James Townsend

Decision field theory provides for a mathematical foundation leading to a dynamic, stochastic theory of decision behavior in an uncertain environment. This theory is used to explain (1) violations of stochastic dominance,(2) violations of strong stochastic transitivity,(3) violations of independence between alternatives,(4) serial position effects on preference,(5) speed–accuracy trade-off effects in decision making,(6) the inverse relation between choice probability and decision time,(7) changes in the direction of preference under time pressure,(8) slower decision times for avoidance as compared with approach conflicts, and (9) preference reversals between choice and selling price measures of preference. The proposed theory is compared with 4 other theories of decision making under uncertainty.(PsycINFO Database Record (c) 2016 APA, all rights reserved)

It takes only a little reading of late nineteenth-and early twentieth-century philosophical literature to arrive at the conclusion that many of the existing ideas about human cognition were present even before much rigorous experimentation had been accomplished. Ideas about memory, perception, discrimination, motivation, will (conation), attention, intelligence, and courage, to name a few, were discussed by people like James, Sully, Hamilton, Ladd, Wundt, Cattell, Fechner, Stumpf, and Helmholtz. The data varied from nil to impressive, and hardly a year goes by without the design of some famous recent experiment being discovered buried away in the older literature. Nevertheless, the concepts were not always cleanly defined, particularly in what we would now call operational terms; the theories were typically amorphous and qualitatively drawn (with the notable exception of some parts of psychophysics and, to a reasonable extent, physiological psychology); introspection was sometimes relied on too extensively; and the experiments did not always allow one to confidently embrace a" winning" theory or hypothesis while disposing of the alternatives. It is our opinion that the most significant contribution of twentieth-century psychology has been in developing and refining the theories, concepts, and methodologies concerned with explaining in an elegant and nontrivial fashion how reasonably complex organisms go about their business. Our own bias, which is apparent on simply leafing through the pages of the book, is that mathematical work, when directed toward specific psychological questions or problems, has led to and will continue to lead to …

Several varieties of perceptual independence are investigated. These include sampling independence, dimensional orthogonality, stimulus separability and integrality, and performance parity. A general multivariate perceptual theory is developed, and a precise definition of perceptual independence is offered. Each of these related concepts is then examined within the framework of this theory, and their theoretical interrelationships are explicated. It is shown that none of the concepts are equivalent to perceptual independence but that if separability holds, then sampling independence is equivalent to perceptual independence. Several simple tests of separability are suggested that can be applied to the same data as sampling independence. Dimensional orthogonality is shown to test for independence only if some strong distributional assumptions are made about the perceptual effects of stimuli. Reaction time and …

The authors interpret decision field theory (JR Busemeyer & JT Townsend, 1993) as a connectionist network and extend it to accommodate multialternative preferential choice situations. This article shows that the classic weighted additive utility model (see RL Keeney & H. Raiffa, 1976) and the classic Thurstone preferential choice model (see LL Thurstone, 1959) are special cases of this new multialternative decision field theory (MDFT), which also can emulate the search process of the popular elimination by aspects (EBA) model (see A. Tversky. 1969). The new theory is unique in its ability to explain several central empirical results found in the multialternative preference literature with a common set of principles. These empirical results include the similarity effect, the attraction effect, and the compromise effect, and the complex interactions among these three effects. The dynamic nature of the model also implies …

A number of important models of information processing depend on whether processing is serial or parallel. However, many of the studies purporting to settle the case use weak experimental paradigms or results to draw conclusions. A brief history of the issue is given along with examples from the literature. Then a number of promising methods are presented from a variety of sources with some discussion of their potential. A brief discussion of the topic with regard to overall issues of model testing and applications concludes the paper.

A mathematical theory and related experimental methodology are developed that permit strong, converging tests of parallel versus serial versus channel summation processing and of exhaustive versus self-terminating processing. An experimental design is used for two studies, in which the presence or absence of a target in each of two positions, is factorially combined with two levels of brightness (a version of the double factorial paradigm). When both targets are present (redundant target condition) the two levels of brightness permit factorial technology to determine mental architecture and stopping rules. Comparison of the single versus double target conditions allows capacity analyses that strongly reinforce the double target factorial phase of the investigation. The results provide decisive support for parallel channels with either a self-terminating stopping rule or a coactive summation of information. General …

A quantum dynamic model of decision-making is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.

Due to the significant research effort devoted to discovering whether certain psychological processes are serial or parallel, it seems important to establish the degree to which such processes are identifiable and to investigate possible ways in which such knowledge can improve our experiments. General definitions of parallel and serial systems are given, followed by a qualitative summary of identifiability results obtained with special classes of exponential systems. Some of these results are applied to a current experimental paradigm, and possible

A study was undertaken to acquire a confusion matrix of the entire upper-case English alphabet with a simple nonserifed font under tachistoscopic conditions. This was accomplished with two experimental conditions, one with blank poststimulus field and one with noisy poststimulus field, for six Ss run 650 trials each. Three mathematical models of recognition, two based on the concept of a finite number of sensory states and one being the choice model, were compared in their ability to predict the confusion matrix after their parameters were estimated from functions of the data. In order to ascertain the facility with which estimates of similarity among the letters could lead to a psychological space containing the letters, η_ij, the similarity parameter of the choice model was input to an ordinally based multidimensional scaling program. Finally, correlation coefficients were computed among parameters of the …

The study of capacity, empirically and theoretically, is of considerable impor tance in cognitive psychology (see, eg, Kahneman, 1973; Townsend, 1974a). Yet there are relatively few mathematical techniques within psychology designed to assess or analyze capacity, much less a systematic theory that interrelates the various and sundry uses of the concept.Although we cannot hope to completely attain the latter goal in this chapter, we attempt to initiate development of some of the many possible branches that a mathematical knowledge-tree or theory-tree of capacity might possess. One appropriate milieu in which to discuss and construct these branches could well be that of pattern recognition (Townsend, 1971) and multisymbol search situations (eg, Sternberg, 1966; Townsend & Roos, 1973). The matching or comparison of patterned information from the environment with information that has previously been stored …

Eighty years ago or so the title would probably have been something like" An Attempt at Clarification of Proposed and Counter-Proposed Properties of Consciousness." The revolution in information, computer, and communication sciences (a la Shannon, Von Neumann, and Wiener) and the growing vapidity of behaviorism led in the 1950's and 1960's to a resurgent interest in centralism, that is, a renewed interest in the study of properties of the mind, as opposed to the exclusive peripheral ist; c study of stimulus-response correspondences. The terminology of the" new" psychology has been almost completely drawn from the above disciplines, but very recently investigators have become less self-conscious about employing mentalistic terms and concepts that would have brought applause from the structuralists and phenomenologists of yesteryear (see, eg. Boring, 1950). Although skirting the interesting questions involving possible fruits and pitfalls of this trend, I might simply note that this chapter continues, after the introduction, in the recent tradition of use of information-processing argot. In the present approach, we go inside the human qua information processor to as shallow or deep a level as we care to, and seize upon an abstract black box residing there in the processing chain. We shall think of our black box as engaging in the processing of some finite number of inputs (or elements). Words like" processing" II am grateful to WK Estes for the opportunity to spend the year 1972-1973 at Rockefeller University under Grant GM16735 from the National Institute for General Medical Sciences. During that time, much of the writing of this chapter was …

The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallel-channel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural-holistic processing systems.

Comments on an article by J. Gaito (see record 1980-22405-001) in which Gaito assailed the proposition that fundamental measurement theory has any relevance to statistical theory and procedures. The present authors contend that Gaito's arguments contain nothing that constitutes a logical or empirical refutation of the tenets of fundamental measurement theory or its implications for statistical analyses of data. Examples of statistical pitfalls to be met in ignorance of measurement considerations are given.(9 ref)(PsycINFO Database Record (c) 2016 APA, all rights reserved)

The analysis of reaction time (RT) additivity and interactions via factorial manipulation is a widely used and potentially powerful tool for elucidating mental processing; however, current implementation is limited by the scope of systems for which predictions are available, as well as statistical weakness. Predictions for an expanded set of system dimensions (serial/parallel, independent/dependent, and selective/nonselective influence) are given. The theorems are not limited to particular families of distributions. Statistical considerations are examined in the context of an exemplary nonadditive parallel system which adequately fits “additive” data but will only be rejected as additive when power is increased beyond the traditional criteria.