A multiple-choice task with changes of mind

Abstract

The role of changes of mind and multiple choices has recently received increased attention in the study of perceptual decision-making. Previously, these extensions to standard two-alternative tasks have been studied separately. Here we explored how changes of mind depend on the number of choice-alternatives. To this end, we tested 14 human subjects on a 2- and 4-alternative direction-discrimination task. Changes of mind in the participants' movement trajectories could be observed for two and for four choice alternatives. With fewer alternatives, participants responded faster and more accurately. The frequency of changes of mind, however, did not significantly differ for the different numbers of choice alternatives. Nevertheless, mind-changing improved the participants' final performance, particularly for intermediate difficulty levels, in both experimental conditions. Moreover, the mean reaction times of individual participants were negatively correlated with their overall tendency to make changes of mind. We further reproduced these findings with a multi-alternative attractor model for decision-making, while a simple race model could not account for the experimental data. Our experiment, combined with the theoretical models allowed us to shed light on: (1) the differences in choice behavior between two and four alternatives, (2) the differences between the data of our human subjects and previous monkey data, (3) individual differences between participants, and (4) the inhibitory interaction between neural representations of choice alternatives.

Figure 1. Experimental paradigm: setup, time course and conditions.

(A) Participants had to decide on the net direction of coherent motion in a cloud of randomly moving dots. They indicated their choice by moving a computer mouse pointer towards the respective visual R-target on the computer screen in front of them. Yellow dots denote the R-targets. The number (two or four) and position of the visual R-targets corresponded to the possible directions of coherent motion in a particular trial. (B) Examples of possible R-target arrangements in the 2- and 4-choice experiment. In the 4-choice condition the four R-targets were placed equidistantly, each in one corner of the screen (up-right panel). For two alternatives the possible direction of motion could either be located in opposite corners of the screen (one example shown up-left), or at the same side of the screen (two examples, bottom panels). (C) To start a trial, the subjects had to click on the starting position (screen center) whereon the visual R-targets showed up on the screen, indicating the possible directions of motion. After a random delay the RDM stimulus appeared in the screen center. The motion stimulus was switched off once the mouse pointer left the starting position and the trajectory to the R-target was recorded. (D) Example traces from one participant (4-choice condition). In the majority of trials the subjects moved directly to one of the visual R-targets (black traces). Some trajectories, however, revealed a change of mind during the movement: they started towards one, but terminated at another R-target. Changes could be observed between adjacent (green) and opposite (red) R-targets.

Figure 2. Computational model: populations, connectivity and input.

(A) Diagram of the attractor model for decision-making between up to four choice alternatives. The network consists of a population of excitatory pyramidal neurons, structured into four selective pools (red, each contains 20% of the excitatory neurons) and a nonselective population, that inhibit each other through shared feedback from an inhibitory pool of interneurons (orange). Unlabeled arrows denote a connectivity of 1 (baseline). Recurrent connectivity within a selective pool is high, ω₊ = 1.48, whereas the connection weight between the selective pools is below average ω₋ = 0.88. Inhibitory connections have a weight ω_I = 1.125. The network consists of 500 neurons. (B) Time course of target and motion input to the selective populations in order to model the experimental design of the RDM task (see methods). (C) Example trial with “change of mind” for four alternatives at 3.2% coherence. The initially winning population (first threshold crossing) is overtaken by the other transient. The horizontal black line at 37 Hz indicates the threshold. Dotted vertical lines mark times of threshold crossings.

Figure 3. Mean reaction times and initial performance.

(A) Reaction times decreased with increasing coherent motion and were larger for four alternatives. (B) Initial performance, that is the percentage of initially correct choices, started at chance level (50% for two and 25% for four choice alternatives) and increased to almost perfect accuracy for 100% coherent motion.

Figure 4. Comparison between changes of mind and performance improvement for two and four alternatives.

Changes of mind are displayed as percentage of all valid trials. In the top row (A–D) the data for two and four choice alternatives is shown separately in black and red. As the percentage of changes of mind did not vary significantly between the two experimental conditions, we also plotted the average data in the bottom row (E–H) to emphasize the dependence of changing on the motion coherence. (A,E) Percentage of changes of mind at 0% motion coherence. (B,F) Correcting changes, that is changes from an initially wrong to the correct R-target. (C,G) Erroneous changes from correct to wrong. Given four choice-alternatives, also changes between two wrong R-targets occurred (w→w, dashed line in C and G). For an overall comparison, the bar plots indicate the average of all correcting (B) and erroneous (C) changes of mind for two and four choice alternatives. (D, H) Performance improvement through changes of mind (absolute difference of initial and final performance considering changes of mind). Participants' accuracy consistently improved with changes of mind, especially for intermediate coherence levels. The performance gained through changes of mind was comparable for the different number of possible choices.

Figure 5. Correlation between absolute number of changes, mean reaction time and overall accuracy of individual participants.

(A) The overall number of changes is plotted against the mean reaction time (mRT) of all valid trials (2- and 4-choice condition together) for each participant (colored dots and circles). (B) Relation of overall fraction of correct choices to mRT. Individual subjects are marked as in (A). On average, participants with longer reaction times changed significantly less (A) and tended to be more accurate (B). Red lines denote linear fits to the data.

Figure 6. Comparison between simulated and experimental reaction times and accuracy.

(A) Reaction times simulated with the attractor model include a non-decision time (t_ND) of 330 ms. (B) Accuracy of the attractor model. The respective motion input ν_motion for a given level of coherence was set according to equation 2 in the methods section. The initial decision was determined by a firing rate threshold of 37 Hz. For comparison the experimental data from Figure 3 is shown again in lighter colors. The model fits experimental reaction times and performance well. The difference in RT between 2- and 4-choice trials is only slightly overestimated, so is the accuracy. Error bars of simulated data (SEM) are mostly hidden behind the dot markers.

Figure 7. Simulated changes of mind using the attractor model.

A model trial was counted as a change of mind, if, after the initial threshold crossing (first choice), the firing rate of an initially-losing selective pool surpassed the other pools and crossed the decision threshold. Changes of mind are displayed as percentage of all valid trials. The attractor model generally replicated the frequency of changes observed experimentally for two (A) and four (B) alternatives. The experimental results of Figure 4 are plotted in lighter colors for comparison. Congruent with our experimental findings, the attractor model predicted similar percentages of changes in the 2- and 4- choice condition. Only at the lowest coherence level (3.2%), even fewer changes occurred for four choices, than were observed experimentally. Besides, in the model, changing improved the performance somewhat more for low coherence levels in the same way for the 2- and 4-choice condition (right column).

Figure 8. Threshold variation in the attractor model accounts for differences in choice behavior of participant subgroups.

(A,C) Average experimental data of the three participants with most and fewest overall changes of mind. The experimental results of all participants (Fig. 3) are plotted in lighter colors without dots for comparison. Reaction times (top row) in both the 2- and 4-choice conditions varied substantially between the subgroups: participants with the fewest changes had much higher reaction times. However, the initial performance (middle row) was almost identical between the two subgroups. The overall percentage of correcting and erroneous changes is displayed in the bottom row. (B,D) Simulated data. Just by modifying the decision threshold, the attractor model accounted for the quantitative differences in choice behavior of the two participant subgroups. With a lower threshold (22 Hz), reaction times were faster (top row) and more changes occurred (bottom row), fitting the experimental subgroup with the most changes. The opposite is true for a higher decision threshold (52 Hz), fitting the subgroup with the fewest changes. As in the experiment, the simulated performance (B,D, middle row) varied only slightly with threshold alteration. Apart from the decision threshold, all other model parameters were kept constant. For a comparison of the changes of mind frequency for different coherence levels see Figure S3.

Figure 9. Reaction times, performance, and changes of mind simulated with a simple race model.

(A) Reaction times and (B) initial performance obtained from the race model. The race parameters were estimated by fits to the experimental data and are given in Table 1. For comparison, the experimental data from Figure 3 is shown in lighter colors. The initial performance for high coherence levels is somewhat underestimated by the race model. (C, D) Example trials of a simulated change of mind at 6.4% motion coherence in the 2- and 4-choice conditions with ΔB = 0 and t_out = t_ND. (E) Changes of mind from the race model for the same physiologically-plausible conditions as used in the attractor model (see Table 1, Fit A). That is, the threshold to detect changes of mind was the same as the decision threshold (ΔB = 0) and the timeout for changing corresponded to the estimated non-decision time (t_out = t_ND). With these assumptions, the race model predicts ten times more changes than were observed experimentally. Moreover, in the race model, changes of mind are then more frequent for four than for two choice alternatives. (F) Changes of mind with fitted parameters for the change threshold and timeout (see Table 1, Fit B). By setting the change threshold much higher than the decision threshold and using a higher change threshold for four than for two choice alternatives, the percentage of changes of mind produced with the race model is now in the right order of magnitude. Yet, the dependence of changes on the motion coherence does not match our experimental observations (Fig. 4, see text for details). Changes of mind are displayed as percentage of all valid trials.