Choice certainty is informed by both evidence and decision time

Abstract

"Degree of certainty" refers to the subjective belief, prior to feedback, that a decision is correct. A reliable estimate of certainty is essential for prediction, learning from mistakes, and planning subsequent actions when outcomes are not immediate. It is generally thought that certainty is informed by a neural representation of evidence at the time of a decision. Here we show that certainty is also informed by the time taken to form the decision. Human subjects reported simultaneously their choice and confidence about the direction of a noisy display of moving dots. Certainty was inversely correlated with reaction times and directly correlated with motion strength. Moreover, these correlations were preserved even for error responses, a finding that contradicts existing explanations of certainty based on signal detection theory. We also contrived a stimulus manipulation that led to longer decision times without affecting choice accuracy, thus demonstrating that deliberation time itself informs the estimate of certainty. We suggest that elapsed decision time informs certainty because it serves as a proxy for task difficulty.

Figure 1. Choice-reaction time task with simultaneous report of choice and certainty

A. Stimulus display. Observers reported the direction of dynamic random dot motion (up or down) and choice certainty by making a single saccadic eye movement to one of the two bar-shaped targets. The landing point of the saccade along the target indicated the degree of certainty, which ranged from guessing (red) to full confidence (green). B. Task sequence. After acquiring a fixation point the two targets appeared on the screen, followed by the motion stimulus. The subject made a saccadic eye movement when ready. The motion stimulus was extinguished when the observer initiated an eye movement. C. Probability correct and reaction time conformed to expectations of a bounded accumulation mechanism (see Methods). Each column shows data from one subject (S1–S6). The model was fit to the overall distribution of RTs. Then the parameters were used to predict the subject’s accuracy (gray curves, upper panel) and the correct RTs (solid black curves, lower panel). Error bars are s.e.m.

Figure 2. Certainty varies as a function of both RT and motion strength. Each column shows data from one subject (S1–S6)

A. Certainty on correct choices. The horizontal position of the saccade end points are grouped by motion strength and RT. Positive endpoints connote greater certainty. For 0% coherence all trials are included. RTs are grouped in quintiles for each motion strength. B. Certainty on errors. Error bars are s.e.m.

Figure 3. The inverse relationship between RT and certainty is not explained by trial-to-trial fluctuations of the random dot stimulus. Each column represents data from one subject (S1–S6)

For each subject and response condition (correct or error), trials are grouped into quintiles based on RTs (indicated by color). Each RT group is further divided into quintiles based on average motion energy (filled circles). A. Correct trials. Certainty grows with average motion energy but for each average motion energy longer RTs are associated with lower certainty. B. Error trials. For each level of motion energy, certainty is inversely related to RT. Error bars are s.e.m.

Figure 4. Certainty grows with stimulus strength for both correct and error responses

A. The horizontal position of the saccade end points are averaged across all RTs for the correct (solid) and error (dashed) responses for each motion strength. Overall, subjects were less certain when they made errors, but five of the six subjects were more certain when those errors were made in response to stronger motion. Each panel shows the data from one subject (S1–S6). Error bars are s.e.m.

Figure 5. A simple bounded accumulation model predicts choice, RT, and certainty

A. The model. Two accumulators compete by integrating noisy momentary evidence in favor of the two choices. Momentary evidence (e₁, e₂) is drawn from a bivariate normal distribution. The accumulator that first reaches the absorbing bound dictates the choice and decision time. B. The choices and decision times of the model across trials can be formalized by propagation of a probability distribution over time in the space confined by the bounds of the two accumulators. The figure shows the joint distribution of decision variable at 1 s for upward 12.8% coherence. The correlation between e₁ and e₂ is −0.79. C. At the time of the decision, the DV of the winning accumulator (v_j) is at the upper bound, but the DV of the losing accumulator (v_i) can span a range of values. Panels depict DV distributions associated with correct and incorrect choices for the same motion strength as in B. Note that the distribution depends on decision time. D. The probability of a correct response depends on both the decision variable and decision time. Colors correspond to the log odds of a correct response across all motion strengths (Eq. 3). The inverted wedge at the left side of the figure corresponds to combinations of the DV and decision time that have extremely low probabilities. Termination of the decision-making process in that region is due to noise and unlikely to lead to better-than-chance accuracy. Combinations of the DV and decision time to the right of the wedge are much more likely and show the dependence of expected accuracy on the DV and time. E. Model predictions for the subject’s certainty. The model parameters were estimated by fitting the overall distribution of RTs, irrespective of choice and certainty (same parameters as those used in Fig. 1C). These parameters were then used to predict the model certainty for correct and error choices as a function of motion strength. The exact mapping between certainty and saccade landing positions varies from subject-to-subject, as expected from idiosyncratic interpretation of task instructions. However, the model correctly predicts the form of the certainty functions for each of the six subjects (Fig. 4). F. Fit of the model’s predicted certainty to confidence ratings. For each subject, we assume a monotonically increasing relationship between saccade end point and certainty.

Figure 6. Decoupling RT and accuracy via insertion of a “reverse pulse”

On half of the trials for the two lowest motion strength (0% and 3.2% coherence) a 160 ms pulse of reverse motion was presented to cancel the evidence from the preceding stimulus. A. The reverse pulse causes approximate cancellation of the immediately preceding motion sequence. Traces show average motion energy profiles for 3.2% coherence trials for 360 ms of normal stimulus (blue) or a 160 ms reverse pulse following 200 ms of normal stimulus (red). Positive values correspond to the correct direction, which is opposite to the reverse pulse. Shaded area represents s.e.m. In a bounded accumulation model, the reverse pulse is expected to increase RT without changing the proportion of correct choices. B. Probability correct and reaction times in the presence (gray) and absence (white) of reverse pulse. Each column displays data from one subject. Error bars show s.e.m.

Figure 7. The reverse pulse reduced choice certainty. Each column represents one subject

A. Certainty judgments with and without a reverse pulse. Bar graphs show the average horizontal position of saccadic end points in the presence (gray) and absence (white) of the reverse pulse. Error bars represent s.e.m. All 0% coherence trials and correct 3.2% coherence trials are shown. B. Change of saccade end points as a function of reaction time and motion strength in the presence (solid symbols) and absence (hollow symbols and dashed line) of reverse pulse. Conventions are similar to Fig. 2A.