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Sequential sampling decision making models

Dr. Simon Moss

Overview

Most individuals assume that our decisions reached rapidly tend to be less accurate. That is, increases in speed or haste should impair decisions, called a speed-accuracy trade-off. However, in some circumstances, individuals seem to be more accurate when they need to reach a decision rapidly.

Sequential sampling models of decision making can accommodate this phenomenon as well as many other interesting patterns of observations (e.g., Wallsten & Jang, 2008). According to these models, individuals form an initial estimate, such as which of several options, such as cars or strategies, to choose. Gradually, memories of previous incidents, or other information, modify this estimate. If the initial estimate, for some reason, is often correct, the subsequent perturbations can compromise the decision.

Evolution of the sequential sampling models

Adaptive strategy selection

Many models of decision making predict that decisions are more likely to be accurate when individuals are granted more time to consider the options. For example, according to the concept of adaptive strategy selection, the decision making strategy that individuals apply depend on the time that is available (e.g., Payne, Bettman, & Johnson, 1988 & Payne, Bettman, & Johnson, 1993).

When time is constrained, individuals apply strategies that are efficient, but not entirely accurate. For example, in these instances, individuals often apply the lexicographic heuristic. Specifically, they compare the alternatives-such as three courses of action or products-on only the most important attribute.

Alternatively, individuals might apply the elimination by aspects strategy (see Tversky, 1972). In particular, they first discard all the alternatives that do not exceed some criterion on the most important attribute. They then apply the same approach to the next most important attribute, and continue this algorithm until only one alternative remains.

When time is not limited, however, individuals might apply strategies that are less efficient, but utilize more information and hence tend to be more accurate.

Violations of speed-accuracy trade-offs

This assumption that time enables individuals to scan more information, improving decisions, presupposes a speed-accuracy trade-off. As individuals are granted more time, the accuracy of their decisions should improve. Indeed, many other models assume a speed-accuracy trade-off.

Busemeyer (1985), however, showed that speed-accuracy trade-offs are not always observed. Indeed, Busemeyer showed that speed can sometimes improve accuracy.

In his study, participants needed to select one of two options: a certain choice and an uncertain choice. For the certain choice, they received a specific outcome. On some trials, they would receive 30 cents if they chose this option. On other trials, they would receive no money. Finally, on some trials, they would incur a cost of 30 cents.

For the uncertain choice, the outcome was not specified, but instead was unpredictable, with a mean of 0 and a standard deviation that depended on the condition. Because the mean of the uncertain option is zero, the correct choice would be to select the certain option when the outcome is of this selection is a 30 cent gain. In addition, the correct choice would be to select the uncertain option when the outcome of the certain option is a 30 cent loss.

Participants were granted either 1, 2, or 3 seconds to decide between these two alternatives. Interestingly, provided the standard deviation of the uncertain choice was sufficiently high, individuals were more likely to reach a correct decision when granted 1 rather than 3 seconds. The traditional speed-accuracy trade-off was violated.

An example of a sequential sampling model

To accommodate these findings, Busemeyer (1993) proposed a model-which represents one example of sequential sampling. To illustrate this model, consider the decision in which individuals need to select one of two options: a certain or uncertain alternative. Individuals begin with a specific preference. For example, from the outset, individuals might prefer the certain option by a specific extent, perhaps a factor of 1.5. Alternatively, they might prefer the uncertain option by a factor of 2.3.

Over time, individuals remember a random sample of past instances in which they choose the uncertain option. These recollections then bias their preference. For example, if they recollect an occasion in which the uncertain option yielded a significant loss, their preference towards the certain option will rise. Once, the extent to which one alternative is preferred to the other alternative exceeds some threshold, individuals will then select this option. This threshold increases if more time is allocated to the decision.

According to Busemeyer (1993), when the initial preference tends to be biased towards the correct answer-and when the uncertain outcome is often similar to the certain outcome-speed-accuracy trade-offs are often violated. That is, the initial estimation, which is often correct, may be obscured by additional recollections of past incidents.

Applications sequential sampling models

Perceptual discrimination

Diederich and Busemeyer (2006) applied sequential sampling models to explain perceptual discrimination-that is, in decisions in which participants must decide which of two stimuli were presented.

The classical sequential sampling models need to be extended. For example, in their model, individuals do not only need to decide which stimulus presents the best outcome. They also need to process which stimulus is most likely to have been presented. These two processes, according to Diederich and Busemeyer (2006), are assessed separately. That is, participants seem to switch from process to the other process within trials.

References

Busemeyer, J. R. (1985). Decision making under uncertainty: A comparison of simple scalability, fixed sample, and sequential sampling models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 538-564.

Busemeyer, J. R. (1993). Violations of the speed-accuracy tradeoff relation. In O. Svenson & A. J. Maule (Eds.), Time pressure and stress in human judgment and decision making (pp. 181-193). New York: Plenum Press.

Busemeyer, J. R., & Diederich, A. (2002). Survey of decision field theory. Mathematical Social Sciences, 43, 345-370.

Busemeyer, J. R., & Myung, I. J. (1988). A new method for investigating prototype learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 3-11.

Busemeyer, J. R., & Townsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432-459.

Diederich, A. (1997). Dynamic stochastic models for decision making under time constraints. Journal of Mathematical Psychology, 41, 260-274.

Diederich, A. (2003). MDFT account of decision making under time pressure. Psychonomic Bulletin & Review, 10, 157-166.

Diederich, A., & Busemeyer, J. R. (2006). Modeling the effects of payoff on response bias in a perceptual discrimination task: Boundchange, drift-rate-change, or two-stage-processing hypothesis. Perception & Psychophysics, 68, 194-207.

Payne, J. W. (1976). Task complexity and contingent processing in decision processing: An information search and protocol analysis. Organizational Behavior & Human Decision Processes, 16, 366-387.

Payne, J. W. (1982). Contingent decision behavior. Psychological Bulletin, 92, 382-402.

Payne, J. W., Bettman, J. R., & Johnson, E. J. (1988). Adaptive strategy selection in decision making. Journal of Experimental Psychology: Learning, Memory, & Cognition, 14, 534-552.

Payne, J. W., Bettman, J. R., & Johnson, E. J. (1993). The adaptive decision maker. Cambridge, England: Cambridge University Press.

Tversky, A. (1972). Elimination by aspects: a theory of choice. Psychological Review 79, 281-299.

Wallsten, T. S., & Gonzalez-Vallejo, C. (1994). Statement verification: A stochastic model of judgment and response. Psychological Review, 101, 490-504.

Wallsten, T. S., & Jang, Y. (2008). Predicting binary choices from probability phrase meanings. Psychonomic Bulletin & Review, 15, 772-779.






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Last Update: 6/13/2016