Decision Field Theory - Decision Field Theory

The name of decision field theory was chosen to reflect the fact that the inspiration for this theory comes from an earlier approach - avoidance conflict model contained in Kurt Lewin's general psychological theory, which he called field theory. 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. The horizontal axis on the figure represents deliberation time (in seconds), and the vertical axis represents preference strength. Each trajectory in the figure represents the preference state for one of the risky prospects at each moment in time.

Intuitively, at each moment in time, the decision maker thinks about various payoffs of each prospect, which produces an affective reaction, or valence, to each prospect. These valences are integrated across time to produce the preference state at each moment. In this example, during the early stages of processing (between 200 and 300 ms), attention is focused on advantages favoring prospect B, but later (after 600 ms) attention is shifted toward advantages favoring prospect A. The stopping rule for this process is controlled by a threshold (which is set equal to 1.0 in this example): the first prospect to reach the top threshold is accepted, which in this case is prospect A after about one second. Choice probability is determined by the first option to win the race and cross the upper threshold, and decision time is equal to the deliberation time required by one of the prospects to reach this threshold.

The threshold is an important parameter for controlling speed–accuracy tradeoffs. If the threshold is set to a lower value (about .50) in Figure 1, then prospect B would be chosen instead of prospect A (and done so earlier). Thus decisions can reverse under time pressure. 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. Under high time pressure, decision makers must choose a low threshold; but under low time pressure, a higher threshold can be used to increase accuracy. Very careful and deliberative decision makers tend to use a high threshold, and impulsive and careless decision makers use a low threshold.

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. Thus each action is defined by a probability distribution across these four outcomes. The affective values produced by each payoff are represented by the values m_j. At any moment in time, the decision maker anticipates the payoff of each action, which produces a momentary evaluation, U_i(t), for action i. This momentary evaluation is an attention-weighted average of the affective evaluation of each payoff: U_i(t) = Σ W_ij(t)m_j. The attention weight at time t, W_ij(t), for payoff j offered by action i, is assumed to fluctuate according to a stationary stochastic process. This reflects the idea that attention is shifting from moment to moment, causing changes in the anticipated payoff of each action across time. The momentary evaluation of each action is compared with other actions to form a valence for each action at each moment, v_i(t) = U_i(t) – U.(t), where U.(t) equals the average across all the momentary actions. The valence represents the momentary advantage or disadvantage of each action. The total valence balances out to zero so that all the options cannot become attractive simultaneously. Finally, the valences are the inputs to a dynamic system that integrates the valences over time to generate the output preference states. The output preference state for action i at time t is symbolized as P_i(t). The dynamic system is described by the following linear stochastic difference equation for a small time step h in the deliberation process: P_i(t+h) = Σ s_ijP_j(t)+v_i(t+h).The positive self feedback coefficient, s_ii = s > 0, controls the memory for past input valences for a preference state. Values of s_ii < 1 suggest decay in the memory or impact of previous valences over time, whereas values of s_ii > 1 suggest growth in impact over time (primacy effects). The negative lateral feedback coefficients, s_ij = s_ji < 0 for i not equal to j, produce competition among actions so that the strong inhibit the weak. In other words, as preference for one action grows stronger, then this moderates the preference for other actions. The magnitudes of the lateral inhibitory coefficients are assumed to be an increasing function of the similarity between choice options. These lateral inhibitory coefficients are important for explaining context effects on preference described later. Formally, this is a Markov process; matrix formulas have been mathematically derived for computing the choice probabilities and distribution of choice response times.

The decision field theory can also be seen as a dynamic and stochastic random walk theory of decision making, presented as a model positioned between lower-level neural activation patterns and more complex notions of decision making found in psychology and economics.