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.

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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. The stimuli of perception are many dimensional. Tones may vary in frequency, intensity, and duration. Individual characters in text may vary in size, orientation, shape, and the number of line segments they contain (among other things). Even the fruit that we eat may vary in size, shape, texture, sugar content, and the wavelength of light it reflects. A fundamentally important problem is to determine how these dimensions are combined in perceptual processing. Because of this, a notion central to almost all theories of perception, whether they are aimed at the visual, the auditory, or some other modality, is that of perceptual independence. At a macroscopic verbal level, there is agreement among most theoreticians about the meaning of this term. The components A and B of the two-dimensional stimulus AB are said to be independently perceived if the perception of each is in no way contingent on or interacts with the perception of the other, or somewhat more rigorously, if the probability of simultaneously perceiving both components A and B is equal to the probability of perceiving component A times the probability of perceiving component B (e.g., Garner & Morton, 1969; Green & Birdsall, 1978; Wandmacher, 1976). Unfortunately, perceptions are not usually directly observable; instead they first pass through some decision process that uses the perceptions to select a response appropriate to the general experimental milieu. Decision or judgment processes therefore fundamentally alter direct perceptions (i.e., the early stages of perception), thereby making the above definition of perceptual independence difficult to test.

The authors interpret decision field theory (J. R. Busemeyer & J. T. 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 R. L. Keeney & H. Raiffa, 1976) and the classic Thurstone preferential choice model (see L. L. 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 strong testable predictions concerning the moderating effect of time pressure on these three effects.