Motor effort and adaptive sampling in perceptual decision-making

People usually switch their attention between the options when trying to make a decision. In our experiments, we bound motor effort to such switching behavior during a two-alternative perceptual decision-making task and recorded the sampling patterns by computer mouse cursor tracking. We found that the time and motor cost to make the decision positively correlated with the number of switches between the stimuli and increased with the difficulty of the task. Specifically, the first and last sampled items were chosen in an attempt to minimize the overall motor effort during the task and were manipulable by biasing the relevant motor cost. Moreover, we observed the last-sampling bias that the last sampled item was more likely to be chosen by the subjects. We listed all possible Bayesian Network models for different hypotheses regarding the causal relationship behind the last-sampling bias, and only the model assuming bidirectional dependency between attention and decision successfully predicted the empirical results. Meanwhile, denying that the current decision variable can feedback into the attention switching patterns during sampling, the conventional attentional drift-diffusion model (aDDM) was inadequate to explain the size of the last-sampling bias in our experimental conditions. We concluded that the sampling behavior during perceptual decision-making actively adapted to the motor effort in the specific task settings, as well as the temporary decision.

where β 0 , β 1 , β 2 and β 3 were free parameters, X was the predictor variable, and I was the 1 9 2 indicator variable whose value was 0 for the reference group and 1 for the other group. 1 9 3 To compare two psychometric curves, we fitted the data to the following logistic Then, we tested the null hypotheses β 2 = 0 and β 3 = 0 with the two-tailed one-sample t-test to 1 9 7 compare the intercepts and slopes (steepness) of the two curves. Bayesian Network modeling 2 0 0 We listed all three possible Bayesian Network models for different hypotheses 2 0 1 regarding the causal relationship between the decision variable before the last sampling, the 2 0 2 last sampled item and the final choice in the trial. The conditional probability of choosing the 2 0 3 right item given that it is last sampled was calculated under each hypothesis and compared 2 0 4 with the empirical results. 2 0 5 For mathematical details of the models, see S1 Supporting Information. 2 0 6 To calculate the conditional probability p(right chosen | right last sampled) from the 2 0 7 behavioral data, we first fitted a psychometric choice curve (probability of choosing the right 2 0 8 item vs. difference between the proportions of white dots in the stimuli) to the trials in which 2 0 9 the right item was sampled last for each subject individually, and then marginalized the 2 1 0 difference between the stimuli. The mean p(right chosen | right last sampled) across the 2 1 1 subjects in each group was compared with the value 0.5 (the probability without bias) using 2 1 2 the one-tailed one-sample t-test. The One-Switch group and the Right-Biased group were 2 1 3 compared with the Control group using Dunnett's test after a one-way ANOVA.
where d was the value scaling parameter, and θ was the multiplicative attentional discounting 2 2 3 parameter. Specifically, during the first sampling, the unattended stimulus was assigned a 2 2 4 mean value r mean = 0.5 instead of the real value because the subject had not sampled that 2 2 5 stimulus yet. Let DV t denote the value of the decision variable at time t. For every time step where ε t was drawn from a zero-mean Gaussian distribution with standard deviation σ . We 2 2 9 assumed that the first sampling falls on the left stimulus with a fixed probability (Control: subjects in the Control group, the max number of switches in a single trial was 10, so we 2 3 7 discarded simulations with more than 10 switches. 2 3 8 We fitted the three parameters in the model (θ, d and σ ) to the empirical data pooled 2 3 9 across all subjects: For each set of parameters, we ran a fixed number of valid simulations 2 4 0 (240 for the coarse search and 960 for the finer search) and compared the results with 2 4 1 behavioral data using the following error metric: 2 4 2 2 2 ' ' = a a n n a n y y y y Err y y where y a = 0.9042 and y n = 2.0698 were the accuracy and the mean number of switches 2 4 4 calculated from the 960 trials pooled across the 8 subjects in the Control group, while y a ' and The total motor effort within one single trial consisted of three parts: first, to drag the 3 1 2 cursor from the start position to the first sampled item; second, to switch between the items 3 1 3 one or more times during sampling (each switch took approximately the same moving 3 1 4 distance, as discussed previously); third and lastly, to drag the cursor from the last sampled item to the choice buttons. We studied how motor cost in the different parts interacted with 3 1 6 the decision-making process (Fig 4): conditions: There was no statistically significant difference between the two curves (intercept: 3 2 6 P = 0.0958; slope: P = 0.1358), and the overall accuracy was also similar (Control: 90.4%; 3 2 7 Right-Biased: 91.5%; unpaired two-tail t-test between individual subjects in the two groups: P 3 2 8 = 0.4599). The difference in motor costs during the action phase did not bias the decisions of 3 2 9 the subjects in our experimental paradigm. One possible reason is that the difference was not 3 3 0 directly related to the final choice; another possibility is that explicit knowledge of the motor 3 3 1 cost would help to avoid integrating irrelevant factors into the decision to maintain high 3 3 2 We plotted the number of switches made in the trials against trial difficulty (measured 3 3 4 by the absolute difference between the proportions of white dots in the stimuli) in Fig 4B: In 3 3 5 both conditions, the number of switches decreased with trial difficulty (significant slopes in 3 3 6 mixed-effects regression: P = 4.8×10 -10 for Control and P = 1.9×10 -8 for Right-Biased). There 3 3 7 was no significant difference between the two conditions (intercept: P = 0.5216; slope: P = 3 3 8 0.8516). The motor cost during sampling correlated with the number of switches, therefore we concluded that the more difficult the trials were, the more motor effort would be invested into 3 4 0 the sampling process. dealing with items in left-to-right order (for example, people usually read from left to right).

4 7
In the Right-Biased condition, subjects showed an extra tendency to go for the left item first 3 4 8 parameters (d, σ and θ ) and the relative values for the two stimuli. 3 9 9 In the One-Switch condition, the dependency structure between DV, the last sampled sampled) and p(DV) will be larger than that in the Control condition. 4 0 7 In the Right-Biased condition, the value of p(right chosen | right last sampled) will not 4 0 8 change because no term in Equation (6) depends on the motor cost to reach for the buttons. On the contrary, the second model assumes that the last sampled item depends on DV, 4 1 1 but the final decision is independent of the last sampled item. Therefore, in the Control 4 1 2 Under that hypothesis, the last-sampling bias is due to the term p(right last sampled | DV), 4 1 5 which is also a function of DV: When DV > 0, p(right last sampled | DV) > p(right last 4 1 6 sampled); when DV < 0, p(right last sampled | DV) < p(right last sampled). 4 1 7 In the One-Switch condition, the last sampled item no longer depends on DV, so: Thus p(right chosen | right last sampled) will fall back to 0.5. 4 2 0 In the Right-Biased condition, subjects tend to sample the right item last. We assumed 4 2 1 that such a tendency is independent of DV, so the probability p(right last sampled | DV) and 4 2 2 p(right last sampled) will rise by the same additive amount. Compared with the Control 4 2 3 condition, the term p(right last sampled | DV)p(right last sampled) -1 will become smaller 4 2 4 when DV > 0 and larger when DV < 0, resulting in a decreased size of the last-sampling bias. In Equation (9), the total bias in p(right chosen | right last sampled) has two sources: p(right 4 3 0 chosen | DV, right last sampled) and p(right last sampled | DV). The last sampled item is more 4 3 1 likely to be chosen, and the temporarily winning item is more likely to be sampled last.

3 2
Under such assumptions, the last-sampling bias should remain in the One-Switch 4 3 3 condition because the term p(right chosen | DV, right last sampled) is biased, but the size will 4 3 4 decrease because the term p(right last sampled | DV) now disappears. 4 3 5 In the Right-Biased condition, p(right chosen | right last sampled) will also become 4 3 6 smaller similar to that in Model (b). 4 3 7

3 8
Let p Control , p One-Switch and p Right-Biased denote p(right chosen | right last sampled) in each 4 3 9 specific experimental condition. We summarized different model predictions and the 4 4 0 empirical results in bias, and a value of 0.5 means that there is no bias. **P < 0.01, ***P < 0.001. The cross (×) 4 5 0 marks that the prediction contradicted empirical results. On top of the theoretical Bayesian Network analysis, we also ran an aDDM simulation 4 5 4 to test whether the decision variable can feedback into the sampling patterns. In our 4 5 5 simulations, each sampling epoch was focused alternatively on the two stimuli until it reached 4 5 6 a time limit randomly drawn from a distribution fitted to the empirical data. In the One-4 5 7 Switch condition, only one switch of attention was allowed. Each simulation ended when one 4 5 8 of the decision boundaries was reached. Therefore, the allocation of attention in the aDDM 4 5 9 was independent of the current decision variable. Firstly, we compared the psychometric choice curves: There was no statistically 4 7 4 significant difference between the psychometric choice curves for the simulations and the 4 7 5 human subjects (intercept: P = 0.0679; slope: P = 0.0610) in the Control condition ( Fig 6A). 4 7 6 In the One-Switch condition, there was no significant difference between the intercepts of the 4 7 7 curves (P = 0.7116), but the slope (steepness) for the simulated data was significantly smaller 4 7 8 than that of the empirical data (P = 3.2×10 -4 ), meaning that the overall accuracy in the 4 7 9 simulations was lower ( Fig 6D). When only one switch was allowed, the choice accuracy of Finally, we focused on the last-sampling bias: In Fig 6C and 6E, we plotted the 4 9 1 probability of choosing the last sampled item against the difference between the proportions 4 9 2 of white dots between the last sampled stimulus and the other. All the curves had an intercept 4 9 3 larger than 0.5, showing a tendency to choose the last sampled item, but the sizes of the bias 4 9 4 were different: The curve intercept for the simulations was significantly lower than empirical motor effort and how it is related to cost minimization in decision-making as well as motor 5 2 0 control [25,26]; future studies may quantify the effect of motor cost on sampling behavior 5 2 1 with similar methods. 5 2 2 The relationship between attention and eye movement during decision-making has 5 2 3 been studied abundantly [27], but researches highlighting limb and body movements during 5 2 4 the sampling process are rare, even though in naturalistic circumstances such movements 5 2 5 usually cooperate with eye movements to sample relevant information better. In our research, 5 2 6 we designed a paradigm based on computer mouse tracking in which both gaze shift and hand 5 2 7 movement (moving the mouse) were necessary to switch attention between the options. 5 2 8 Although mouse tracking and eye tracking are both commonly applied process tracking 5 2 9 methods in decision-making research, their original purposes are slightly different: While eye 5 3 0 tracking mostly target on attention and information searching strategies, mouse cursor 5 3 1 tracking data reflect more about indecision and momentary preference [28]. In our paradigm, 5 3 2 however, subjects must move the cursor closer to get a better view of each stimulus, as if 5 3 3 approaching a real object to have a better look. In this way, the mouse trajectory can reflect 5 3 4 attention during sampling as eye traces did in previous studies. Moreover, our paradigm can 5 3 5 be applied to study eye-hand cooperation and coordination during decision-making as well. 5 3 6 Traditionally, sequential sampling models assume that during decision-making, 5 3 7 subjects sample their options continuously until the relative evidence for one option reaches a 5 3 8 predetermined threshold, and such models capture the speed-accuracy trade-off phenomenon 5 3 9 well [19,29,30]. Interestingly, our results showed that subjects would make extra sampling 5 4 0 epochs during which the accuracy of the decision has not been improved significantly. One 5 4 1 possible explanation is that subjects were switching back to the previously sampled stimuli 5 4 2 again to verify their preliminary decision [31]. Similar to other studies [18, 32, 33], we 5 4 3 observed an attentional bias to the finally chosen option during the later sampling epochs.