# Decision field theory

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Decision Field Theory (DFT), a computational model of decision making, a decision theory that models deliberation as a diffusion process. The Decision Field Theory(DFT) was published by Jerome R. Busemeyer and James T. Townsend in the Psychological Review in 1993 under the title “Decision Field Theory: A Dynamic-Cognitive Approach to Decision Making in an Uncertain Environment.” It is a process model used to predict decision making under uncertainty. This model can be used to predict not only choice outcomes but also response times and context effects. The DFT also offers a bridge to neuroscience. The DFT can explain violations of stochastic dominance, violations of strong stochastic transitivity, 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.

## Decision Field Theory (from Busemeyer, J. R. and J. G. Johnson, in press)Edit

DFT is a member of a general class of sequential sampling models that are commonly used in a variety of fields in cognition (Ashby 2000; Laming, 1966; Link & Heath, 1975; Nosofsky & Palmeri, 1997; Ratcliff, 1978; Smith, 1995; Usher & McClelland, 2001). 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 (see Diederich, 2003). 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.

Another interpretation of DFT is the connectionist network interpretation. Figure 2 provides a connectionist interpretation of DFT for the example shown in Figure 1. Assume once again that the decision maker has a choice among three risky prospects, and also suppose for simplicity that there are only four possible final outcomes. Thus each prospect is defined by a probability distribution across these same four payoffs. The subjective, affective values produced by each payoff are represented by the inputs, mj, shown on the far left side of this network. At any moment in time, the decision maker anticipates the payoff of each prospect, which produces a momentary evaluation shown as the first layer of nodes in Figure 2. This momentary evaluation is an attention-weighted average of the affective evaluation of each payoff. The attention weight 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 prospect across time.

The momentary evaluation of each prospect is compared with other prospects to form a valence for each prospect at each moment. The valence represents the momentary advantage or disadvantage of each prospect, and this is shown as the second layer of nodes in Figure 2. 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, which is represented by the last layer of nodes in Figure 2 (and plotted as the trajectories in Figure 1). As preference for one prospect grows stronger, this moderates the preference for other prospects. 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.

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.

## Decision Field Theory- Explaining Context EffectsEdit

The DFT is capable of explaining context effects that many decision making theories are unable to explain. In classic probabilistic choice decisions, the probability of picking a given option is only dependent on the number of options. With two choices the probability of picking either is approximately .5, with the introduction of a third option or choice this probability theoretically decreases to approximately .33 for all. However, context effects are tested examples in which the addition of a third choice to the binary choice alters the probabilities so that each option does not have the same likelihood.

The first context effect is the similarity effect. This effect occurs with the introduction of a third point S that is similar but is not dominated and itself does not dominate X. If X is similar to S which are both very different from Y, the human mind will tend to view X and S as one choice option and Y as another. Thus the probability of Y remains the same whether S is presented as an option or not. However, the probability of X will decrease by approximately half (to about .25) with the introduction of S. The sum of the probability of X and S is still about .5, thus the first choice seems to be between X, S and Y. If the group of X and S is chosen then a second choice comes in to play- X or S. The choices that would have originally gone to X are now divided between X and S.

The second context effect is the compromise effect. This effect occurs when an option C is added that is a compromise between X and Y. For example if you are picking between a pair of shoes and debating between the most stylish but least comfortable (option X) and the most comfortable but least stylish (option Y) option C would be a pair of shoes that is more stylish than option Y and more comfortable than option X, providing a compromise. The introduction of this third option causes options X and Y to be picked with a probability of approximately .25 whereas option C will be picked about 50% of the time. This is most likely due to the brain grouping X and Y together as extreme options and C as a less extreme option. Thus the first choice is whether a person wants the extreme options or the compromise. Then, only if the extreme options are chose are X and Y seen as separate choices.

The third effect is called the attraction effect. This effect occurs when the third option A is similar to X but is clearly dominated by X. In this situation A is rarely chosen but it does boost the probability of X being chosen, thus decreasing the probability of choosing Y. It seems as if the presence of A causes the mind to perceive X to be more attractive overall, possibly because it clearly dominates choice A. This effect also violates the principle of regularity which says that adding another option cannot increase the popularity of an option in the original subset.

According to DFT, the attention switching mechanism is crucial for producing the similarity effect, but the lateral inhibitory connections are critical for explaining the compromise and attraction effects. If the attention switching process is eliminated, then the similarity effect disappears, and if the lateral connections are all set to zero, then the attraction and compromise effects disappear. This property of the theory entails an interesting prediction about the effects of time pressure on preferences. The contrast effects produced by lateral inhibition require time to build up, which implies that the attraction and compromise effects should become larger under prolonged deliberation (see Roe, et al, 2001). 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. Empirical tests show that prolonging the decision process increases the effects (Simonson, 1989) and time pressure decreases the effects (Dhar, Nowlis, & Sherman, 2000).

## DFT and Neuroscience (from Busemeyer, J. R., R. K. Jessup, Joseph G. Johnson, James T. Townsend, 2006)Edit

The Decision Field Theory has demonstrated an ability to account for a wide range of findings from behavioral decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. 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 decision processes of sensory-motor decisions are beginning to be fairly well understood both at the behavioral and neural levels. Typical findings indicate that neural activation regarding stimulus movement information is accumulated across time up to a threshold, and a behavioral response is made as soon as the activation in the recorded area exceeds the threshold (see Schall, 2003; Gold & Shadlen, 2000; Mazurek, Roitman, Ditterich, & Shadlen, 2003; Ratcliff, Cherian, & Segraves, 2003; and Shadlen & Newsome, 2001, for examples). A conclusion that one can draw is that the neural areas responsible for planning or carrying out certain actions are also responsible for deciding the action to carry out, a decidedly embodied notion.

Mathematically, the spike activation pattern, as well as the choice and response time distributions, can be well described by what are known as diffusion models (see Smith & Ratcliff, 2004, for a summary). Diffusion models, such as the decision field theory, can be viewed as stochastic recurrent neural network models, except that the dynamics are approximated by linear systems. 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 (Smith, 1995), and perceptual discrimination (Laming, 1968; Link & Heath, 1978; Usher & McClelland, 2001), to memory recognition (Ratcliff, 1978), and categorization (Nosofsky & Palmeri, 1997; Ashby, 2000). Thus, diffusion models provide the potential to form a theoretical bridge between neural models of sensory-motor tasks and behavioral models of complex-cognitive tasks.

## ReferencesEdit

• Ashby, F. G. (2000). A stochastic version of general recognition theory. Journal of Mathematical Psychology, 44, 310-329.
• Busemeyer, J. R. & Diederich, A. (2002) Survey of decision field theory. Mathematical Social Sciences, 43, 345-370.
• Busemeyer, J. R. and J. G. Johnson (in press). Micro-process Models of Decision Making. R. Sun (Ed.) Cambridge Handbook of Computational Cognitive Modeling. Cambridge University Press.
• Busemeyer, J. R., R. K. Jessup, Joseph G. Johnson, James T. Townsend. (2006). Building bridges between neural models and complex decision making behavior. Neural Networks 19(8): 1047-1058.
• Dhar, R., Nowlis, S. M., & Sherman, S. J. (2000). Trying hard or hardly trying: An analysis of context effects in choice. Journal of Consumer Psychology, 9, 189-200.
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