Humans actively sample evidence to support prior beliefs
- Department of Experimental Psychology, University of Oxford, United Kingdom
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, United Kingdom
- Institute of Cognitive Neuroscience, University College London, United Kingdom
- Department of Mathematics and Computer Science, Rutgers University, United States
- Centre for Business Research, Cambridge Judge Business School, University of Cambridge, United Kingdom
- Department of Economics and Woodrow Wilson School, Princeton University, United States
- Wellcome Centre for Human Neuroimaging, University College London, United Kingdom
Figures
Figure 1
Task design and participant behaviour for experiment 1.
(A) Task structure. Participants had to choose which of two dot patches contained the most dots after viewing each for 700ms (phase 1) and rate their confidence in this choice. Then participants …
Figure 2 with 1 supplement
The effect of choice on sampling behavior is mediated by confidence in experiment 1.
Participants were less likely to change their mind if they showed a strong sampling bias for their initially chosen option in the sampling phase. (A) Sampling bias in favour of the chosen option …
Figure 2—figure supplement 1
Confidence in the second choice is significantly predicted by trial difficulty (dot difference) and change of mind.
In experiment 1, it is also affected by sampling bias, such that the more time participants spent sampling the initially chosen stimulus, the more confidence they had in their second choice. Plotted …
Figure 3 with 1 supplement
Task design and participant behaviour for experiment 2.
(A) Task structure. Participants had to choose which of two dot patches contained the most dots after viewing each for 500ms (phase 1) and rate their confidence in this choice. Then participants …
Figure 3—figure supplement 1
Mean sampling time viewing the initially chosen and unchosen patch in the sampling phase in study 2 for each sampling phase length and each condition.
For the fixed condition, trials have been split into trials where the stimulus chosen in the first choice phase was shown for longer (‘chosen presented longer’), trials where the unchosen was shown …
Figure 4 with 12 supplements
The effect of choice on sampling behaviour is mediated by confidence in experiment 2.
Participants were less likely to change their mind if they showed a strong sampling bias for their initially chosen option in the sampling phase, but this was only the case in the free sampling …
Figure 4—figure supplement 1
Confidence in the first choice reduces the total amount of time spent sampling (gazing at the two stimuli) in the free sampling trials in experiment 2.
Plotted are fixed-effect coefficients from a hierarchical regression model predicting total sampling time (the total time spent gazing at the stimuli). Data points represent regression coefficients …
Figure 4—figure supplement 2
In Figure 4D, we plotted the probability of changes of mind as a function of actual gaze time by participants in the fixed viewing condition.
Even though stimulus presentation was fixed, participants could still choose to saccade back to the central fixation cross before the end of stimulus presentation. Therefore, actual gaze time is a …
Figure 4—figure supplement 3
Numerosity has no significant effect on sampling bias in a regression analysis predicting sampling bias with total numerosity (total number of dots present on a trial) included as a predictor.
Plotted are fixed-effect coefficients from hierarchical regression models predicting the sampling time (how long each patch was viewed in the sampling phase) difference between the left and right …
Figure 4—figure supplement 4
Numerosity has no significant effect on sampling bias in a regression analysis predicting sampling bias with numerosity of the chosen stimulus (dots in the chosen stimulus) included as a predictor.
Plotted are fixed-effect coefficients from hierarchical regression models predicting the sampling time (how long each patch was viewed in the sampling phase) difference between the left and right …
Figure 4—figure supplement 5
Numerosity had a small significant effect on accuracy in the first choice phase in experiment 1, such that participants made more mistakes on trials with high total numerosity (total number of dots).
This effect was not significant for the second choice phase and for neither choice phase in experiment 2. Plotted are fixed-effect coefficients from hierarchical logistic regression models …
Figure 4—figure supplement 6
Confidence was not affected by numerosity in a linear regression model.
Plotted are fixed-effect coefficients from hierarchical regression models predicting confidence ratings on the first and second choice phases. Data points represent regression coefficients for each …
Figure 4—figure supplement 7
Confidence change in experiment 1 was negatively affected by total numerosity (total number of dots), although it is a small effect.
This means confidence from the first to the second choice phase changed less on trials with higher total numerosity. Plotted are fixed-effect coefficients from hierarchical regression models …
Figure 4—figure supplement 8
A sampling bias towards the stimulus that participants would end up choosing was found in an independent dataset from a perceptual experiment presented in Sepulveda et al., 2020, and this was not affected by total numerosity ()on a trial.
In this experiment, participants performed a dot numerosity task in two frames: in the ‘most’ frame they chose the alternative with more dots, in the ‘fewest’ frame they indicated the option with …
Figure 4—figure supplement 9
Order of presentation has no significant effect on sampling bias in experiment 2.
Plotted are fixed-effect coefficients from a hierarchical regression model predicting the sampling time (how long each patch was viewed in the sampling phase) difference between the left and right …
Figure 4—figure supplement 10
Choice behaviour in Experiment 2.
(A) Initial choice (pre-sampling) (B) Final choice (post-sampling). (C) Participants were more precise in selecting the circle with more dots in the Free sampling trials, as seen from participants’ …
Figure 4—figure supplement 11
There was no significant difference in the number of changes of mind from the incorrect to the correct option (A) or in the total number of changes of mind (B) between the free and fixed sampling conditions.
Data points represent individual participants.
Figure 4—figure supplement 12
Confidence ratings experiment 2.
Each dot represents a single participant. The segmented lines connect the same participant in both conditions.
Figure 5 with 4 supplements
Gaze impacted evidence accumulation (for the 2nd choice) more strongly in the free than in the fixed sampling condition.
(A) Free and fixed sampling condition trials were fitted separately using a Gaze-weighted Linear Accumulator Model (GLAM). In this model there are two independent accumulators for each option (left …
Figure 5—figure supplement 1
GLAM results with down-sampled gaze information in the free sampling condition.
To check whether the results reported in the main text are an artefact of the low variability in relative gaze in fixed sampling trials, we reduced the variability of free sampling trials to only 3 …
Figure 5—figure supplement 2
Individual out-of-sample GLAM predictions for behavioural measures in free and fixed sampling conditions.
The correlations between observed data and predictions of the model for individual (A) mean RT, (B) the probability of choosing the correct patch, and (C) the gaze influence in choice probability …
Figure 5—figure supplement 3
GLAM model comparison for free and fixed sampling conditions.
(A) WAIC scores for free and fixed sampling models did not report significant difference in fit between the conditions (mean WAICFree = –524.58; mean WAICFixed = –531.472; t17 = 1.33, p = 0.19, ns). …
Figure 5—figure supplement 4
GLAM parameters for free and fixed sampling conditions.
Participants for which parameter estimation did not converge were removed from the analysis (7 participants). The results reported in the main text were still observed: a higher gaze bias (lower γ …
Appendix 4—figure 1
Linear scoring rule.
Appendix 5—figure 1
BIC comparison of the sampling time models for experiments 1 and 2.
Appendix 5—figure 2
BIC comparison of the change of mind models for experiments 1 and 2.
Model 3 fit the data from experiment 1 the best (BIC = 4760.8), whereas Model 5 was the best fit for the data in experiment 2 (BIC = 4251.7).
Tables
Appendix 1—table 1
Hierarchical Regression Model Predicting Sampling Time Difference, Experiment 1.
| Predictor | Coefficient | SE | t-value | DF | p-value |
|---|---|---|---|---|---|
| Intercept | –0.27 | 0.03 | –8.48 | 26.28 | < 0.0001 |
| Choice | 0.51 | 0.05 | 9.64 | 26.87 | < 0.0001 |
| Dot Difference | 0.05 | 0.004 | 13.02 | 26.80 | < 0.0001 |
| Confidence | –0.08 | 0.03 | –2.88 | 28.74 | 0.007 |
| Choice x Confidence | 0.19 | 0.04 | 5.26 | 26.59 | < 0.0001 |
Appendix 1—table 2
Hierarchical Regression Model Predicting Sampling Time Difference, Experiment 2.
| Predictor | Coefficient | SE | t-value | DF | p-value |
|---|---|---|---|---|---|
| Intercept | –0.15 | 0.06 | –2.63 | 16.94 | 0.017 |
| Choice | 0.30 | 0.10 | 2.90 | 16.75 | 0.01 |
| Dot Difference | 0.04 | 0.005 | 9.21 | 68.14 | < 0.0001 |
| Confidence | –0.09 | 0.04 | –2.43 | 18.31 | 0.03 |
| Choice x Confidence | 0.21 | 0.05 | 4.29 | 32.00 | 0.0005 |
Appendix 2—table 1
Hierarchical Logistic Regression Model Predicting Change of Mind, Experiment 1.
| Predictor | Coefficient | SE | z-value | p-value |
|---|---|---|---|---|
| Intercept | –1.18 | 0.21 | –5.65 | < 0.0001 |
| Sampling Bias | –1.24 | 0.08 | –11.0 | < 0.0001 |
| Dot Difference | –0.24 | 0.11 | –3.06 | 0.002 |
| Confidence | –0.58 | 0.06 | –10.12 | < 0.0001 |
Appendix 2—table 2
Hierarchical Logistic Regression Model Predicting Change of Mind, Experiment 2.
| Predictor | Coefficient | SE | z-value | p-value |
|---|---|---|---|---|
| Intercept | –1.05 | 0.28 | –3.76 | 0.0002 |
| Sampling Bias | –1.39 | 0.19 | –7.20 | < 0.0001 |
| Dot Difference | –0.25 | 0.10 | –2.66 | 0.008 |
| Confidence | –0.57 | 0.07 | –8.73 | < 0.0001 |
| Fixed Sampling | –0.09 | 0.14 | –0.61 | 0.54 |
| Sampling Bias x Fixed Sampling | 1.30 | 0.19 | 6.77 | < 0.0001 |
Appendix 5—table 1
Sampling Time Models.
| Models | Formula |
|---|---|
| 1 | Sampling Time Difference ~ (β0 + β1[Choice] + ε) |
| 2 | Sampling Time Difference ~(β0 + β1[Dot Difference] + ε) |
| 3 | Sampling Time Difference ~(β0 + β1[Choice] + β2[Dot Difference] + ε) |
| 4 | Sampling Time Difference ~ (β0 + β1[Choice] + β2[Confidence] + β3[Choice * Confidence] + ε) |
| 5 | Sampling Time Difference ~(β0 + β1[Choice] + β2[Dot Difference] + β3[Confidence] + β4[Choice * Confidence] + ε) |
| 6 | Sampling Time Difference ~(β0 + β1[Choice] + β2[Dot Difference] + β3[Confidence] + β4[Reaction Time] + β5[Choice * Confidence] + β6[Choice * Reaction Time] + ε) |
