Movement Vigor as a Reflection of Subjective Economic Utility

Abstract

To understand subjective evaluation of an option, various disciplines have quantified the interaction between reward and effort during decision making, producing an estimate of economic utility, namely the subjective 'goodness' of an option. However, variables that affect utility of an option also influence the vigor of movements toward that option. For example, expectation of reward increases speed of saccadic eye movements, whereas expectation of effort decreases this speed. These results imply that vigor may serve as a new, real-time metric with which to quantify subjective utility, and that the control of movements may be an implicit reflection of the brain's economic evaluation of the expected outcome.

Keywords: Parkinson’s disease; aging; basal ganglia; effort; motor control; movement speed; reaction time; reward; vigor.

Fig. 1.. Key Figure.

Hypothetical relationship between utility, choice, and movement vigor. Utility: The utility function for apples (the function U (a), shown in blue, where a is number of apples, is concave, exhibiting diminishing marginal returns. This means that the more apples one has in hand, the smaller is the utility of an additional apple. The utility of one apple is determined by finding the risky choice that an individual has equal preference for (the indifference point). For example, in this subject, for one apple the equivalent risky lottery is a 50% chance of three apples. That is, U(1) ≈ 1/2U(3). If we assume that U(1) =1 utils, then we infer that U(3) =2 utils. For 3 apples, we observe U(3) ≈1/2U(10). From this we infer that U(10) =4 Similar indifference points are obtained for all possible outcomes (# of apples) and the resulting curve yields the utility function. Vigor: defined as the reciprocal of the time it takes to reach to a given number of apples (reciprocal of the sum of reaction and movement time). On each trial, some number of apples is presented at an eccentric location, resulting in reaching movement. Reaches toward two apples will be faster than toward one apple, but the margin will decrease as the number of apples increases. Not only would reaches be more vigorous towards the higher utility option, but the difference in vigor between options should scale with the difference in utility.

Fig. 2.

Saccade vigor is modulated by both expected reward and expenditure of effort. A. (Left panel) As subjects fixated a cued location on one side of a screen, an image was briefly flashed on the other side of the screen. Upon removal of the fixation point, subjects were to saccade to the new location at which time the image would reappear. (Right) Saccade peak velocity is higher in anticipation of viewing a facial image as compared with image of noise. B. Subjects made out-and-back reaching movements in four different directions and were either predictably rewarded or not rewarded for each trial. Reaction-times (left) and reach speeds (right) were faster when reaching in a rewarded direction compared to when that same direction was not rewarded. Error bars are between-subject whereas change is within-subject. From [10]. C. Expectation of effort increases reaction-time. With increasing target distance, reaction-times for the arm and eye increased. In all graphs, curves are averages across subjects. Shaded areas or bars represent SEM. From [15].

Fig. 3.

Vigor may be a real-time proxy for utility during deliberation. A. Volunteers made choices between a small, immediate monetary reward and a larger, but delayed reward. Options were presented on a computer screen; as subjects made their choices, their eye position was tracked. B. Eye position traces during a typical trial, demonstrating saccade patterns. The subject made saccades between the options, and at some point indicated her choice (red arrow). C. (Left panel) Saccade velocity relative to baseline was elevated as the decision time approached, and abruptly decreased after the decision. (Right panel) Saccades to the preferred option were faster than saccades to the non-preferred option (as measured immediately before and after the time of decision). D. The difference in saccade velocity between the immediate to delayed reward (delayed – immediate) correlated with the difference in utility between the delayed and immediate reward. From [33].

Fig. 4.

Between-subject differences in vigor. A. Eye velocity traces during saccades in the horizontal direction in two young adults (left). Subject 4H consistently moved his eyes with greater velocity than subject 16P. Data from [34]. (Right and middle) Head and hand velocity profiles during reaching from two other subjects. The targets were placed across the midline at distances of 15–18 cm. Shaded areas are SD over all trials for each subject. Data from [15]. B. (Left) Velocity profiles for 12–14° horizontal saccades in high vigor and low vigor individuals, selected from the top and bottom quartile of a population of around 300 subjects. (Right) Hand velocity during reaching for individuals with high and low vigor. Shaded areas are SEM. Data from [15]. Individuals with high vigor responded sooner and started their movements earlier than individuals with low vigor. C. Individuals with faster reaching movements also generated faster head movements. Each data point depicts a single subject. From [15]. D,E. Peak horizontal saccade velocity decreases with age after the teenage years, while saccade reaction-time increases with age beyond the teenage years. Error bars are SEM. Data from [55].

Fig. 5.

Relationship between willingness to wait and movement vigor. A. The trial began with a central fixation spot. Two targets were presented at 20° from fixation along with an instruction at the fixation spot indicating which target was the direction of the correct saccade. In some blocks, there was a 25% probability that following a variable delay period a second instruction would be given, indicating the previously instructed saccade should be canceled. The delay period was adaptively adjusted to the success and failure of the subject on previous trials: success made the delay period 30ms longer. The experiment attempted to measure the length of time the subject was willing to wait to improve their probability of success. B. Schedule of instruction probabilities. C. Willingness to wait, as measured via latency of saccades for two subjects, one with high saccade vigor (subject 4H, also shown in Fig. 4A), and one which low saccade vigor (subject 16P). The vertical lines denote breaks between blocks. Subject 4H (high vigor) is relatively unwilling to wait, whereas subject 16P (low vigor) is more willing to wait to improve probability of success. From [34].