Decision field theory
The paper "Decision Field Theory" was published by Jerome R. Busemeyer and James T. Townsend in 1993.
[1][2][3][4] The DFT has been shown to account for many puzzling findings regarding human choice behavior including violations of stochastic dominance, violations of strong stochastic transitivity,[5][6][7] violations of independence between alternatives, serial-position effects on preference, speed accuracy tradeoff effects, inverse relation between probability and decision time, changes in decisions under time pressure, as well as preference reversals between choices and prices.
[8] Recently, the authors of decision field theory also have begun exploring a new theoretical direction called Quantum Cognition.
DFT is a member of a general class of sequential sampling models that are commonly used in a variety of fields in cognition.
The basic ideas underlying the decision process for sequential sampling models is illustrated in Figure 1 below.
Suppose the decision maker is initially presented with a choice between three risky prospects, A, B, C, at time t = 0.
Each trajectory in the figure represents the preference state for one of the risky prospects at each moment in time.
[16] High thresholds require a strong preference state to be reached, which allows more information about the prospects to be sampled, prolonging the deliberation process, and increasing accuracy.
Low thresholds allow a weak preference state to determine the decision, which cuts off sampling information about the prospects, shortening the deliberation process, and decreasing accuracy.
[4] To provide a bit more formal description of the theory, assume that the decision maker has a choice among three actions, and also suppose for simplicity that there are only four possible final outcomes.
The attention weight at time t, Wij(t), for payoff j offered by action i, is assumed to fluctuate according to a stationary stochastic process.
The dynamic system is described by the following linear stochastic difference equation for a small time step h in the deliberation process: Pi(t+h) = Σ sijPj(t)+vi(t+h).The positive self feedback coefficient, sii = s > 0, controls the memory for past input valences for a preference state.
The negative lateral feedback coefficients, sij = sji < 0 for i not equal to j, produce competition among actions so that the strong inhibit the weak.
The magnitudes of the lateral inhibitory coefficients are assumed to be an increasing function of the similarity between choice options.
The Ford focus is different from the BMW and Audi because it is more economical but lower quality.
This property of the theory entails an interesting prediction about the effects of time pressure on preferences.
Alternatively, if context effects are produced by switching from a weighted average rule under binary choice to a quick heuristic strategy for the triadic choice, then these effects should get larger under time pressure.
Recent studies that record neural activations in non-human primates during perceptual decision making tasks have revealed that neural firing rates closely mimic the accumulation of preference theorized by behaviorally-derived diffusion models of decision making.
The linear approximation is important for maintaining a mathematically tractable analysis of systems perturbed by noisy inputs.
In addition to these neuroscience applications, diffusion models (or their discrete time, random walk, analogues) have been used by cognitive scientists to model performance in a variety of tasks ranging from sensory detection,[13] and perceptual discrimination,[11][12][14] to memory recognition,[15] and categorization.
