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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

Mean-variance trade-off. The result of the experiment for all 14 subjects ordered from the most risk-seeking to the most risk-averse. The indifference points ±s.d. obtained from the five psychometric curves are shown in black. The best lines of fit obtained using weighted linear regression are shown in blue. The risk-attitude parameter θ1 is the line's slope and is shown in the right-hand corners of the subplots. For all but three subjects, the  hypothesis of risk-neutrality could be rejected with p < 0.05 (marked with an asterisk).
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RSPB20102518F2: Mean-variance trade-off. The result of the experiment for all 14 subjects ordered from the most risk-seeking to the most risk-averse. The indifference points ±s.d. obtained from the five psychometric curves are shown in black. The best lines of fit obtained using weighted linear regression are shown in blue. The risk-attitude parameter θ1 is the line's slope and is shown in the right-hand corners of the subplots. For all but three subjects, the hypothesis of risk-neutrality could be rejected with p < 0.05 (marked with an asterisk).

Mentions: Figure 2 shows the indifference points at the five variance levels for all 14 subjects. We used weighted least-squares regression to obtain linear fits of the five mean-variance indifference points. The slope of these fits informs us about the risk-sensitivity. A slope of zero is compatible with risk-neutrality. A non-zero slope of these fits implies that subjects modulated their indifference points depending on the level of variance. As can be seen by the regressions marked with an asterisks in figure 2, for all except three subjects, the hypothesis of risk-neutrality, i.e. a line indistinguishable from the horizontal, could be rejected with p < 0.05.


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

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

Mean-variance trade-off. The result of the experiment for all 14 subjects ordered from the most risk-seeking to the most risk-averse. The indifference points ±s.d. obtained from the five psychometric curves are shown in black. The best lines of fit obtained using weighted linear regression are shown in blue. The risk-attitude parameter θ1 is the line's slope and is shown in the right-hand corners of the subplots. For all but three subjects, the  hypothesis of risk-neutrality could be rejected with p < 0.05 (marked with an asterisk).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSPB20102518F2: Mean-variance trade-off. The result of the experiment for all 14 subjects ordered from the most risk-seeking to the most risk-averse. The indifference points ±s.d. obtained from the five psychometric curves are shown in black. The best lines of fit obtained using weighted linear regression are shown in blue. The risk-attitude parameter θ1 is the line's slope and is shown in the right-hand corners of the subplots. For all but three subjects, the hypothesis of risk-neutrality could be rejected with p < 0.05 (marked with an asterisk).
Mentions: Figure 2 shows the indifference points at the five variance levels for all 14 subjects. We used weighted least-squares regression to obtain linear fits of the five mean-variance indifference points. The slope of these fits informs us about the risk-sensitivity. A slope of zero is compatible with risk-neutrality. A non-zero slope of these fits implies that subjects modulated their indifference points depending on the level of variance. As can be seen by the regressions marked with an asterisks in figure 2, for all except three subjects, the hypothesis of risk-neutrality, i.e. a line indistinguishable from the horizontal, could be rejected with p < 0.05.

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