Analyzing proximity matrices: The assessment of internal variation in combinatorial structure

A data analysis strategy is discussed for evaluating the degree to which a subset D of a larger object set S satisfies a particular algebraic property. Based on a set measure f(D) and a proximity function on S × S, two separate evaluation tasks, referred to as confirmatory and exploratory, are considered. In a confirmatory task the subset D is identified a priori and f(D) is compared against the distribution of f(·) over all subsets containing the same number of objects. The exploratory task, on the other hand, treats f(·) as an objective function to be optimized over all subsets of a given size. Examples of these two notions include the assessment of symmetry, cluster compactness, and the extent to which D satisfies the error-free conditions for a hierarchical model or a unidimensional scale.     

Changing Types: Information Dynamics for Qualitative Type Spaces

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces).     

Shen Dao��s Own Voice in the Shenzi Fragments

Shen Dao ???? is known as one of the Legalists who influenced Han Feizi ?n???? in terms of the concept of shi ?? (circumstantial advantage, power, or authority). This argument is based on the ??A Critique of Circumstantial Advantage (Nanshi ?y??)?? chapter of the Hanfeizi, where Han Feizi advances his own idea of shi after criticizing both Shen Dao and an anonymous Confucian. However, there are other primary sources to contain Shen Dao??s thought, namely, seven incomplete Shenzi ???? chapters of the Essentials on Government from the Assemblage of Books (Qunshu zhi yao ??????) and other fragments preserved in other Chinese texts. This article examines the Shenzi fragments in order to ask whether Shen Dao stresses the concept of shi.     

Pseudodiagnosticity

Subjects selected data in order to decide from which of two ‘islands’ an ‘archeological find’ had come. The results replicated two established phenomena in cognitive psychology: (1) the tendency to ignore base rate data given individuating information, and (2) the tendency to seek confirmatory evidence.The major outcome of the study was, however, to reveal a new phenomenon in information search. Subjects displayed a surprising and strong tendency to seek diagnostically worthless information. They then altered their conclusion based on that information. For example, subjects who had already obtained P(D₁/H₁) selected P(D₂/H₁) when P(D₁/H₂) was equally easily available, and when they had no relevant experience to bring to bear on the estimation of P(D₁/H₂). This phenomenon, which appears to be a wholly dysfunctional cognitive tendency, was labeled pseudodiagnosticity.     

Social facilitation in chickens: A different level of analysis

An assumption of the arousal (D × H) model of social facilitation effects is that in an otherwise constant stimulus situation the simple presence or absence of a conspecific has a quantitative influence on the D component, and that the habit hierarchy in the situation (H) is unaffected. However, certain evidence from avian subjects seemed inconsistent with the multiplicative effects predicted by the model, and experiments were conducted with the aim of resolving this discrepancy. In general, chickens were tested for consummatory responses in the company of companions, in isolation, or in the company of strangers. Clear findings emerged from these tests that showed that only the companion conditions were “facilitative”. Under the other test conditions there were qualitative (as opposed to merely quantitative) shifts in responses. Apparently, the different social test conditions evoked qualitatively different response hierarchies, and “facilitation” reflected this sort of shift rather than simple quantitative changes in arousal (D) across conditions. It was argued, therefore, that the appropriate level of analysis for facilitation effects for animals in a free response situation is not within the (D × H) envelope, but rather at the level of S (stimulus situation) in the S → (D × H) → R formulation. Implications for the analysis of social facilitation effects in humans were discussed.     

Effects of stimulus differentiation training upon hypotheses,strategies, and stereotypes in discrimination learning among kindergarten children

Two groups of kindergarten children received stimulus differentiation training either with feedback (experimental Ss) or without (controls), prior to presentation of a series of discrimination-learning problems using blanktrial probes. Results were as follows: Performance of both groups was virtually perfect during differentiation training (less than one error per 1000 trials). In transfer, however, experimental Ss solved more problems, generated more consistent Ss during blank-trial probes, manifested fewer response sets, were more likely to abandon a disconfirmed H, sampled more locally consistent Ss following errors, and retained a confirmed H more frequently than control Ss. Experimental Ss also manifested strategy Sys (hypothesis sampling systems) predominately, while controls generated only stereotypes. Findings were discussed in relation to theoretical perspectives derived from Piagetian theory and developmental learning theory.     

Effects of two levels of stimulus complexity upon hypothesis sampling systems among second and sixth grade children

Groups of second and sixth grade children each solved a series of discrimination-learning problems involving four and eight dimensions that contained blanktrial probes for the S′s hypothesis (H). There were significant effects of grade level on three dependent measures (learning, generating consistent H patterns, sampling locally consistent Hs). Main effects of stimulus complexity were significant on five measures (the three above, rejecting disconfirmed Hs, maintaining confirmed Hs). There were no interactions involving any of these measures. The hypothesis sampling system (Sy) observed in each problem was also determined. Among sixth grade Ss this measure was unaffected by stimulus complexity level. Second grade Ss generated logically structured Sys in 65% of four-dimensional, but only 30% of eight-dimensional problems. They generated stereotyped behaviors or unsystematic sequences of Hs in 70% of eight-dimensional, but only about 35% of four-dimensional problems. Detailed analyses revealed that among second grade Ss good information processors (in terms of four component processes above) usually imposed a logical structure on four-dimensional, but generated unsystematic sequences of Hs in many of eight-dimensional problems. Poor processors generated stereotyped behaviors in both four- and eight-dimensional problems.     

Determination of the number of independent parameters of a score matrix from the examination of rank orders

Two ordinal consequences are drawn from the linear multiple-factor analysis model. First, the numberR(s, d) of distinct ways in whichs subjects can be ranked by linear functions ofd factors is limited by the recursive expressionR(s, d)=R(s?1,d)+(s?1)R(s?1,d?1). Second, every setS ofd+2 subjects can be separated into two subsetsS* andS ? S* such that no linear function ofd variables can rank allS* over allS ? S*, and vice versa. When these results are applied to the hypothetical data of Thurstone's “box problem,” three independent parameters are found. Relations to Thurstone's suggestion for a non-correlational factor analysis are discussed.     

Similarity of rectangles: An analysis of subjective dimensions

Two defining properties of psychological dimensions (intradimensional subtractivity and interdimensional additivity) are introduced and their consequences, formulated in terms of an ordinal dissimilarity scale, are derived. These consequences are investigated using dissimilarity judgments between rectangles to determine which of two alternative dimensional structures area (A) and shape (S), or width (W) and height (H), satisfies additivity and/or subtractivity. The results show that neither dimensional structure is acceptable, although A × S provides a better account for the data of most Ss than does W × H. Tests of relative straightness show that A is the least “curved” of the four attributes. Methodological and substantive implications of the study are discussed.     

Paired-associate learning by normal children and retardates with relevant redundant compound stimuli

During daily sessions four first-grade boys each played a two-choice marble dropping game. When one colored light was presented a plain token was dispensed as soon as S dropped a marble, and when another light was on a token with a hole in its center was delivered. During choice trials that were interspersed among single-color trials S had to choose one of the two different colored holes. At the end of each session S traded tokens with holes for pennies and then turned in the remaining plain tokens which were not exchanged for money. After S had developed a preference for the response that earned the tokens with holes (tokens that were backed up with pennies) E instructed S to try to get as many plain tokens (unexchangeable tokens) as he could. All Ss immediately switched to the response that earned unexchangeable tokens but as soon as E left they returned to choosing the backed up response. When the adult reentered, Ss again chose to work for unexchangeable tokens. Two different Es (male and female) served and the instructions of each were effective in controlling responding as long as the adult was present, except for one S who did not respond to one E, but did respond as described for the other.     

Age differences in organization and recall: The effects of training in categorization

An alternating sort/recall task was employed to train fourth graders and college students in organizational strategies. Free-sorting Ss, at both age levels, sorted a group of words into two to seven categories. Analyses of final sorting patterns indicated reliable differences between the children and adults. The organizational schemes thus developed by the free-sorting Ss were taught, by means of a yoking procedure, to other Ss. Results indicated that the recall of fourth graders was improved when they were forced to learn the sorting patterns developed by the older Ss. Similarly, impairment in the recall of college students was observed when they were required to sort according to the organization employed by the fourth graders. These findings imply that changes in organization can result in changes in recall performance.     

Storage and later recognition of exemplars of concepts

This paper concerns the problem of abstraction: whether when we encounter several exemplars of a concept, we retain only the abstracted concept, only the exemplars, or both. Although many studies concur that both are stored, a recent article argued strongly that only the abstracted concept is stored. The present study, aimed at replication of this recent finding, follows the earlier procedural details but adds appropriate controls and uses simpler material. A set of 24 exemplars of four concepts, in the form of four-tuples of letters and numbers, was presented to Ss who, after presentation, rated a larger set of exemplars for recognition. One group of Ss experienced the conceptual exemplars; control group Ss experienced items that were similar in composition but not exemplars of a concept. Two major results appeared: Unlike the study on which this was based, all Ss were able to distinguish those items that were originally experienced from those that were not. And, the more completely an exemplar fit the concept (the longer the item), the more confident the S was that it had been presented. In contrast, in the control condition, the longer the item, the more confident the S was that it had not been presented earlier. Two models are described to account for these results. One is based on the S's initial storage of the exemplars in a concept-plus-correction format; the other is based on a procedure whereby the S can make recognition judgments without having previously abstracted and retained the concepts.     

Conditional Random Quantities and Compounds of Conditionals

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH +  P(E|H)H ^c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold.     

Effects of a coactor's prediction on latencies to predict and indentify stimuli

On each of 300 trials E's confederate (C) verbalized which of two stimuli would occur; then S made a prediction. Following each presentation, S and C pulled a trigger to identify the stimulus. Two latencies were measured: the interval between C's and S's prediction (prediction time), and the interval between stimulus presentation and S's identification response (choice RT). Prediction times were significantly shorter when S's prediction agreed rather than disagreed with C's prediction, when S's preceding prediction was correct rather than incorrect, and when S was female rather than male. Choice RT was influenced by distributions of C's stimulus predictions and C's prediction outcomes in directions supporting an expectancy model.     

Effectiveness of debriefing after a stress-producing deception

This experiment was carried out to determine if after deceiving Ss an E had sufficient credibility to effectively debrief the Ss. Ss in two stress groups were given false information indicating that when a signal light came on they would receive painful electric shocks. Ss in a no-stress group were not told about shocks. After being given the threatening instructions, Ss in one of the stress groups were debriefed concerning the deception (but the “shock electrodes” were not removed) while Ss in the other group were not debriefed. After this the signal light came on for all groups. Arousal was measured by pulse rates and self-reports. The results revealed that (a) the instructions about electric shocks increased the arousal levels of the two stress groups relative to the no-stress group, thus indicating that the deception was effective, and (b) after the signal light came on the stress group which had not been debriefed continued to show a high degree of arousal while the stress group which had been debriefed showed a reduction of arousal to the same low level of arousal as the no-stress group, thus indicating that the process of debriefing had been effective.     

Comparatives,logical structures,and encoding in a transitive inference task

Four- to five-year-old children were asked questions on length involving single or double comparatives in a transitive inference task. The number of comparatives varied within or across pairs. The pairs of sticks were colorcoded. Initial pair-wise discrimination training on four adjacent pairs from a five-stick array with only verbal feedback was followed by tests, without feedback, on all possible pairs. When both comparatives were used, Ss learned adjacent pairs faster and more often reached criterion than when only one comparative term was used in training. In testing, Ss were successful on transitive inference tests only when the double-comparative relation was used within pairs during training. Retraining with visual feedback increased the number of Ss solving the inference test only in this condition. The findings are discussed in terms of how children may use processes other than logical operations to make transitive inferences.