Research Article: Sub-Optimal Allocation of Time in Sequential Movements

Date Published: December 9, 2009

Publisher: Public Library of Science

Author(s): Shih-Wei Wu, Maria F. Dal Martello, Laurence T. Maloney, Edward Vul.

Abstract: The allocation of limited resources such as time or energy is a core problem that organisms face when planning complex actions. Most previous research concerning planning of movement has focused on the planning of single, isolated movements. Here we investigated the allocation of time in a pointing task where human subjects attempted to touch two targets in a specified order to earn monetary rewards. Subjects were required to complete both movements within a limited time but could freely allocate the available time between the movements. The time constraint presents an allocation problem to the subjects: the more time spent on one movement, the less time is available for the other. In different conditions we assigned different rewards to the two tokens. How the subject allocated time between movements affected their expected gain on each trial. We also varied the angle between the first and second movements and the length of the second movement. Based on our results, we developed and tested a model of speed-accuracy tradeoff for sequential movements. Using this model we could predict the time allocation that would maximize the expected gain of each subject in each experimental condition. We compared human performance with predicted optimal performance. We found that all subjects allocated time sub-optimally, spending more time than they should on the first movement even when the reward of the second target was five times larger than the first. We conclude that the movement planning system fails to maximize expected reward in planning sequences of as few as two movements and discuss possible interpretations drawn from economic theory.

Partial Text: A central concern shared by microeconomics, behavioral ecology, psychology, and neurobiology is how well organisms allocate limited resources. For economists, knowing how buyers allocate their financial budgets is essential for understanding consumer behavior [1]. In animal foraging, behavioral ecologists seek to formalize how animals allocate time and energy constraints to maximize survival [2].

We first tested hypotheses needed to develop a model of the subject’s movement error and speed-accuracy tradeoff. The outcomes of these tests allowed us to formulate an accurate model of SAT for each of two successive movements. Given this model, we could then compare human performance to ideal performance maximizing expected gain.

Recent studies concerning movement planning have compared how humans plan movements to the predictions of decision-theoretic models of ideal movement that maximizes expected gain [3]–[5], [8]–[14]. Battaglia and Schrater [3] examined how humans trade off viewing time and movement time to minimize visuomotor variability; Dean, Wu and Maloney [5] looked at how humans trade off speed against accuracy in tasks where subjects were rewarded for both speed and accuracy. Together, the evidence thus far indicates a near-optimal planning system that takes into account visual and motor variability when solving the tradeoff problem (but see Wu et al. [14], Mamassian [34] and Burr, Banks & Morrone [35] for examples of suboptimal performance in perceptual and motor tasks).



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