Shared Mechanisms in the Estimation of Self-Generated Actions and the Prediction of Other’s Actions by Humans

Darts performance measures and nomenclature. The darts error of each throw in the VF and nVF blocks was defined as the unsigned distance of the dart-landing position (solid-outlined circle) from the board center (closed circle). The self-estimation error of each throw in the nVF blocks was defined as the unsigned distance between the dart-landing position and the self-estimated position (dotted circle).

Relation between observation prediction and motor action. The darts experts’ outcome prediction of observed darts actions (left red bar) and bowling actions (left blue bar) improved in the trainable observation sessions (Experiment 1). The outcome prediction of observed darts actions did not improve in the untrainable observation session (Experiment 2), although between them the experts watched dart actions by the same novice throwers in Experiments 1 and 2. The experts’ self-estimation error and darts error increased only when they watched the novice’s darts actions and their outcome prediction improved (Exp. 1, middle and right red bars) but not when they watched bowling actions (Exp. 1, middle and right blue bars) or when they failed to improve their outcome prediction of observed darts actions (Exp. 2, middle and right gray bars). Error bars indicate standard error.

Experimental results of behavioral trends. Increase in dart-landing position bias: The dart-landing position deviated progressively from the board center after outcome prediction of observed darts actions (B, red trace) but not after outcome prediction of bowling actions (A, blue trace) in Experiment 1. Constant self-estimated position bias: The self-estimated position did not change through the experiment, both after outcome prediction of darts actions (B, magenta trace) and after outcome prediction of bowling actions (A, cyan trace). Correlation between dart-landing and self-estimated positions: However, a substantial correlation was observed between dart-landing and their self-estimated positions in both darts (C, D) and bowling (C) observation sessions. Individual data from a representative darts expert in the dart observation session is shown in D, and the correlation coefficient averaged over the x- and y-axis across all darts experts is shown in C. The dashed line in C represents the significance level at p = 0.05. Error bars indicate standard error.

Proposed model. The model assumes that given a darts goal, a darts expert utilizes his controller to plan an appropriate motor command M, which is then fed to the musculoskeletal system to execute the required dart throw. The error in the throw is observed by the visual system when the room light is on and is used to correct the action in the next trial. The model assumes that in addition, the motor command M can be used to self-estimate the outcome of a throw using the outcome forward model, the output from which is used to correct the subsequent throw even when the room light is off. The model assumes the controller, the outcome forward model, and the muscular skeletal system to be affected by planning noise (δ_M), self-estimation noise (δ_SE), and execution noise (δ_E), respectively.

Simulation results for behavioral trends. Compare A–D with Fig. 4A–D, which uses the same plots of actual experiment data. The simulations using the C^×F⁺ model can reproduce the evolution of the experts’ behavior: dart-landing position (blue and red traces in A and B, respectively), self-estimated position (cyan and magenta traces in A and B, respectively), and the substantial correlations between these two positions (C) in both the bowling (square) and darts (circle) observation sessions. The dashed line in C represents the significance level at p = 0.05. Error bars indicate standard error.