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Risk-sensitivity and the mean-variance trade-off: decision making in sensorimotor control.

Nagengast AJ, Braun DA, Wolpert DM - Proc. Biol. Sci. (2011)

Bottom Line: Numerous psychophysical studies suggest that the sensorimotor system chooses actions that optimize the average cost associated with a movement.We designed a motor task in which participants could choose between a sure motor action that resulted in a fixed amount of effort and a risky motor action that resulted in a variable amount of effort that could be either lower or higher than the fixed effort.Most subjects were risk-sensitive in our task consistent with a mean-variance trade-off in effort, thereby, underlining the importance of risk-sensitivity in computational models of sensorimotor control.

View Article: PubMed Central - PubMed

Affiliation: Computational and Biological Learning Lab, Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK. arne.nagengast@gmail.com

ABSTRACT
Numerous psychophysical studies suggest that the sensorimotor system chooses actions that optimize the average cost associated with a movement. Recently, however, violations of this hypothesis have been reported in line with economic theories of decision-making that not only consider the mean payoff, but are also sensitive to risk, that is the variability of the payoff. Here, we examine the hypothesis that risk-sensitivity in sensorimotor control arises as a mean-variance trade-off in movement costs. We designed a motor task in which participants could choose between a sure motor action that resulted in a fixed amount of effort and a risky motor action that resulted in a variable amount of effort that could be either lower or higher than the fixed effort. By changing the mean effort of the risky action while experimentally fixing its variance, we determined indifference points at which participants chose equiprobably between the sure, fixed amount of effort option and the risky, variable effort option. Depending on whether participants accepted a variable effort with a mean that was higher, lower or equal to the fixed effort, they could be classified as risk-seeking, risk-averse or risk-neutral. Most subjects were risk-sensitive in our task consistent with a mean-variance trade-off in effort, thereby, underlining the importance of risk-sensitivity in computational models of sensorimotor control.

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Related in: MedlinePlus

Schematic of experiment. A trial in the ‘mean-variance session’ consisted of two stages: a decision stage and an effort stage. Three possible circular targets were displayed (green, the closest; red, the furthest; yellow, always at 10 cm from the origin). The target selection from these depended on the outcome of the decision stage. (1) In limited time, subjects chose to move their hand (represented by the small blue circle) either to the left or to the right. The left-hand side was a sure bet and the yellow circular target was always selected. Moving to the right was risky and subjects attempted to hit a small green target. Having established the subjects' Gaussian endpoint distribution for this movement previously, a given target size corresponded to a particular probability of hitting the target phit. Therefore, if subjects chose the risky strategy they would have a probability of phit of hitting the green target-wall and 1− phit of hitting the red target-wall. The size of the yellow wall was always the same. (2) In the effort stage, subjects moved to the corresponding target where they had to push against a stiff spring requiring a force Fright. We varied the probability phit and the red and green circular target positions to establish for which effort level subjects were indifferent between the sure bet and the risky option for five levels of effort variance.
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RSPB20102518F1: Schematic of experiment. A trial in the ‘mean-variance session’ consisted of two stages: a decision stage and an effort stage. Three possible circular targets were displayed (green, the closest; red, the furthest; yellow, always at 10 cm from the origin). The target selection from these depended on the outcome of the decision stage. (1) In limited time, subjects chose to move their hand (represented by the small blue circle) either to the left or to the right. The left-hand side was a sure bet and the yellow circular target was always selected. Moving to the right was risky and subjects attempted to hit a small green target. Having established the subjects' Gaussian endpoint distribution for this movement previously, a given target size corresponded to a particular probability of hitting the target phit. Therefore, if subjects chose the risky strategy they would have a probability of phit of hitting the green target-wall and 1− phit of hitting the red target-wall. The size of the yellow wall was always the same. (2) In the effort stage, subjects moved to the corresponding target where they had to push against a stiff spring requiring a force Fright. We varied the probability phit and the red and green circular target positions to establish for which effort level subjects were indifferent between the sure bet and the risky option for five levels of effort variance.

Mentions: The decision stage started with three effort circles (green, yellow and red; 0.75 cm radius) being displayed along the vertical axis of the screen (figure 1). The effort circles represented all the possible effort levels that could be experienced by the subject in the effort stage of that trial. The yellow circle was always xyellow = 10 cm from the start location (the sure bet), while the test stimuli were represented by the green and red circles, with the green circle always having a shorter distance, xgreen < 10 cm (lower effort), and the red circle always a greater distance, xred > 10 cm (higher effort), from the starting location. The colours of the three effort circles corresponded to the colours that were used to indicate different target regions on two walls that were located 20 cm lateral to the starting location and extended the full height of the screen. Subjects moved from the starting location to hit one of the two walls. The left wall was entirely yellow, whereas the right wall was red with a green region embedded whose height was varied between trials (figure 1). The green region determined the probability of phit, which was equilibrated in a test session to fit subjects' individual motor variability (compare experimental sessions). Depending on which of the three colour regions subjects hit they would have to move to the corresponding effort circle. Therefore, they could always choose the yellow effort circle if they wished (sure bet) or take the risky option of aiming for the green region and either reach to the green or red effort circle depending on the outcome. To make the task more demanding, the movement time was limited to 0.3 s (if longer, subjects had to repeat the trial) and we introduced a visual gain of 3 in the y-direction relative to the starting location (i.e. errors were magnified threefold) and this gain was kept constant throughout the experiment.


Risk-sensitivity and the mean-variance trade-off: decision making in sensorimotor control.

Nagengast AJ, Braun DA, Wolpert DM - Proc. Biol. Sci. (2011)

Schematic of experiment. A trial in the ‘mean-variance session’ consisted of two stages: a decision stage and an effort stage. Three possible circular targets were displayed (green, the closest; red, the furthest; yellow, always at 10 cm from the origin). The target selection from these depended on the outcome of the decision stage. (1) In limited time, subjects chose to move their hand (represented by the small blue circle) either to the left or to the right. The left-hand side was a sure bet and the yellow circular target was always selected. Moving to the right was risky and subjects attempted to hit a small green target. Having established the subjects' Gaussian endpoint distribution for this movement previously, a given target size corresponded to a particular probability of hitting the target phit. Therefore, if subjects chose the risky strategy they would have a probability of phit of hitting the green target-wall and 1− phit of hitting the red target-wall. The size of the yellow wall was always the same. (2) In the effort stage, subjects moved to the corresponding target where they had to push against a stiff spring requiring a force Fright. We varied the probability phit and the red and green circular target positions to establish for which effort level subjects were indifferent between the sure bet and the risky option for five levels of effort variance.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3119020&req=5

RSPB20102518F1: Schematic of experiment. A trial in the ‘mean-variance session’ consisted of two stages: a decision stage and an effort stage. Three possible circular targets were displayed (green, the closest; red, the furthest; yellow, always at 10 cm from the origin). The target selection from these depended on the outcome of the decision stage. (1) In limited time, subjects chose to move their hand (represented by the small blue circle) either to the left or to the right. The left-hand side was a sure bet and the yellow circular target was always selected. Moving to the right was risky and subjects attempted to hit a small green target. Having established the subjects' Gaussian endpoint distribution for this movement previously, a given target size corresponded to a particular probability of hitting the target phit. Therefore, if subjects chose the risky strategy they would have a probability of phit of hitting the green target-wall and 1− phit of hitting the red target-wall. The size of the yellow wall was always the same. (2) In the effort stage, subjects moved to the corresponding target where they had to push against a stiff spring requiring a force Fright. We varied the probability phit and the red and green circular target positions to establish for which effort level subjects were indifferent between the sure bet and the risky option for five levels of effort variance.
Mentions: The decision stage started with three effort circles (green, yellow and red; 0.75 cm radius) being displayed along the vertical axis of the screen (figure 1). The effort circles represented all the possible effort levels that could be experienced by the subject in the effort stage of that trial. The yellow circle was always xyellow = 10 cm from the start location (the sure bet), while the test stimuli were represented by the green and red circles, with the green circle always having a shorter distance, xgreen < 10 cm (lower effort), and the red circle always a greater distance, xred > 10 cm (higher effort), from the starting location. The colours of the three effort circles corresponded to the colours that were used to indicate different target regions on two walls that were located 20 cm lateral to the starting location and extended the full height of the screen. Subjects moved from the starting location to hit one of the two walls. The left wall was entirely yellow, whereas the right wall was red with a green region embedded whose height was varied between trials (figure 1). The green region determined the probability of phit, which was equilibrated in a test session to fit subjects' individual motor variability (compare experimental sessions). Depending on which of the three colour regions subjects hit they would have to move to the corresponding effort circle. Therefore, they could always choose the yellow effort circle if they wished (sure bet) or take the risky option of aiming for the green region and either reach to the green or red effort circle depending on the outcome. To make the task more demanding, the movement time was limited to 0.3 s (if longer, subjects had to repeat the trial) and we introduced a visual gain of 3 in the y-direction relative to the starting location (i.e. errors were magnified threefold) and this gain was kept constant throughout the experiment.

Bottom Line: Numerous psychophysical studies suggest that the sensorimotor system chooses actions that optimize the average cost associated with a movement.We designed a motor task in which participants could choose between a sure motor action that resulted in a fixed amount of effort and a risky motor action that resulted in a variable amount of effort that could be either lower or higher than the fixed effort.Most subjects were risk-sensitive in our task consistent with a mean-variance trade-off in effort, thereby, underlining the importance of risk-sensitivity in computational models of sensorimotor control.

View Article: PubMed Central - PubMed

Affiliation: Computational and Biological Learning Lab, Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK. arne.nagengast@gmail.com

ABSTRACT
Numerous psychophysical studies suggest that the sensorimotor system chooses actions that optimize the average cost associated with a movement. Recently, however, violations of this hypothesis have been reported in line with economic theories of decision-making that not only consider the mean payoff, but are also sensitive to risk, that is the variability of the payoff. Here, we examine the hypothesis that risk-sensitivity in sensorimotor control arises as a mean-variance trade-off in movement costs. We designed a motor task in which participants could choose between a sure motor action that resulted in a fixed amount of effort and a risky motor action that resulted in a variable amount of effort that could be either lower or higher than the fixed effort. By changing the mean effort of the risky action while experimentally fixing its variance, we determined indifference points at which participants chose equiprobably between the sure, fixed amount of effort option and the risky, variable effort option. Depending on whether participants accepted a variable effort with a mean that was higher, lower or equal to the fixed effort, they could be classified as risk-seeking, risk-averse or risk-neutral. Most subjects were risk-sensitive in our task consistent with a mean-variance trade-off in effort, thereby, underlining the importance of risk-sensitivity in computational models of sensorimotor control.

Show MeSH
Related in: MedlinePlus