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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

Parameter estimates for the prospect theory fits and control results. (a) The estimated value function for each subject (blue) and the mean across subject (red). The dashed line indicates a risk-neutral value function. (b) The estimated probability weighting function w(p) for each subject (blue) and the mean across subject (red). The dashed line indicates no distortion of probabilities. (c) The empirical probability of hitting the target in the ‘mean-variance session’ versus the hitting probability predicted by using subjects' endpoint variability from the ‘σ-estimation session’ with 1 s.e.m. across subjects. The dashed lines indicates a perfect match between the two.
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RSPB20102518F3: Parameter estimates for the prospect theory fits and control results. (a) The estimated value function for each subject (blue) and the mean across subject (red). The dashed line indicates a risk-neutral value function. (b) The estimated probability weighting function w(p) for each subject (blue) and the mean across subject (red). The dashed line indicates no distortion of probabilities. (c) The empirical probability of hitting the target in the ‘mean-variance session’ versus the hitting probability predicted by using subjects' endpoint variability from the ‘σ-estimation session’ with 1 s.e.m. across subjects. The dashed lines indicates a perfect match between the two.

Mentions: A different way of looking at human decision-making has been suggested by Kahnemann & Tversky. In their original formulation of prospect theory [3] and its later extension cumulative prospect theory (CPT) [35], deviations from risk-neutrality are due to two factors—the distortion of probabilities in the probability weighting function and the curvature in the value function. In CPT, people's value function is described as convex for monetary losses and concave for monetary gains. In addition, people act as if they misperceive probability, putting too much weight on small probabilities and too little weight on large probabilities. This is captured by a value function and probability weighting function whose shape is determined by a parameter α and γ, respectively (see §2 for details). We repeated the maximum-likelihood analysis for a CPT decision-maker and estimated the parameters α and γ (see table 1 and figure 3a,b). The three subjects that had been classified as risk-averse had convex value functions, the remaining subjects had concave value functions. In general, the estimated θ2 and α were anti-correlated (ρ = −0.89, p < 0.001). The picture was more mixed for the probability weighting function (ρ = −0.43, p > 0.05) but the majority of subjects seemed to be under rather than overweight small probabilities (γ = 1.51 ± 0.23). Based on BIC, a model comparison with the risk-neutral model was not in favour of the CPT model (risk-neutral decision-maker: BIC = 6256.1, CPT decision-maker: BIC = 6293.9); however, based on the Akaike information criterion (AIC) the CPT model was preferred (risk-neutral decision-maker: AIC = 6163.2, CPT decision-maker: AIC = 6015.4). Comparing the CPT model to the mean-variance model, we found that the mean-variance model was preferred both based on BIC (mean-variance model: BIC = 6156.2, CPT decision-maker: BIC = 6293.9) and based on AIC (mean-variance model: AIC = 5970.6, CPT decision-maker: AIC = 6015.4).


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

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

Parameter estimates for the prospect theory fits and control results. (a) The estimated value function for each subject (blue) and the mean across subject (red). The dashed line indicates a risk-neutral value function. (b) The estimated probability weighting function w(p) for each subject (blue) and the mean across subject (red). The dashed line indicates no distortion of probabilities. (c) The empirical probability of hitting the target in the ‘mean-variance session’ versus the hitting probability predicted by using subjects' endpoint variability from the ‘σ-estimation session’ with 1 s.e.m. across subjects. The dashed lines indicates a perfect match between the two.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSPB20102518F3: Parameter estimates for the prospect theory fits and control results. (a) The estimated value function for each subject (blue) and the mean across subject (red). The dashed line indicates a risk-neutral value function. (b) The estimated probability weighting function w(p) for each subject (blue) and the mean across subject (red). The dashed line indicates no distortion of probabilities. (c) The empirical probability of hitting the target in the ‘mean-variance session’ versus the hitting probability predicted by using subjects' endpoint variability from the ‘σ-estimation session’ with 1 s.e.m. across subjects. The dashed lines indicates a perfect match between the two.
Mentions: A different way of looking at human decision-making has been suggested by Kahnemann & Tversky. In their original formulation of prospect theory [3] and its later extension cumulative prospect theory (CPT) [35], deviations from risk-neutrality are due to two factors—the distortion of probabilities in the probability weighting function and the curvature in the value function. In CPT, people's value function is described as convex for monetary losses and concave for monetary gains. In addition, people act as if they misperceive probability, putting too much weight on small probabilities and too little weight on large probabilities. This is captured by a value function and probability weighting function whose shape is determined by a parameter α and γ, respectively (see §2 for details). We repeated the maximum-likelihood analysis for a CPT decision-maker and estimated the parameters α and γ (see table 1 and figure 3a,b). The three subjects that had been classified as risk-averse had convex value functions, the remaining subjects had concave value functions. In general, the estimated θ2 and α were anti-correlated (ρ = −0.89, p < 0.001). The picture was more mixed for the probability weighting function (ρ = −0.43, p > 0.05) but the majority of subjects seemed to be under rather than overweight small probabilities (γ = 1.51 ± 0.23). Based on BIC, a model comparison with the risk-neutral model was not in favour of the CPT model (risk-neutral decision-maker: BIC = 6256.1, CPT decision-maker: BIC = 6293.9); however, based on the Akaike information criterion (AIC) the CPT model was preferred (risk-neutral decision-maker: AIC = 6163.2, CPT decision-maker: AIC = 6015.4). Comparing the CPT model to the mean-variance model, we found that the mean-variance model was preferred both based on BIC (mean-variance model: BIC = 6156.2, CPT decision-maker: BIC = 6293.9) and based on AIC (mean-variance model: AIC = 5970.6, CPT decision-maker: AIC = 6015.4).

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