James T. Townsend

Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment

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 (a) violations of stochastic dominance, (b) violations of strong stochastic transitivity, (c) violations of independence between alternatives, (d) serial position effects on preference, (e) speed-accuracy trade-off effects in decision making, (f) the inverse relation between choice probability and decision time, (g) changes in the direction of preference under time pressure, (h) slower decision times for avoidance as compared with approach conflicts, and (i) preference reversals between choice and selling price measures of preference. The proposed theory is compared with 4 other theories of decision making under uncertainty.

Varieties of perceptual independence.

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 information-based performance parity criteria are examined. The potential for empirically testing each of these concepts is discussed.

Serial vs. Parallel Processing: Sometimes They Look Like Tweedledum and Tweedledee but They Can (and Should) Be Distinguished

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 note on the identifiability of parallel and serial processes

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

Theoretical analysis of an alphabetic confusion matrix

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, ηij, 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 models, the scaled space, and a crude measure of physical similarity. Briefly, the results were: (1) the finite-state model that assumed stimulus similarity (the overlap activation model) and the choice model predicted the confusion-matrix entries about equally well in terms of a sum-of-squared deviations criterion and better than the all-or-none activation model, which assumed only a perfect perception or random-guessing state following a stimulus presentation; (2) the parts of the confusion matrix that fit best varied with the particular model, and this finding was related to the models; (3) the best scaling result in terms of a goodness-of-fit measure was obtained with the blank poststimulus field condition, with a technique allowing different distances for tied similarity values, and with the Euclidean as opposed to the city-block metric; and (4) there was agreement among the models in terms of the way in which the models reflected sensory and response bias structure in the data, and in the way in which a single model measured these attributes across experimental conditions, as well as agreement among similarity ami distance measures with physical Similarity.

Lateral masking for letters with unlimited viewing time

Linear arrays of 1, 8, and 9 letters were exposed while S read off the items of the letter sequence while maintaining constant fixation. By this procedure, serial position effects were studied in the absence of requirements for scanning the array quickly, as in a tachistoscopic display, and for remembering a large number of items, as in a delayed whole report. Despite the absence of these requirements, typical serial position curves were generated. Serial position effects were partially ameliorated by the introduction of blank spaces into the array. Performance was influenced both in the immediate vicinity of the blank spacings, as well as extending over a large portion of the array. The data were interpreted in terms of lateral masking effects associated with adjacent elements.

A trichotomy: Interactions of factors prolonging sequential and concurrent mental processes in stochastic discrete mental (PERT) networks☆

Abstract Suppose the mental processes required for performing a task are partially ordered, so that some pairs of processes are sequential and some are concurrent. Then they can be represented in a directed acyclic network, a PERT network. Suppose the duration of each process is a nonnegative random variable. Suppose two experimental factors are available, each selectively prolonging a different process by adding a nonnegative random variable to its duration. Sternberg (1969) pointed out that if all the processes are in series, the factors will have additive effects on reaction time. Here we show that if the factors affect concurrent processes, the factors will have subadditive effects. Subadditive effects are also possible if the prolonged processes are sequential, but in a Wheatstone bridge. If the PERT network has no subnetwork homeomorphic to a Wheatstone bridge, then ineractions between factors prolonging sequential processes will be nonnegative, and in practice will often be positive. The results are illustrated in a detailed analysis of a particular network, the Embellished Wheatstone Bridge.

Truth and Consequences of Ordinal Differences in Statistical Distributions: Toward a Theory of Hierarchical Inference

A theory is presented that establishes a dominance hierarchy of potential distinctions (order relations) between two distributions. It is proposed that it is worthwhile for researchers to ascertain the strongest possible distinction, because all weaker distinctions are logically implied. Implications of the theory for hypothesis testing, theory construction, and scales of measurement are considered. Open problems for future research are outlined.

The serial-parallel dilemma: A case study in a linkage of theory and method

The question as to whether humans perceive, remember, or cognize psychological items simultaneously (i.e., in parallel) or sequentially (i.e., serially) has been of interest to philosophers and psychologists since at least the 19th century. The advent of the information-processing approach to cognition in the 1960s reopened the inquiry, initiating a flood of experiments and models in the literature. Surprisingly for so elemental an issue, persuasive experimental tests have, until recently, proven rather elusive. Several decades of theoretical, methodological, and experimental effort, propelled and shaped by a meta-theoretical perspective, are leading to powerful strategies for assessing this and related cognitive issues. The present article reviews the theoretical and empirical history of these inquiries and details situations in which decisive experimental tests are possible.

Fundamental derivations from decision field theory

Abstract Decision field theory is a stochastic dynamic model of decision-making based on psychological principles of approach-avoidance behavior. This paper provides a summary of the main mathematical derivations for the distribution of choice response times obtained from binary choice tasks, and the distribution of matched values obtained from a matching task. The relations of decision field theory to a number of other theories of decision-making are also pointed out.