive difference model is used as an algebraic framework for analyzing such so-called attribute-based choice rules. Sufficient (and in the continuous case also necessary) conditions are presented which guarantee that the additive difference model will also be single-peaked on efficient sets. These conditions show that the behavioral principles yielding single-peaked preferences are far more general than Coombs and Avrunin assumed and include most of the empirically substantiated forms of attribute-based choice rules. Further, a necessary and sufficient condition is derived which insures that elimination rules, like the conjunctive rule, for instance, and generalizations thereof are single-peaked. Finally, making use of a result by Edgeworth, (Mathematical Psychics, London, Paul, 1881), it is shown that efficient sets per se may originate in quite different ways. It is concluded that the phenomenon of single-peakedness is mainly a function of the task rather than of some specific behavior.     

On resolving conflicting views of cognitive conflict

F. B. Murray's (Developmental Review, 1983, 3, 54–61) conclusion that a theoretically ambiguous relationship exists between cognitive conflict and Piaget's notion of equilibration was considered. It was suggested that theoretical clarity can be achieved if a distinction is drawn between conflict induction (disequilibrium) and conflict resolution (equilibration). Murray's suggestion that in Piaget's theory internal (cognitive) conflict can be mentally created was disputed. G. N. Cantor's (Developmental Review, 1983, 3, 39–53) concerns about the adequacy of the measures of internal conflict in B. J. Zimmerman & D. E. Blom's (Developmental Review, 1983, 3, 18–38) study due to their independence from external conflict manipulations was discussed. We agreed with Cantor that such findings obviate direct disconfirmation of an internal conflict construct; however, we suggested that evidence of conservation learning in the absence of either external or internal conflict renders Piaget's account less tenable.     

Equity judgments in hypothetical,four-person partnerships

Subjects' ratings of the fairness of a set of suggested allocations in hypothetical, four-person partnerships demonstrated that an ordinal relationship between inputs and outcomes is not a sufficient definition of equity. Subjects' suggestions for fair distributions of outcomes failed to conform to G. W. Walster's (Representative Research in Social Psychology, 1975, 6, 65–67) increasing-profits and profit-sign criteria, and were better fit by R. J. Harris' (Journal of Experimental Social Psychology, 1976, 12, 194–209) linear formula than by any other formula thus far proposed.     

Subjective utility,anticipated utility,and the Allais paradox

One of the most notable counterexamples to expected utility theory is the “Allais paradox” (M. Allais, 1953, Econometrica, 31, 503–546). A number of alternative theories have been proposed in an attempt to resolve this paradox, notably including Karmarkar, 1978, Karmarkar, 1979, 24, 67–72). It is shown that SWU theory necessarily involves violations of dominance, but that the theory can be modified to avoid these violations. The result is a special case of J. Quiggin's anticipated utility theory (1982, Journal of Economic Behaviour and Organisation, 3, 323–343).     

A reexamination of the faithful subject role

Fillenbaum (Journal of Personality and Social Psychology, 1966, 4, 532–537; Fillenbaum & Frey, Journal of Personality, 1970, 38, 43–51) has proposed that a relatively large number of subjects within certain experiments will adopt a faithful subject role, that is, they will intentionally avoid basing their behavior on any suspicions they may have regarding the experimenter's hypothesis. However, examination of the studies on which this conclusion was based casts doubt on whether Fillenbaum's subjects were truly faithful or whether they may have become aware of the nature of the deception after all opportunity for awareness to influence their responses had passed. To test this hypothesis, awareness measures were administered to subjects either before they took an incidental learning test or (as in Fillenbaum's studies) after the test. As predicted, fewer subjects were classified as faithful in the first condition than in the second. It was concluded that, in fact, very few if any subjects are actively faithful. Discussion also concerned the problems associated with role analyses of subject behavior.     

Elkind on egocentrism

The purpose of this paper is to respond to D. Elkind's (1985, Developmental Review, 5, 218–226) reply to D. Lapsley and M. Murphy's (1985, Developmental Review, 5, 201–217) critique of the adolescent egocentrism theory. After a reprise of the issues in contention, we address the problem of theoretical consistency and self-other differentiation in Dr. Elkind's (1967, Child Development, 38, 1025–1034) theory. The role of formal operations in the Lapsley and Murphy (1985) account of the imaginary audience and personal fable is revised, and the empirical support for Elkind's theory is reviewed. We conclude that there are good conceptual and empirical grounds for doubting the major assumptions of the adolescent egocentrism theory, and that the Lapsley and Murphy (1985) framework has promise in suggesting theoretical integration with other approaches to the self.     

On aspiring to present a developmental theory of occupational aspirations: A reader's guide to Gottfredson

L. S. Gottfredson's preceding comment (Journal of Vocational Behavior 1983, 23, 203–212)is characterized by undocumented and arbitrary assertions. Moreover, we still maintain and cite further evidence that the features of the stages she describes represent an implausible account of development. We conclude that there is nothing in either L. S. Gottfredson's original (Journal of Counseling Psychology 1981, 28, 545–579) article or her preceding paper that leads us to alter our belief that the views we present in our own article (Journal of Vocational Behavior 1983, 23, 179–212) will be useful for the future development of vocational theory and intervention.     

Do birds of a feather flock together? A test of the similarities within and the differences between five occupations

Two sets of samples of 40 women from each of five different occupations were subjected to J. H. Ward's (Journal of the American Statistical Association, 1963, 58, 236–244) hierarchical cluster analysis, using an index of similarity from Kuder, 1977, Kuder, 1980, 40, 1–8). The five-group solution in neither case adequately recaptured the occupational membership of the original groups. This finding was interpreted to mean that there may be important differences in the interests of person in the same occupation, which in turn has implications for occupational scaling on interest inventories and theories of career development and counseling.     

Motivation to manage among college business students: A reassessment

The present study reassesses trends in motivation to manage among college business students (N = 216). Motivation to manage scores are compared with J. B. Miner's (Personnel Psychology, 1974, 27, 605–613) results for three periods since the early 1960s, across two types of universities—public and private, and between males and females. Results indicate that the downward trend in motivation to manage scores appears to be reversing; business students at the private university scored higher on motivation to manage than those at the public university, and males scored higher than females. Implications for vocational research are discussed.     

Developmental changes in incidental memory as a function of processing level,congruity, and repetition

Second-, fifth-, and ninth-grade students (8, 11, and 14 years of age, respectively) answered acoustic and semantic questions about words which were either congruent or incongruent with the questions. Subsequently, students' free recall of the words was unexpectedly tested. For words presented once in the list, only orienting task and congruity main effects were found. For twice-presented words, grade level interacted with both variables in that older students' recall was better than younger students' only for semantically encoded, congruent words. This finding is consistant with the hypothesis that developmental increases in semantic knowledge enhance the potential for encoding elaboration, but is in apparent conflict with the results of M. F. Geis and D. M. Hall (Child Development, 1978, 49, 857–861) who found no such interaction for second- and fifth-grade children. The different age spans included in the two studies provides one resolution of the discrepancy in results. However, a second experiment tested the importance of a procedural difference between the two studies. M. F. Geis and D. M. Hall (Journal of Experimental Child Psychology, 1976, 22, 58–66; 1978) presented the question after the stimulus word while we presented the question before the word. For ninth-grade students, the question after condition resulted in an attenuation of the recall difference between semantic and acoustic questions compared to the question before condition. It was argued that the pattern of developmental differences in incidental memory that is obtained may be related to which procedure is utilized.     

Informational cues and attributions based on role behavior

A recent experiment by Messick and Reeder (Journal of Experimental Social Psychology, 1972, 18, 482–491) attempted to extend Jones, Davis, and Gergen's (Journal of Abnormal and Social Psychology, 1961, 63, 302–310) classic finding that out-of-role behavior.is more informative for person perception than in-role behavior. It is argued, however, that this study confounded two variables, role performance and occupation. Evidence is presented that the occupation variable alone could have produced Messick and Reeder's results. Both variables seem to affect attributions. The importance of these findings for relating attribution theory and role theory is discussed.     

The case of the disappearing disagreements: A reply to Yussen

S. R. Yussen (1984, Developmental Review, 4, 139–144) and I have few disagreements. The major one seems to be in what the purpose of my article (R. J. Sternberg, 1984, Developmental Review, 4, 113–138) should have been. I believe the article fulfills my own purpose, if not Yussen's.     

Measured interests versus expressed interests as predictors of long-term occupational membership

This study compared the predictive accuracy of measured versus expressed interests over a 21-year period using as a criterion occupational membership at age 36. Subjects were 83 males whose measured and expressed interests were elicited at ages 15, 18, and 25. The Strong Vocational Interest Blank was used to determine measured interests while expressed interests were determined through a combination of questionnaires and interviews. C. McArthur's (Journal of Applied Psychology, 1954, 38, 346–353) method was employed to determine the predictive validity of subjects' measured interests. The predictive validity of expressed interests was determined by using A. Roe's (The psychology of occupations. New York: Wiley, 1956; Journal of Counseling Psychology, 1957, 4, 212–217) scheme for occupational classification to code occupational preferences and compare them to age 36 occupations. Results indicated that at each point in the study expressed interests were slightly better predictors of age 36 occupational membership than measured interests. Supplementary analyses revealed no relationship between the extent to which subjects' measured or expressed interests corresponded to age 36 occupations and either overall job or career satisfaction.     

Preferences of infants for regular and distorted natural speech stimuli

The schema hypothesis proposed by Kagan (Science, 1970, 170, 826–832) andLewis (Developmental Psychology, 1969, 1, 75–86) was used to make predictions concerning the preferences of infants 3 to 14 months old for speech stimuli. An operant response method was used in determining the infants' preferences for inflected, monotone, and scrambled natural speech stimuli. Although the infants' preferences did not change with age as predicted, the infants produced clear preference orderings for the three stimuli. The speech preferences were interpreted as being based on stimulus variables (e.g., word order, inflection, and speech rate) in addition to the realism variables assumed by the schema hypothesis.     

A maximum likelihood hierarchical disaggregate model for predicting choices of individuals

The absence of operational disaggregate lexicographic decision models and Tversky's observation that choice behavior is often inconsistent, hierarchical, and context dependent motivate the development of a maximum likelihood hierarchical (MLH) choice model. This new disaggregate choice model requires few assumptions and accommodates the three aspects of choice behavior noted by A. Tversky (1972, Journal of Mathematical Psychology, 9, 341–367). The model has its foundation in a prototype model developed by the authors. Unlike the deterministic prototype, however, MLH is a probabilistic model which generates maximum likelihood estimators of the aggregate “cutoff values.” The model is formulated as a concave programming problem whose solutions are therefore globally optimal. Finally, the model is applied to data from three separate studies where it is demonstrated to have superior performance over the prototype model in its predictive performance.     

Types produce types—Especially fathers

Employing a larger sample and a more stringent statistical criterion, this study replicated an attempt by T. G. Grandy and R. F. Stahmann (Journal of Vocational Behavior, 1974, 5, 231–239.) to test Holland's hypothesis that parents' personality types foster similar offspring personality development. The relationships between paternal and offspring personality types were consonant with the findings of Grandy and Stahmann but the role of maternal personalities remained unclear. An explanation was offered that fathers' personality types carry more weight in the development of offspring types.     

Estimation of probabilities subject to linear inequality constraints

Based on Falmagne's representation theorem for finite random scale systems (J. C. Falmagne, Journal of Mathematical Psychology, 1978, 18, 52–72), simulated data are used to estimate choice probabilities such that a random representation exists. For the estimation a least-squares method is used constrained by linear inequalities. The minimization problem is solved by the method of quadratic programming.