Two-stage perceptual decision making: the effect of choice commitment on the repulsion bias

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Two-stage perceptual decision making: the

effect of choice commitment on the

repulsion bias

First- year Internship Project Report

15 October 2014

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Ana Vojvodic

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Master Brain and Cognitive Sciences, Track - Cognitive Science

Brain & Cognition Group, University of Amsterdam

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Supervisor: Anne Urai, MSc

Co-Assessor & UvA representative: Dr. Tobias Donner

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Student Number 10628916 *

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Abstract !

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Every day, we make numerous decisions based on sensory information we perceive from our environments. Incoming sensory information is noisy and dynamic, and we must discriminate relevant evidence from the noise to formulate these choices. Prior research suggests that perceptual decision-making involves two processing stages: encoding incoming sensory information and decoding this information towards a categorical choice (Gold & Shadlen, 2007; Jazayeri & Movshon, 2007; Usher, 2013; Shadlen & Kiani, 2013). However, little is known about the processing of subsequent sensory evidence after a choice has been made. To further research this topic, we elaborated on the work of our collaborators in Marius Usher’s group at Tel Aviv University (Bronfman et al., 2014, personal communication). Their experimental results

suggested that making an abstract perceptual choice in a number integration task results in a choice-dependent aftereffect — a bias in the interpretation of subsequently perceived evidence. In this experiment, we aimed to replicate this effect in the context of visual sensory evidence. Using random dot kinematogram stimuli for fine discrimination tasks, we observed an analogous bias in subjective choice reports for certain stimulus types. Thus, it is plausible that that the mechanism applied in abstract perceptual decision-making might be translated to different types of stimuli and cognitive tasks, such as visual perceptual decision-making.

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Introduction !

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In a 2007 study, Jazayeri & Movshon observed a phenomenon termed the repulsion bias in fine perceptual discrimination tasks. Subjects viewed a random dot kinematogram (RDK, see Figure 1a for example) and made a binary discrimination choice regarding the overall dot motion direction (either clockwise or counterclockwise) from a reference mark. Jazayeri & Movshon compared whether this bias was found in coarse discrimination tasks, where overall dot motion is far from the reference mark (e.g. 180° away from the reference), and fine discrimination tasks, where overall dot motion is much closer (e.g. 25° or less from the reference). In some trials, following the binary choice task, subjects were asked to estimate the dots’ angle of motion relative to the reference mark on a continuous scale (Figure 1b). The closer the veridical angle was to the reference mark, the reported estimates deviated more from the veridical angle of motion, increasingly away from the reference mark, and in the direction of the binary choice. This movement away from the reference, or repulsion bias, was found to be unique to fine discrimination tasks, presumably because of different stimulus representation decoding strategies in fine and coarse discrimination (Jazayeri & Movshon, 2006; Jazayeri & Movshon, 2007).

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As an alternative explanation, Stocker & Simoncelli (2008) modelled the repulsion bias as a post-decisional effect rather than an intra-decisional mechanism. In their model, making a perceptual choice results in enhancement of conditioned perception, where perceptual inference after a decision is forced to remain consistent with the previously reported choice. This conditioned perception bias ensures self-consistency with previous categorical perceptions and choices by suppressing cognitive dissonance and sacrificing optimality in subsequent stimulus perception tasks. This model differs from the mechanism suggested by Jazayeri & Movshon in that the repulsion bias is then a result of commitment to a choice rather than an effect of only viewing and decoding the visual stimulus.

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Bronfman et al., (2014, personal communication) expanded on the aforementioned findings by testing if the repulsion bias is possibly induced by commitment to a binary categorical choice before making a

continuous estimation choice. Commitment is in this case defined as having externally reported the formulated choice based on internally accumulated evidence. Although Bronfman et al. used an abstract cognitive task, where subjects viewed a number series and then estimated the series’ mean value, their findings suggested an analogous repulsion bias to the one observed by Jazayeri & Movshon (2007). They reported a repulsion bias when subjects committed to a binary choice, and disappearance of this bias when subjects did not commit to a choice. Bronfman et al. further investigated the effects of additional evidence in a second stimulus interval after the subject made a binary choice regarding a first stimulus interval. They observed that relative to when they did not report an initial binary choice, subjects lost sensitivity to integrating additional evidence into the reported continuous estimation after making the binary choice. This observation is consistent with Stocker & Simoncelli’s idea of suppressing cognitive dissonance and enhancing conditioned perception.

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We combined these concepts to explore whether it is possible that choice commitment could also induce the repulsion bias in the same visual task originally used by Jazayeri & Movshon. We made an analogous study to Bronfman et al.’s by applying a similar experimental design and analysis approaches (see section

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Materials & Methods: Data & Analysis). One key difference is that instead of a number integration task, we

used RDK stimuli in a fine discrimination task followed by a second interval and a continuous estimation task, thereby extending the Jazayeri & Movshon (2007) experiment as well. Jazayeri & Movshon’s experiment involved the binary choice and estimation tasks only after a single stimulus interval, thus, including a second interval could provide insight into whether the repulsion bias could be an intra-decisional process, reflecting Jazayeri & Movshon’s theory of fine discrimination decoding strategy

optimisation, or a post-decisional process, reflecting Stocker & Simoncelli’s idea of conditioned perception.

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We hypothesised that: 

1. Committing to a binary fine discrimination choice would bias a later continuous estimation in the direction of the binary choice (clockwise or counterclockwise), inducing the repulsion effect as observed in Jazayeri & Movshon (2007). Further, we expected to see the same effect in trials where no directional evidence is presented, indicating that choice commitment, rather than stimulus processing, underlies the repulsion effect.

2. When integrating evidence over two intervals, a binary choice after the first interval would bias the final estimation direction more towards the evidence presented in the first interval, demonstrating a primacy effect. We expected this bias to be dependent on commitment to a binary choice, so evidence perceived prior to the choice would be up-weighted, whereas evidence perceived after the choice would be down-weighted.

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Figure 1. Example of Random Dot Kinematogram (RDK) with a) Binary Discrimination Task and

b) Continuous Estimation Task. Figure 1 from Jazayeri & Movshon (2007).

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Materials and Methods!

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Subjects!

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This project was approved by the University of Amsterdam Faculty Ethics Review Board, and all subjects gave written informed consent prior to participation. Subjects were compensated for their time with research participant university credits and one subject instead participated for compensation of €45 total for all six sessions. The study initially consisted of eleven subjects, all right-handed with normal or corrected-to-normal vision. The subjects were five males and six females between the ages of 18 and 29 (mean = 20.73), all naïve to the aim of the experiment. One was disqualified for being unable to complete the thresholding task properly, thus, the reported results are based on the remaining ten subjects. Eight of the subjects completed 3,795 trials in a total of six separate sessions of two hours each. Two subjects only completed three of these sessions, resulting in a total of 1,725 trials each. Each session was broken down into two sub-sessions of five experimental blocks, with the exception of the first session, which consisted of a training session and one session of five experimental blocks. This resulted in a total of 11 sub-sessions across the six sub-sessions. Each sub-session consisted of 345 trials divided into five experimental blocks of 69 trials per block (see details in Experimental Trials section).

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Stimuli !

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Stimuli were presented using PsychToolBox (Brainard,1997) in MATLAB and were viewed in a dark, quiet room on a CRT monitor with a resolution of 1024 x 768 and a refresh rate of 60 Hz. Subjects placed their heads in a stationary head rest with a viewing distance of 50 cm from the screen to minimise head movement and ensure stabilisation of eye tracking recordings for data to be analysed and reported in a future project. In each trial, subjects viewed a random dot kinematogram (RDK), a field of moving white dots on black background with 100% contrast in a circular aperture and a 12-degree radius (see Figure 2 as an example). The dots moved at a constant speed of 11.5 degrees/second with an individualised motion coherence determined by the procedure described in the section Thresholding & Training. Dots were of the limited lifetime motion type (Pilly & Seitz, 2009) with a lifetime of four frames, and were interleaved with three variants of the stimulus. Each dot’s size was 0.2 degrees and overall dot density was 1.7 dots/degree2_{. The}

red fixation cross in the center was based on the fixation point described by Thaler et al. (2013) and was 0.2 degrees in size with a 2-degree radius circle around the fixation point to separate it from the stimuli and help subjects maintain fixation. Precise dot coordinates were replicated so that the exact dot positions and order appeared one time each in the choice, no-choice, and choice-only conditions (further detailed in the section Experimental Trials) within each sub-session. The order of experimental condition and stimulus presentation was random across all sub-sessions and it was ensured that already presented dot coordinates per condition were not repeated in the same experimental condition.

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Figure 2. A random dot kinematogram (RDK) with red fixation point and white reference mark.

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Thresholding & Training!

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The first half of the first session was dedicated to preliminary training and thresholding before starting the main experiment. To familiarise the subject with RDK stimuli and the general idea of perceptual

discrimination tasks, the first portion of the training session involved only a coarse discrimination task. The dots moved either up or down with a maximum viewing time of 10 seconds, and auditory and text feedback were provided after each trial. After obtaining 100% accuracy in a short block of 10 trials, the dot motion coherence was then gradually decreased from 80% to 20% by increments of 20%. Once the subject mastered this portion by achieving 100% accuracy for the lowest coherence level, they were ready for the thresholding session.

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In order to ensure the subject was able to detect the coherent dot motion signal in the presented stimuli, the individual subject’s motion coherence threshold was determined. Each subject performed a thresholding session consisting of 600 trials of a coarse discrimination task. 100 trials of 6 different coherence levels (0, 2.5, 5, 10, 20, 40%) were presented in a randomised order with a viewing time of 750 ms, and no feedback was provided. The individual threshold was determined as the 80% point of a cumulative Weibull

distribution fit, with a chance level of 0.5. For instance, if the subject’s threshold at the 80% point was 15.00, this means that when this individual views stimuli with 15% coherence, they will achieve 80% accuracy in discriminating upwards or downwards motion. Across all ten subjects, the average motion coherence threshold was 17.45% (range = 12.93, std = 4.75). Figures 3 and 4 illustrate example curves generated by the psychometric functions used to determine the coherence threshold (Wichmann & Hill, 2001). The example in Figure 3 illustrates a subject with good performance and the expected S-shaped curve. Subjects with poor performance in the thresholding session did not exhibit the expected S-curves in their performance graphs, and were disqualified from the study because they were unable to complete the basic coarse discrimination task properly, thus would not be able to complete the more complex fine

discrimination tasks. Figure 4 illustrates a poor example of a psychometric curve as this subject is unable to properly detect and report the coherently moving signal within the stimulus. This subject was excluded from the study on this basis.

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Once the individual threshold level was established, the subject proceeded to go through a training session to become familiar with first the binary choice task, then the continuous estimation task, followed by the full combined two-interval task as described in the following section, Experimental Trials.

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Figure 3. Cumulative Weibull distribution curve of a subject with good performance in the coarse

discrimination thresholding task.

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Figure 4. Cumulative Weibull distribution curve of a subject with poor performance in the coarse

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Experimental Trials !

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The motion coherence of all trials was at the individually titrated threshold at the 80% point for each subject and this coherence level was used in the remainder of the experiment. Each trial had at least one RDK stimulus interval, and depending on the condition, some trials were followed by a second RDK stimulus interval. Each trial began with the appearance of a red fixation point for 600-800 ms, with randomly varied duration from trial to trial. The reference mark then appeared at a randomly selected position along the stimulus circle along with the first motion stimulus interval (Figure 2). To minimise confusion about the mapping between clockwise/counterclockwise motion and left/right button presses, each subject saw the reference mark in a random position in only the top 0-180° of the stimulus unit circle or only in the bottom 180-360° and was asked to discriminate motion to the left or to the right of the reference mark. The

assignment of the reference mark in either the top or bottom half of the circle was counterbalanced across subjects.

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The details of the binary choice and continuous estimation tasks are as follows:

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• Binary choice task: Following stimulus offset in the first interval, the subject received an auditory prompt to report a binary choice whether the dots were moving to the left or to the right of the reference mark. The subject then pressed the left or right button of a mouse to report their response. Left or right corresponded to clockwise or counterclockwise motion depending on the assignment of the reference mark appearing on the top or bottom half of the circle. The binary choice task had a time limit of two seconds for a response before continuing to the next segment.

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• Continuous estimation task: Following stimulus offset in the second interval, the reference mark turned red to cue the start of the estimation task (Figure 5). The task was to estimate the average angle of motion across the first and second intervals. The subject dragged the mouse to move the red line to the angle which they perceived as the average while the reference mark remained in place. The range of motion was around the entire unit circle so that subjects could correct their estimates if needed before submitting their response. Once the subject made the estimate, they confirmed their response with a mouse click. The estimation task had a time limit of ten seconds for a response before continuing to the next segment.

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Figure 5. RDK with red estimation line moved by the subject to the perceived average dot motion angle of

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The first motion stimulus interval was presented for 750 ms, and the subjects were asked to maintain fixation during this time. The dots moved in one of five directions relative to the reference mark: -20°, -10°, 0° (aligned with reference mark), 10°, or 20°. The trial continued in one of the following three conditions, as illustrated in the schematic diagram in Figure 6:

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• Choice-only: Subject received an auditory prompt to report a binary choice regarding the direction of the motion stimulus interval. Once the choice was reported, the subject received auditory feedback. If the stimulus’ veridical angle of motion was at 0°, at the reference mark (no angular motion evidence), random feedback was provided. The screen then turned blank to allow the subject to blink and to signify the end of the trial. Subjects were able to click after each blink break to advance to the next trial.

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• Choice and estimation: Referred to as simply choice condition in the remainder of this report. Following stimulus offset, the subject received an auditory prompt to perform the binary choice task as described above. However, following the choice, the subject did not receive feedback, and then viewed a second motion stimulus for 750 ms. After 750 ms, the dots remained stationary and the reference mark turned red as a visual cue to signify the estimation task. Once the response was confirmed, the screen turned blank to allow for a blink break and signify the end of the trial. These trials most closely match those of Jazayeri & Movshon (2007), with the exception of the additional stimulus interval on which the estimation is also based.

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• No-choice and estimation: Referred to as simply no-choice condition in the remainder of this report. Following stimulus offset, the subject received an auditory prompt to press the center wheel of the mouse instead of clicking the left or right button to report a binary choice. The aim of this neutral motor action is to maintain consistency in performing a button press between the first and second interval but without committing to a binary choice. The maximum time interval for this motor action is the same as the maximum response time in the choice condition, at 2 seconds, to also maintain consistent timing for the motor action responses. Following the wheel press, the subject viewed the second motion stimulus for 750 ms and, as in the choice condition, was visually cued to perform the estimation task. Once the response was confirmed, the screen turned blank to allow for a blink break and signify the end of the trial.

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Auditory prompts and feedback were counterbalanced across subjects. Half the subjects heard a low tone (150 ms, 200 Hz) for incorrect response and a high tone (150 ms, 880 Hz) for a correct response, and the other half received the reverse auditory feedback pairing. The auditory prompts were chosen from default Apple OS X alert sounds. Half the subjects heard the alert “Sosumi” for binary choice prompt and the alert “Hero” for the no-choice prompt, and the remaining half of subjects received the reverse auditory pairing.

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The pairs of angles were classified by the nature of their permutations in three categories: both-evidence (both intervals have non-0° angular motion), half-evidence (first interval only or second interval only had 0° motion), and no-evidence (both intervals contain 0° motion). Twenty-three permutations of the angle pairs for the directions of motion were used with the five possible angles (-20°, -10°, 0°, 10°, or 20°). The most extreme both-evidence angle permutations were removed from the possible permutations in the

experimental design (first interval/second interval: -20°/20° and 20°/-20°). 55 trials for each permutation per choice condition were presented across all sessions, resulting in 3,795 trials total. See Appendix Table 1 for a list of the permutations.

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Figure 6. Schematic flow diagram of experimental trials.

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66% of all trials 33% of all 33% of all trials Additional RDK (~500 ms) + 10º - 10º 0º + 20 º - 20 º Additional RDK (~500 ms) + 10º - 10º 0º + 20 º - 20 º First RDK (~500 ms)!

Angle of motion from reference mark

+ 10º - 10º

0º

+ 20 º - 20 º

Estimate Mean Angle of Motion Across the Two RDKs

No Choice Binary Choice: CW or CCW

Blink Break

Next Trial

33% of all trials

33% of all trials 33% of all trials

66% of all trials 33% of all trials

Feedback

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Data & Analysis:!

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All data were processed and analysed in MATLAB.

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i) Mode analysis

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To assess Hypothesis 1, namely, that commitment to a binary choice would induce the repulsion bias in the continuous estimation task, we followed Bronfman et al.’s method termed the mode analysis. We expected that the binary choice would not only influence the direction of the estimate, but also the error of the

estimate — the difference between estimated mean angle of motion and the veridical mean angle of motion. The binary choice would then bias the error of the estimate in the direction of the choice. Using only trials that had non-0° evidence in the first interval, we first divided the trials into two categories based on the stimulus identity, or veridical direction of the evidence in the first interval (clockwise or counterclockwise). Then, for each of these two groups of trials, we computed the single-trial distributions of estimate errors, conditioned on the initial binary choice the subject reported. This resulted in separate distributions for correct and incorrect binary responses within each group of trials. From the correctly reported binary choice trials, we then extracted the mode value of the distribution. If a repulsion bias was present, we would expect the mode value of the distribution of estimation errors to be different from 0 and in the direction of the reported binary choice. If there was no repulsion bias, then the mode of the distribution of estimation errors would be expected to be around 0.

Bronfman et al. rationalise using the mode rather than the mean or median of the distribution because these values include a bias that already takes into account the direction of the reported choice. This is built on the assumption that “each evaluation of a mean can be considered as a 'sample' from a Gaussian around the actual mean” (Bronfman et al., 2014). For example, if the veridical mean is in the clockwise direction, the subject may still perceive and incorrectly report a counterclockwise mean angle across both intervals. The subject’s motion coherence threshold is at the 80% point of a cumulative Weibull distribution, so errors in binary choice and estimation accuracy are expected to sometimes occur, both within and beyond of the bounds of the Gaussian around the veridical mean value. In this situation, if there was no repulsion bias present, then the mean and median of clockwise estimates (estimate direction in accordance with the veridical mean) would be quantified as higher than the mode of estimation errors. This is because the counterclockwise response samples of the Gaussian would be “cut” or removed from this distribution on the basis of the clockwise choice conditioning the direction of the estimation. The mode would then be

expected to be 0, and would serve as an unbiased quantifier of the absent repulsion bias in the distribution of estimation errors. If there was a repulsion bias present, then the mode would be different from 0 and in the direction of the binary choice.

To isolate the effect of choice without the variable of angular motion in the stimuli presented, we ran a separate mode analysis on no-evidence trials. In these trials, both stimulus intervals moved at the reference mark (0°), moving neither counterclockwise nor clockwise. The subject must guess the initial binary choice as there is no veridical evidence in the first stimulus interval, thus, we would expect symmetric chance levels for clockwise and counterclockwise binary choices. Further, the subject must rely on guessing again to perform the estimation task as there is no veridical evidence to integrate. However, in the choice

condition, even in the absence of veridical visual evidence, the subject has one piece of “evidence” in forming their estimation — the initially reported discrimination choice, re-enforcing the idea of conditioned perception. The effect of conditioned perception was expected to be dependent on the uncertainty level, which is highest in the no-evidence trials. So, we expected the two distributions, again conditioned on the two possible choices, to have their modes shifted symmetrically toward or away from 0.

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ii) Regression!

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To assess Hypothesis 2, that a binary choice after the first interval would bias the final estimation direction towards evidence presented in the first interval, we assessed this effect in terms of regression of veridical evidence in both stimulus intervals onto the subjects’ estimation. We expected to observe a possible primacy effect: evidence from the first interval may have stronger impact on the mean angle direction estimate than evidence from the second interval. Critically, we expected the primacy effect to be boosted in the choice condition and weaker or absent in the no-choice condition as a reflection of the commitment bias. We expected commitment to a binary choice to decrease subjects’ sensitivity to integrating evidence

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presented in the second interval into the estimation task, aligning with the idea of conditioned perception as a possible mechanism of the repulsion bias and with Bronfman et al.’s findings.

We approached the regression analysis separately for the choice and no-choice conditions, with X1 representing the angle of motion presented in the first interval and X2 representing the angle of motion presented in the second interval. We first ran the regression with unprocessed data using a robust multilinear regression fit with bi-square weights to minimise the influence of outliers. As the regression analysis is sensitive to outliers, we approached the analysis again with more stringent criteria by excluding all trials where the subject reported a continuous estimate further than 50 degrees away from reference mark. The maximum veridical mean angle of motion was 20 degrees away from the reference mark in either direction, and an estimation more than double this angle indicates the subject did not adequately pay attention, did not properly perceive the stimulus, or did not follow instructions carefully. The robustness of the model yielded significant results in both regression approaches (see Results: Regression section). Bronfman et al., using the regression analysis approach, found a primacy effect in the choice condition, and a weak recency effect in the no-choice condition. We expected then, in the choice condition, to see larger weights in the regression for the first evidence interval (X1), and smaller weights for the second evidence interval (X2) as a result of the commitment-induced primacy bias. In the no-choice condition, we then expected flatter weight distribution across the two intervals with the possibility of a slightly larger weight in the second interval, which would correspond to a weak recency effect due to the absence of a

commitment-induced primacy bias.

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Results!

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Binary Choice Task Performance!

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The mean reaction time for all subjects was 0.87 seconds (range = 0.30, std = 0.10). Figure 7a illustrates the reaction times for all subjects.

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In calculating the binary task accuracy, trials which had 0° motion evidence in the first interval were excluded. The mean accuracy for all subjects was 68.97% correct (range = 27.79, std = 11.56). Figure 7b illustrates the percentage of correct responses for all subjects.

Figure 7. Binary choice task a) reaction times and b) accuracies across all subjects.

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Estimation Task Performance!

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Given the continuous nature of the estimation task, estimation accuracy is expressed as the estimated average angle’s deviation away from the veridical average angle, or the error of the estimation, rather than a discretely measured percentage of correct responses, as was appropriate for the binary task. In all two-interval trials, the mean deviation from the veridical average angle was 4.96° (range = 21.34, std = 6.33). We anticipated estimation accuracy to decrease after commitment to a choice, thus we expected a larger mean deviation in the choice condition. We based this prediction on the rationale that conditioned

perception is thought to be suboptimal for perceptual inference of veridical evidence, but optimal in maintaining self-consistency (Stocker & Simoncelli, 2008). In the choice condition, the mean deviation from the veridical average angle was 5.18° (range = 20.32, std = 5.99). In the no-choice condition, the mean deviation from the veridical average angle was 4.74° (range = 22.55, std = 6.77). A paired t-test showed that there was no significant difference between the mean deviations in the choice and no-choice conditions (t(9) = 0.78, p = 0.46, std = 1.80).

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As another measurement of estimation accuracy, we examined the precision, calculated as the reciprocal of the standard deviation of error of the reported deviations (Bays & Husain, 2008). In all two-interval trials, the precision was 0.05 (range = 0.04, std = 0.01). In the choice condition, the mean precision was 0.05 (range = 0.04, std = 0.01). In the no-choice condition, the mean precision was 0.05 (range = 0.03, std = 0.01). A paired t-test showed that there was a significant difference between the mean precisions in the choice and no-choice conditions (t(9) = -4.78, p = 0.00098, std = 0.0038).

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P0 P1 P3 P4 P5 P6 P8 P9 P10 P11 0 0.2 0.4 0.6 0.8 1

Binary Choice Reaction Times Across All Subjects

Subject Number Seconds

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P0 P1 P3 P4 P5 P6 P8 P9 P10 P11 0 10 20 30 40 50 60 70 80 90 100

Binary Choice Accuracy Across All Subjects

Subject Number

Percent Correct Responses

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Binary Task and Estimation Task Performance Compared!

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We expected subjects who had a higher accuracy in the binary task to have higher performance overall, corresponding to smaller mean deviations in the estimation task. In order to compare performances in the binary task and the estimation task, we computed the Pearson linear correlation coefficient between the percentage of correctly reported binary choice task trials and mean estimation task angular deviations across all subjects. Figure 8 illustrates the relationship between binary choice and estimation task performances. The correlation coefficient for all two-interval trials was -0.35 (r(8) = -0.35, p = 0.32). The general trend and negative correlation supports the prediction that higher accuracy in the binary choice task is associated with smaller mean estimate deviations in the estimation task.

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Figure 8. Correlation plot for binary choice task accuracy vs. estimation errors (deviations) for all

two-interval trials.

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Mode Analysis!

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Following the same rationale as Bronfman et al. to illustrate the repulsion bias, we performed a mode analysis (see section Materials & Methods: Data & Analysis for detailed description) on the distributions of the estimation errors split up by binary choice earlier in the trial. Based on the findings of Bronfman et al. (2014), Jazayeri & Movshon (2007), and Stocker & Simoncelli (2008), we expected to find the presence of a repulsion bias. We hypothesised that the repulsion bias would be induced after committing to a categorical choice. We also predicted that the repulsion bias and corresponding mode value would be greatest in the no-evidence trials because the effect of conditioned perception is thought to be dependent on uncertainty level, which is highest in the no-evidence condition as no angular motion is present in either stimulus interval. 55 60 65 70 75 80 85 0 5 10 15 20 25 Correlation Coefficient = −0.350

Binary Choice Task % Accuracy

Estimation Deviations (Degrees)

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i) Non-zero first evidence interval trials mode analyses

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The first set of mode analyses we performed were on all trials that had non-0° evidence in the first interval or in both intervals, ensuring that the binary choice could be based on angular motion evidence. The analyses were segregated into two different sets of estimation error (deviation) distributions. One set of distributions consists of the estimation errors for when the first evidence interval had clockwise motion from the reference and the other set of distributions consists of the estimation errors for when the first evidence interval had counterclockwise motion from the reference mark. Each distribution was then split up on the condition of the reported binary choice after the first interval. Only trials in which the subject correctly reported the binary choice after the first interval were used in extracting the corresponding clockwise and counterclockwise estimation error mode values. A positive value corresponds to a clockwise angle of motion with respect to the reference mark and a negative value corresponds to a counterclockwise angle of motion with respect to the reference mark.

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Upon inspecting the individual results across participants, we obtained varying patterns in the estimation error distributions. For example, when the first interval had a clockwise RDK stimulus, some subjects had a mode value corresponding to clockwise estimation errors, while others had a counterclockwise estimation error mode value. Conversely, when the first interval had a counterclockwise RDK stimulus, some subjects had a mode value corresponding to counterclockwise estimation errors, while others had a clockwise mode value. One subject had both mode values as clockwise, three subjects had both mode values as

counterclockwise, three subjects had clockwise mode values for the counterclockwise first-interval distributions and counterclockwise mode values for the clockwise first-interval distributions, and the remaining three subjects had mode values that corresponded to the directional identity of the first-interval stimulus. See Appendix for individual subjects’ distributions.

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Across all participants, we found that the mode for trials in which the first interval contained a

counterclockwise angle of motion was -2 degrees estimation error and the mode for trials in which the first interval contained a clockwise angle of motion was also -2 degrees estimation error (Figure 9a-c). Thus, subjects who correctly reported a counterclockwise direction of motion after the first interval overall reported counterclockwise estimates and estimation errors after the second interval, and subjects who correctly reported a clockwise direction of motion after the first interval overall reported counterclockwise estimates and estimation errors after the second interval as well. Thus, the general tendency was to make counterclockwise estimation errors. These results are not completely in alignment with our predictions and the findings of Bronfman et al. When the first interval stimulus direction was counterclockwise and subjects correctly reported counterclockwise motion, we observed the signature of the repulsion bias — the mode value different from zero and in the direction of the initial binary choice. However, we did not observe this when the first interval stimulus direction was clockwise. Possible reasons for these discrepancies are elaborated in the Discussion section.

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ii) No-evidence trials mode analyses

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To isolate the impact of choice commitment on the repulsion bias, we performed a second set of separate mode analyses on only trials that did not contain any evidence— that is, both stimulus intervals had an angular motion of 0°, at the reference mark. These trials were not included in the previously described mode analyses. Rather than conditioning the distributions on the correctly reported initial reported binary choice, the distributions are solely based on the choice as there is no correct response possible. We expected the mode for both clockwise and counterclockwise conditioned estimates to be symmetrically repulsed from zero degrees estimation error and in the direction of the initial binary choice.

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In these no-evidence trials, we obtained varying individual patterns in the deviation distributions. Four subjects had both mode values as counterclockwise, and six subjects exhibited the pattern we had expected — the mode values as clockwise when they initially reported a clockwise binary choice and counterclockwise when they initially reported a counterclockwise binary choice. Subjects did not generally exhibit a symmetrical distribution of the mode values around zero. See Appendix for individual subjects’ distributions.

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Across all subjects, we found that the mode for trials in which subjects reported a counterclockwise direction of motion for the first interval was -8 degrees estimation error and the mode for trials in which subjects reported a clockwise direction of motion for the first interval was 4 degrees estimation error (Figure 9d). The modes values are in accordance with the initially reported binary choice, as we expected.

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However, these results, like those from non-zero first evidence interval trials mode analysis, are slightly skewed towards a counterclockwise estimation error. Possible reasons for these discrepancies are addressed in the Discussion section.

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iii) Comparing mode values

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Comparing across first evidence interval stimulus identities (clockwise or counterclockwise), a paired t-test showed that there was a significant difference between the mode values when subjects made a

counterclockwise estimation error (t(9) = -2.85, p = 0.02, std = 15.31). When subjects made a clockwise estimation error, a paired t-test showed that there was a significant difference between the mode values (t(9) = -5.18, p = 0.00058, std = 10.81).

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When both clockwise and counterclockwise first-evidence interval trials are pooled, a paired t-test showed that there was no significant difference between the clockwise and counterclockwise estimation error mode values (t(9) = -1.48, p = 0.17, std = 14.06). For the no-evidence trials, a paired t-test showed that there was a significant difference between the clockwise and counterclockwise estimation error mode values (t(9) = -3.47, p = 0.0071, std = 14.78).

Figure 9. Distribution of degrees deviations between reported estimated mean angle of motion and

veridical mean angle of motion (estimation error) across all subjects when a) the first evidence interval stimulus is counterclockwise, b) the first evidence interval stimulus is clockwise, c) the first evidence intervals are pooled regardless of directional identity, and d) both evidence intervals contain 0° evidence. The first listed mode value is from the distributions in which subjects reported a counterclockwise binary choice and the second listed mode value is from the distributions in which subjects reported a clockwise binary choice.

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Estimation error Count −40 −20 0 20 40 0 50 100 150 200 250 300 350 Stimulus CCW, modes: −2, 13 Choice CCW Choice CW −40 −20 0 20 40 0 50 100 150 200 250 300 Stimulus CW, modes: −20, −2 −40 −20 0 20 40 0 50 100 150 200 250 300 350 400

Pooled over stimulus identity, modes: −2, −2 Grand Average, n = 10 −40 −20 0 20 40 0 5 10 15 20 25 30 35 40 45 No Evidence, modes: −8, 4

a)

b)

c)

d)

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Regression!

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For each estimation report, the subject had to integrate evidence from the first stimulus interval with evidence from the second evidence interval in order to formulate a decision regarding the mean angle of motion to report in the continuous estimation task. To investigate the effect of choice commitment on the sensitivity of evidence integration from the second stimulus interval with evidence from the first, we followed a similar approach taken by Bronfman et al. to quantify the relative weights of each stimulus interval’s evidence in the subjects’ reported estimates (see Materials & Methods: Data & Analysis for more details).

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Results varied across subjects (Figure 10). Overall in the choice condition, subjects slightly up-weighted evidence from the first interval, suggesting a weak primacy effect. Five subjects up-weighted evidence from the first interval compared to evidence from the second interval, suggesting a primacy effect, while four subjects up-weighted evidence from the second interval, suggesting a recency effect. One subject had relatively flat weights for evidence from both intervals.

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Overall in the no-choice condition, subjects up-weighted evidence from the second interval, suggesting a recency effect. Four subjects up-weighted evidence from the first interval compared to evidence from the second interval, suggesting a primacy effect. However, three of these subjects up-weighted first interval evidence in the choice condition as well, thus it is plausible that these individual subjects were prone to a primacy bias in either condition. Five subjects up-weighted evidence from the second interval, suggesting a recency effect. Four of these subjects also up-weighted evidence from the second interval in the choice condition, so it is possible that these individuals were prone to a recency bias in either condition. One subject had relatively flat weights from both intervals.

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Repeated measures ANOVA on the weights showed that there was not a significant effect for the order of evidence interval presentation (F(1,9) = 0.27, p =0.62), and that there was not a significant effect for the choice condition (F(1,9) = 0.70, p = 0.42). However, there was a significant interaction (F(1,9) = 6.13, p = 0.04).

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This analysis approach excluded outliers (trials in which the subject reported an estimation of greater than 50 degrees away from the reference mark, see Materials & Methods: Data & Analysis). When all trials were included, repeated measures ANOVA on the weights still yielded results where there was not a significant effect for the order of evidence interval presentation (F(1,9) = 0.22, p =0.65), and there was not a significant effect for the choice condition (F(1,9) = 0.30, p = 0.60). There was, again, a significant interaction (F(1,9) = 5.13, p = 0.05).  

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Figure 10. Robust multilinear regression fit with bisquare weights for first interval and second interval per

subject and group average (excluding all trials where the reported estimation was greater than 50 degrees from the reference mark).

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stimulus interval

regression weights

Robust regression with bisquare weights

Repeated Measures ANOVA Interval F_(1,9)=0.2187, p=0.6511 Choice F_(1,9)=0.2988, p=0.5979 Interaction F_(1,9)=5.1332, p=0.0497 choice no choice 1 2 0.1 0.15 0.2 0.25 0.3 0.35 GRAND AVERAGE 1 2 0 0.1 0.2 0.3 0.4 P11 1 2 −0.1 0 0.1 0.2 0.3 0.4 P10 1 2 0.1 0.15 0.2 0.25 0.3 0.35 P09 1 2 0.2 0.25 0.3 0.35 0.4 P08 1 2 −0.2 0 0.2 0.4 0.6 P06 1 2 −0.05 0 0.05 0.1 0.15 0.2 P05 1 2 0.2 0.3 0.4 0.5 0.6 0.7 P04 1 2 0.2 0.3 0.4 0.5 0.6 0.7 P03 1 2 −0.2 −0.1 0 0.1 0.2 0.3 P01 1 2 0 0.1 0.2 0.3 0.4 P00

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Discussion!

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Conclusions!

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The initial predictions in this experiment were based on our primary hypothesis as well as the framework outlined in the idea of conditioned perception (Stocker & Simoncelli 2008). Our main hypothesis was that committing to a binary categorical choice will bias the way subsequent evidence is perceived in order to remain consistent with the initially reported categorical choice. As a result of this choice commitment bias, we expected to replicate the repulsion bias as described by Jazayeri & Movshon (2007) using two

evidence intervals instead of one, and we expected to replicate the repulsion bias that Bronfman et al. (2014) generalised to abstract perceptual decision-making. We successfully replicated some of these effects in the context of visual perceptual decision-making tasks. Possible explanations for any

discrepancies could be attributed to the mechanisms of perceptual decision-making in the context of the particular tasks we used or in experimental design and analysis flaws (see Future research).

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We had predicted that estimation accuracy would decrease after committing to a binary choice, and using the mean deviations as indicators of accuracy, our results did not support this prediction. However, using precision as a metric for accuracy, this approach yielded results that supported this prediction. It is possible that supplementing these analysis approaches using alternative metrics could provide more conclusive results on whether estimation accuracy may decrease after choice commitment. Further, our prediction that subjects with higher binary task performance would have more accurate continuous estimates was supported. These results do not provide substantial evidence for a reliable relationship between choice commitment and estimation task performance. Thus, it is not feasible to conclude that choice commitment may have an effect on estimation accuracy and the subsequent magnitude of the associated repulsion bias based on these results alone.

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In the non-zero first interval evidence and no-evidence mode analyses, we observed the expected repulsion bias effect. However, the repulsion bias as described by Jazayeri & Movshon (2007) and

Bronfman et al. (2014) was observed in only the counterclockwise, but not clockwise, first evidence interval trials mode analysis, yet consistently observed in the no-evidence trials mode analysis. With these results from both sets of mode analyses we performed we can conclude that the impact of choice commitment may plausibly be responsible in part for the repulsion bias in trials when no veridical evidence is present. However, due to the counterclockwise-skewed results from the mode analyses using non-zero evidence intervals, we cannot attribute the presence of the repulsion bias as a consequence of choice commitment in trials when veridical evidence is present in both stimulus intervals. Observation of the repulsion bias as expected in the counterclockwise first evidence interval trials, however, does suggest that this effect may

possibly be attributed to choice commitment. Further, the significant differences between mode values from

the separate distributions based on stimulus identity and the significant difference between the mode values from the no-evidence trials hint towards this possible conclusion as well. Another iteration of this experiment could provide more solid results and clarification.

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Based on the results of the regression analysis, we did not find consistent evidence for either a primacy or recency effect across individual subjects. Overall in the choice condition, subjects slightly up-weighted evidence from the first interval, suggesting a weak primacy effect, and in the no-choice condition, subjects overall up-weighted evidence from the second interval, suggesting a recency effect. However, our repeated measures ANOVA indicated a significant interaction between the evidence interval order and choice, but did not show significant effect of either of these variables. Had our results been more closely in alignment with Bronfman et al., with a higher X1 than X2 in the choice condition, then the repulsion bias could more reliably be attributed as a post-decisional effect from the idea of conditioned perception, rather than an intra-decisional effect, as illustrated by the repulsion bias in Jazayeri & Movshon (2007). If our regression analyses had yielded results with greater significance for the effect of either choice or evidence interval presentation order, further insight could be inferred regarding the temporal nature of the repulsion bias in relation to the decision itself as an intra- or post-decisional process.

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Further research is needed to explore plausible mechanisms of additional evidence integration and

consequent decision making. The observed repulsion biases and absence of significant effects of choice or evidence interval presentation order in the regression results could indicate that the repulsion bias is a by-product of sensory evidence decoding (as suggested by Jazayeri & Movshon, 2007) rather than the result of actively inducing perception of subsequent evidence to remain self-consistent with the initial percept and decision (conditioned perception). Conditioned perception is thought to be suboptimal for achieving

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veridical perceptual inference, yet may be optimal in maintaining self-consistency. It is also possible that subjects employed a different mechanism in integrating evidence from a second stimulus interval into the estimation task after viewing evidence from the first interval from the mechanism applied in conditioned perception or the mechanism resulting from sensory evidence decoding. Future directions in the field may provide further insight on the matter.

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Additionally, the repulsion bias observed in Bronfman et al.’s study investigating the effects of additional evidence on a continuous estimation task is analogous to the one observed by Jazayeri & Movshon (2007). The stimuli used in their experiment were not RDKs, but rather a series of numerical stimuli. So, it is

plausible that the analytical approaches and conclusive results Bronfman et al. obtained are relevant to abstract perceptual decision-making, as well as physical visual perception tasks. If our regression results were more similar to the reportings from Bronfman et al. and we observed the repulsion bias in both clockwise and counterclockwise first-interval evidence trials, then we could conclude that the mechanism used in abstract perceptual decision-making can be translated for different types of stimuli and cognitive perception tasks, such as visual perceptual decision-making.

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Future research!

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This experiment applied a novel design — RDK stimuli containing evidence in two intervals, split by a binary choice in some trials. Here, we suggest considerations for future research directions to successfully replicate the results from Jazayeri & Movshon (2007) and Bronfman et al. (2014) in the context of this design and type of stimuli.

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One consideration for future iterations of this experiment are whether each analytic approach we used are appropriate for the metrics we aim to find in order to answer the questions at hand. For example, the mode analysis and regression rationales provided by Bronfman et al. (2014) describe the mode as an optimum metric for finding the presence or absence the repulsion bias and the regression approach for quantifying the effect of evidence presented in a second interval after choice commitment. However, the nature of the numerical integration task that Bronfman et al. used with only integers provides a discrete measure for quantifying estimate errors and mode distributions. For circular RDK-based continuous estimation tasks, the possible scale for angle reports is continuous and recorded precisely to four decimal places. Thus it may be helpful to modify the way the data is binned, or the change way the reported mean angles of motion are rounded when computing estimation errors. It is then possible that the mode analyses are appropriate for RDK-based tasks as well as numerical integration tasks, but that the regression analyses are more reliable with clearer results using discrete data from the numerical integration estimation tasks rather than

continuous data from the angular estimation tasks. This idea is further illustrated in the analysis for estimation choice accuracy, where we used mean deviations and precision as indicators of accuracy, whereas Bronfman et al. used Pearson linear correlation coefficients between the veridical mean and estimated mean. This metric provided clearer and more reliable results for the smaller range of discrete numerical values from the Bronfman et al. study than it did for our larger range of continuous angular estimation values, thus we approached this analysis differently. Many approaches still remain unexplored for optimal metrics per analysis, so future research is needed to clearly demonstrate which metrics describe possible answers to each question both appropriately and optimally.

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Further, using more stringent criteria in data selection could have yielded results in closer alignment with our hypotheses and predictions. For example, in the regression analysis, the outlier cutoff was an estimate reported +/- 50° from the reference mark. This cutoff was arbitrarily selected as 2.5 times the maximum veridical mean angle across two intervals to allow subjects to overestimate the mean angle, as we predicted they would. Excluding more trials with a stricter cutoff could have perhaps improved the regression analysis results, however, this effect could be minimal due to the robustness of the model we applied to fit the data. In future iterations of this experiment, this could be an aspect to consider when pre-processing the data in order to improve the regression metrics.

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One factor that could have affected binary choice task performance is that the motion coherence threshold was determined by a coarse discrimination task, yet the experimental tasks were based on fine

discrimination, which are thought to have differing sensory encoding and decoding mechanisms (Jazayeri & Movshon 2006). The individual threshold was determined as 80% point of a cumulative Weibull

distribution fit, which might have been too low of a value in translating the threshold determined using coarse discrimination to our particular tasks requiring fine discrimination. Perhaps thresholding with a fine

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discrimination task, increasing the determined coherence level by a specified factor, or raising this point on the cumulative Weibull distribution to 85% or 90% would increase performance across subjects, thereby improving clarity and reliability of the results.

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In this experiment, we also collected pupil dilation data, but due to time constraints, this dataset was not included in this project. Previous research has suggested that there is a phasic relationship between pupil dilation and modulatory neurotransmitter release during decisional processes (Aston-Jones & Cohen, 2005; Eldar et al., 2013; de Gee et al., 2014). Suggestions for future research would be to incorporate analyses of the pupil dilation data to supplement the behavioural results. Pupil dilation can then serve as an index for decision-related neuromodulatory release during various stages of the choice formation process. The correlation of pupil dilation with the magnitude of the commitment bias could provide insight into the role of particular neuromodulators in choice commitment and subsequent aftereffects.

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Overall, we successfully replicated some but not all of our initial predictions. We advise for future research to first repeat the experiment with the aforementioned considerations in order to successfully obtain all the results that could plausibly support the initial hypotheses and replicate the findings and ideas from Jazayeri & Movshon (2007), Stocker & Simoncelli (2008) and Bronfman et al. (2014). Drawing from successful results in both the mode analyses and regression analyses, further insight could then be provided regarding the mechanisms of the repulsion bias in two-interval continuous estimation choices.

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References!

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Aston-Jones, G., & Cohen, J. D. (2005). An integrative theory of locus coeruleus-norepinephrine function: adaptive gain and optimal performance. Annual Review of Neuroscience, 28, 403–50.

Bays, P. M., & Husain, M. (2008). Dynamic shifts of limited working memory resources in human vision. Science, 321(5890), 851-854.

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Brainard, D. H. (1997). The Psychophysics Toolbox, Spatial Vision, 10, 443-446.

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Bronfman Z.Z., Brezis, N., Donner, T., & Usher, M (2014). Decision-induced reduction in gain of additional information in perceptual and value-based decisions (in preparation).

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De Gee, J. W., Knapen, T., & Donner, T. H. (2014). Decision-related pupil dilation reflects upcoming choice and individual bias. Proceedings of the National Academy of Sciences of the United States of America, 111(5), E618–25.

Eldar, E., Cohen, J. D., & Niv, Y. (2013). The effects of neural gain on attention and learning. Nature Neuro- science, 16(8), 1146–53.

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Jazayeri, M., & Movshon, J. A. (2007). A new perceptual illusion reveals mechanisms of sensory decoding. Nature, 446(7138), 912–5.

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Shadlen, M. N., & Kiani, R. (2013). Decision making as a window on cognition. Neuron, 80(3), 791–806. Stocker, A. A., & Simoncelli, E. P. (2008). A Bayesian Model of Conditioned Perception. Advances in Neural

Information Processing Systems, 20, 1409-1416.

Thaler, L., Schütz, A. C., Goodale, M. A., & Gegenfurtner, K. R. (2013). What is the best fixation target? The effect of target shape on stability of fixational eye movements. Vision Research, 76, 31–42.

Usher, M., Tsetsos, K., Yu, E. C., & Lagnado, D. a. (2013). Dynamics of decision-making: from evidence accumulation to preference and belief. Frontiers in Psychology, 4(October), 758.

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Wichmann, F. a, & Hill, N. J. (2001). The psychometric function: II. Bootstrap-based confidence intervals and sampling. Perception & Psychophysics, 63(8), 1314–29.

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Appendix!

Table 1. List of all angle permutations used in this experiment, per classification.

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Angle Permutations (degrees)!

No-evidence Trials 0 0 Half-evidence Trials -20 0 -10 0 0 -20 0 -10 0 0 0 10 0 20 10 0 20 0 Both-evidence Trials -20 -20 -20 -10 -20 10 -10 -20 -10 -10 -10 10 -10 20 10 -20 10 -10 10 10 10 20 20 -10 20 10 20 20

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Mode analysis plots per subject ! Subject 0  Estimation error Count −40 −20 0 20 40 0 10 20 30 40 50 60

First stimulus CCW, modes: 4, 1

Choice CCW Choice CW −40 −20 0 20 40 0 10 20 30 40 50 60

First stimulus CW, modes: −11, −11

−40 −20 0 20 40 0 10 20 30 40 50 60

Pooled over stimulus identity, modes: 4, −11 P00 −40 −20 0 20 40 0 1 2 3 4 5 6 7 8 9 No Evidence, modes: −8, −11

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Subject 1

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Estimation error Count −40 −20 0 20 40 0 5 10 15

First stimulus CCW, modes: −17, 25

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20

First stimulus CW, modes: −26, 4

−40 −20 0 20 40 0 5 10 15 20 25 30

Pooled over stimulus identity, modes: −23, 4 P01 −40 −20 0 20 40 0 1 2 3 4 5 No Evidence, modes: −29, 13

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Subject 3

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Estimation error Count −40 −20 0 20 40 0 10 20 30 40 50

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20 25 30 35 40 45

−40 −20 0 20 40 0 10 20 30 40 50 60

Pooled over stimulus identity, modes: −14, 10 P03 −40 −20 0 20 40 0 1 2 3 4 5 No Evidence, modes: −11, 7

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Subject 4

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Estimation error Count −40 −20 0 20 40 0 5 10 15 20 25 30

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20 25 30 35

−40 −20 0 20 40 0 10 20 30 40 50

Pooled over stimulus identity, modes: −2, 1 P04 −40 −20 0 20 40 0 1 2 3 4 5 6 No Evidence, modes: −8, 13

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Subject 5

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Estimation error Count −40 −20 0 20 40 0 5 10 15 20 25 30 35 40

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20 25 30

−40 −20 0 20 40 0 10 20 30 40 50

Pooled over stimulus identity, modes: −5, 4 P05 −40 −20 0 20 40 0 1 2 3 4 5 6 7 8 No Evidence, modes: −14, 7

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Subject 6

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Estimation error Count −40 −20 0 20 40 0 2 4 6 8 10 12 14 16 18

Choice CCW Choice CW −40 −20 0 20 40 0 2 4 6 8 10 12 14

−40 −20 0 20 40 0 5 10 15 20

Pooled over stimulus identity, modes: −8, 16 P06 −40 −20 0 20 40 0 1 2 3 4 5 No Evidence, modes: −17, −17

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Subject 8

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Estimation error Count −40 −20 0 20 40 0 10 20 30 40 50 60

Choice CCW Choice CW −40 −20 0 20 40 0 10 20 30 40 50

−40 −20 0 20 40 0 10 20 30 40 50 60

Pooled over stimulus identity, modes: −2, −2 P08 −40 −20 0 20 40 0 1 2 3 4 5 6 7 8 9 No Evidence, modes: −2, −2

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Subject 9

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Estimation error Count −40 −20 0 20 40 0 10 20 30 40 50 60 70

Choice CCW Choice CW −40 −20 0 20 40 0 10 20 30 40 50 60 70 80

−40 −20 0 20 40 0 10 20 30 40 50 60 70 80

Pooled over stimulus identity, modes: 1, −2 P09 −40 −20 0 20 40 0 2 4 6 8 10 12 14 16 No Evidence, modes: −5, 4

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Subject 10

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Estimation error Count −40 −20 0 20 40 0 2 4 6 8 10 12 14

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20

−40 −20 0 20 40 0 5 10 15 20 25 30

Pooled over stimulus identity, modes: 4, 4 P10 −40 −20 0 20 40 0 1 2 3 4 5 No Evidence, modes: −35, −2

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Subject 11 Estimation error Count −40 −20 0 20 40 0 5 10 15 20 25

Choice CCW Choice CW −40 −20 0 20 40 0 5 10 15 20 25 30 35 40

−40 −20 0 20 40 0 10 20 30 40 50

Pooled over stimulus identity, modes: 10, 7 P11 −40 −20 0 20 40 0 1 2 3 4 5 No Evidence, modes: −5, 16