We are constantly deciding what information to sample to guide future decisions. This is no easy feat, as there is a vast amount of information available in the world. In theory, an agent should look for information to maximally reduce their uncertainty (Schulz and Gershman, 2019; Schwartenbeck et al., 2019; Yang et al., 2016 ). There is some evidence that this is indeed what humans do (Kobayashi and Hsu, 2019; Meyer and Shi, 1995; Steyvers et al., 2009; Wilson et al., 2014), but a range of other drivers of information search have been identified that make us deviate from the sampling behaviour of optimal agents (Eliaz and Schotter, 2007; Gesiarz et al., 2019; Hunt et al., 2016; Kobayashi et al., 2019; Rodriguez Cabrero et al., 2019; Sharot, 2011; van Lieshout et al., 2018; Wang and Hayden, 2019).

Confirmation bias is defined as the tendency of agents to seek out or overweight evidence that aligns with their beliefs while avoiding or underweighting evidence that contradicts them (Hart et al., 2009; Lord et al., 1979; Nickerson, 1998; Stroud, 2007; Wason, 1960; Wason, 1968). This effect has often been described in the context of what media people choose to consume (Bakshy et al., 2015; Bennett and Iyengar, 2008; Pariser, 2012). Recently, cognitive scientists have realised confirmation bias may not be restricted to this domain and may reveal a fundamental property of the way in which the brain drives information search. As such, researchers have started to investigate confirmation bias in simple perceptual and value-based choice tasks. For example, sensitivity to new information has been shown to decrease after choice (Bronfman et al., 2015), while Talluri et al., 2018 have shown that sensitivity to a stimulus is increased when it is consistent with the stimulus presented before. Furthermore, in Palminteri et al., 2017a learning rates were found to be higher for feedback indicating positive obtained outcomes as well as for negative forgone outcomes. This effect has been replicated in recent studies that suggest confirmation bias during learning might be adaptive in some contexts (Tarantola et al., 2021; Lefebvre et al., 2020; Salem-Garica et al., 2021).

Most of the existing research on perceptual decision-making has focused on the weighting of incoming information during evidence accumulation or belief updating. Other findings suggest that agents also actively search for confirmatory evidence (Hunt et al., 2016; Hunt et al., 2018; Tolcott et al., 1989; Wason, 1968), but none of these experiments investigated the effect of biased information sampling in simple, perceptual choice. As most paradigms currently used to study confirmation bias do not explicitly focus on active information sampling performed by the agent, therefore it is unclear whether confirmation bias arises from evidence underweighting, biased information sampling, or both.

Another important aspect of confirmation bias is how it modulates and is modulated by decision confidence. Confidence is known to play an important role in guiding decisions (Bogacz et al., 2010; Boldt et al., 2019; Folke et al., 2016; Rabbitt, 1966; Yeung and Summerfield, 2012). It is therefore likely it may also guide the information search preceding choice (Desender et al., 2019). In fact, Rollwage et al., 2020 recently showed that confidence indeed affects a neural signal of confirmatory evidence integration. By definition, the higher confidence is in a choice, the stronger the decision-maker’s belief is in the correctness of this choice (Fleming and Lau, 2014; Pouget et al., 2016). Accordingly, we predict that confirmation bias in information sampling will be stronger after choices made with high confidence.

We used two perceptual binary forced choice tasks with two choice phases separated by a free sampling phase to test our hypotheses that confirmation bias arises from biased information sampling, that this effect influences future choice and that confidence mediates this behavioural tendency.

Here, we present the results of two independent experiments we conducted to test our hypotheses.

Experiment 1

Participants performed a perceptual two-alternative forced choice (2AFC) task (Figure 1A), in which they were briefly presented with patches containing multiple dots. Participants were asked to judge which patch contained the most dots. After their initial choice (phase 1), they rated their confidence that they were correct. Subsequently, in the second phase of the trial (phase 2) participants could freely sample (i.e., see) each dot patch using key presses to switch between them as frequently as they liked for 4000ms. Participants could only view one patch at a time. They were then prompted to make a second choice (phase 3), in which they could either confirm their initial choice or change their mind. After this second decision, they again reported their degree of confidence.

Figure 1

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As expected, participants’ performance was highly sensitive to the amount of perceptual evidence presented in a given trial (i.e. the difference in the amount of dots in the left and right patches; Figure 1B). Participants were also more accurate in the second choice compared to the first choice, showing that they used the additional sampling time between choice phases to accumulate additional perceptual evidence that allowed them to increase accuracy on the second choice (t₂₇ = 8.74, p < 0.001).

Our main hypothesis was that participants would prefer to gather perceptual information that was likely to confirm their initial decision. Conversely, we expected them to be less likely to acquire evidence that would disconfirm it. To perform well on this task, an agent would have to attend equally to the two patches, as the goal requires computing the difference in dots between the two patches. Therefore, any imbalance in sampling time would not necessarily be beneficial to completing the task. However, we expected that in the free sampling phase (phase 2) of the trial participants would spend more time viewing their chosen patch. In line with this hypothesis, during the sampling phase, participants spent more time viewing the patch they chose in the first decision phase relative to the unchosen alternative (Figure 1C; t₂₇ = 7.28, p < 0.001).

Confidence in a choice reflects the strength of the participant’s belief that their choice was correct. Consequently, we hypothesised that participants’ preference for gathering confirmatory evidence for a given choice would be modulated by their confidence in that choice. As such, we expected choices made with higher confidence would lead to a stronger sampling bias favouring the chosen patch over the unchosen patch. In a hierarchical regression predicting sampling time difference between the chosen and unchosen stimulus, we found a significant interaction between choice and confidence, such that the higher the degree of confidence was in the first choice, the more sampling was biased in favour of that choice (Figure 2; t_26.96=5.26, p < 0.001; see Appendix 1). Besides this, sampling time difference in turn affected confidence in the second choice, such that the stronger sampling bias was towards the initially chosen stimulus, the higher confidence in the second choice if that same stimulus was chosen again (Figure 2—figure supplement 1; t_26.01=9.40, p < 0.001). Change of mind was a significant negative predictor of the second confidence rating (Figure 2—figure supplement 1; t_23.66=-10.41, p < 0.001). Also, a negative interaction effect between sampling time difference and change of mind on the second confidence rating was observed, meaning that the effect of sampling bias on confidence was reversed in trials where participants changed their mind (Figure 2—figure supplement 1; t_24.48=-10.21, p < 0.001).

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We also saw a significant main positive effect of choice on sampling time difference, such that a chosen stimulus was likely to be sampled for longer during the sampling phase (Figure 2B; t_26.96=9.64, p < 0.001) as shown in the previous section. There was also a significant main positive effect of evidence difference on sampling time difference, whereby the correct stimulus (containing the most dots) was sampled for longer (Figure 2B; t_26.96=13.02, p < 0.001).

Our choices are determined by the evidence we have gathered before making a decision. Therefore, we expected that biased sampling in the free sampling phase (phase 2) would impact decisions in the second decision phase (phase 3). Specifically, we hypothesised that the more strongly participants preferred sampling their chosen patch, the more likely they were to choose it again. Using a multinomial hierarchical logistic regression, we found that bias in sampling time towards the previously chosen option was indeed predictive of future choice. In other words, the more participants sampled a previously chosen option, the more likely they were to choose it again (Figure 2C; z = −11.0, p < 0.001; see Appendix 2). Furthermore, evidence difference and confidence were significantly negatively related to subsequent changes of mind, whereby participants were less likely to change their mind if their initial choice was correct and if it was made with high confidence (Figure 2C; main effect of evidence difference – z = −3.06, p < 0.01, main effect of confidence – z = −10.12, p < 0.001).

Experiment 2

While the results from the first experiment showed an effect of biased sampling on subsequent choice, it was not clear whether this effect arises from biased evidence accumulation caused by differential exposure to the perceptual evidence, or if the sampling choices themselves drive the effect. In other words, would the same choice bias appear if participants were passive recipients of biased sampling, or does the choice bias require that participants make their own sampling decisions?

We addressed this question in a follow-up eye-tracking study (Figure 3A) in which we introduced a control task, a ‘fixed-viewing condition’, in which participants did the same task, but did not have the possibility to freely sample the patches in phase 2. Instead, the dot patches were shown for a set amount of time. In one-third of trials, the patches were shown an equal amount of time; in two-thirds of trials, one patch was shown three times longer than the other. Each participant completed two sessions, one session involved free sampling, similar to Experiment 1. The other involved a fixed-viewing control task. Session order was pseudo-randomized between participants. Furthermore, presentation of the visual stimuli and all the participants’ responses were gaze-contingent. This meant that during the sampling phase (phase 2), the dot patches were only presented when participants fixated inside the patch. Furthermore, we hypothesised that sampling bias might be stronger when more time to sample is available. Specifically, we expected that participants might become more biased in their sampling throughout the sampling phase as they gradually become more confident in their belief. Therefore, we manipulated the length of phase 2 to be either 3000ms, 5000ms, or 7000ms. Again, participants were sensitive to the difficulty of the given trials (Figure 3B) and were more accurate on the second choice compared to the first choice (t₁₇ = 6.80, p < 0.001).

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We also replicated our main result in the free sampling condition showing that participants spent more time viewing the patch they just chose (Figure 3C; t₁₇ = 3.52, p < 0.01). Furthermore, the size of this sampling time bias was proportional to the total amount of sampling time available in study 2 (Figure 3—figure supplement 1), suggesting that there was no particular period of time within the sampling phase where confirmatory information sampling was more likely contrary to our expectation.

This new experiment also replicated the mediating effect of confidence on how sampling bias affects subsequent choice. We again found a significant interaction between choice and confidence (Figure 4A–B; t_16.97=4.29, p < 0.001; see supplemental materials Appendix 1) and replicated the main positive effects of choice and evidence difference on sampling time difference between the chosen and unchosen stimulus (Figure 4B; main effect of choice: t_16.97=2.90, p < 0.01; main effect of evidence difference: t_16.97=9.21, p < 0.001). Confidence was also shown to negatively predict the total amount of time spent sampling, that is, the total time actually spent gazing at the two stimuli during the sampling phase (rather than the central fixation cross; Figure 4—figure supplement 1; t_22.99=-4.01, p < 0.001). Change of mind also negatively predicted confidence in the second choice phase (Figure 2—figure supplement 1; t_16.59=-6.39, p < 0.001), but in contrast to experiment 1 there was no effect of sampling time difference on the second confidence rating (t_161.30=-0.78, p = 0.44).

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Similarly, we replicated the negative effect of sampling bias on subsequent change of mind (Figure 4C; z = −7.20, p < 0.001; see Appendix 2) as well as the main negative effects of evidence difference and confidence on change of mind (Figure 4C; main effect of evidence difference: z = −2.66, p < 0.01; main effect of confidence: z = −8.73, p < 0.001).

It has been shown that the uncertainty around an internal estimate scales with numerosity (Scott et al., 2015). As such, an alternative explanation for the sampling biases found in both experiments might be that participants were minimizing uncertainty by sampling the option with more dots (the correct choice alternative) for longer. To rule out this possibility, we performed some of the regressions presented earlier in the Results section including numerosity (the total number of dots present on the screen) as a predictor (see Figure 4—figure supplements 3–8). We found that neither total numerosity (experiment 1: t_12.71=-1.77, p = 0.10; experiment 2: t_25.07=0.62, p = 0.54) or the number of dots of the chosen option (experiment 1: t_71.10=-1.82, p = 0.07; experiment 2: t_87.40=0.25, p = 0.81) had a significant effect on sampling bias, meaning that participants’ sampling was not biased by a drive to reduce uncertainty by sampling the option with more dots. Furthermore, we reanalysed data from a previous perceptual decision study (Sepulveda et al., 2020) where participants also had to choose between two circle stimuli with dots (but were not requested to resample the stimuli and choose for a second time). In this study, on some trials participants had to choose the option with the most dots (the ‘most’ frame), and on other trials the option with the least dots (the ‘fewest’ frame). In this dataset, we found a significant effect of choice on sampling time difference in both frames (‘most’ frame: t_57.54=24.01, p < 0.001; ‘fewest’ frame: t_33.72=14.97, p < 0.001; Figure 4—figure supplement 8) and no significant effect of the total number of dots on sampling time difference (‘most’ frame: t_31.41=-0.37, p = 0.72; ‘fewest’ frame: t_40.01=1.49, p = 0.14), meaning that participants’ sampling was not biased by numerosity. Overall, these results seem to indicate that numerosity is not significantly affecting the sampling process in this task.

The sequential order of presentation in the initial sampling phase before the first choice might also be expected to affect sampling. To exclude this possibility, we performed a regression analysis predicting sampling time difference as a function of presentation order in experiment 2 and found no effect (Figure 4—figure supplement 9; t_49.65=0.08, p = 0.93). It is also important to note that the stimulus chosen in the first choice phase was highlighted throughout the trial. This was done to reduce the likelihood of working memory being a confound on this task, but we recognise the possibility that it may have interacted with the main effect of choice on sampling.

Once we confirmed all the main findings from the first experiment using this new setup, we were able to test our main hypothesis: does the effect of sampling bias on choice we identified require the participant to actively choose which information to sample? In other words, is the effect of confirmation bias on subsequent choice present when confirmatory evidence is passively presented to participants or does it require that confirmatory evidence is actively sought by the decision-maker? In the first case, we would expect to see the same effect in the fixed-viewing condition (in which asymmetric information is provided by the experimenter) as in the free-sampling condition. In the second case, we would expect that the effect of biased information sampling on the subsequent choice disappears in the fixed-viewing condition.

In line with the second prediction, we found that in the fixed-viewing condition, contrary to the free-sampling condition in this experiment and in the first experiment, the amount of time spent viewing the patches in the sampling phase did not significantly affect subsequent choice. In a multinomial hierarchical logistic regression predicting change of mind from the first choice phase to the second choice phase within a given trial, the main effect of sampling bias on change of mind was completely offset by the positive effect of the interaction term between sampling bias and a dummy variable that was set to 1 if a trial was in the fixed-viewing condition (Figure 4C–D; z = 6.77, p < 0.001; see Appendix 2). This means that there was no effect of sampling bias on change of mind in the fixed-viewing condition. To check that participants were engaging in this version of the task, we looked whether the number of saccades made within each patch during the sampling phase was similar between the two tasks. We found that the number of saccades was actually higher in the fixed-viewing condition than in the main experiment (t₁₇ = −4.22, p < 0.001), which means participants were indeed exploring the information in this condition. Furthermore, no significant difference in accuracy was observed between the two conditions (t₁₇ = 1.51, p = 0.14), though sensitivity to decision evidence was slightly higher in the second choice in the free sampling condition compared to the fixed sampling condition. The number of changes of mind was also equal between the two conditions (t₁₇ = 0.75, p = 0.47) as well as both confidence ratings (confidence in first choice: t₁₇ = −1.38, p = 0.19; confidence in second choice: t₁₇ = 0.5, p = 0.62; for more details see Figure 4—figure supplements 10–12).

To further investigate how attention, when freely allocated, shapes the accumulation of evidence and choice bias, we modelled the data from both viewing conditions using the Gaze-weighted Linear Accumulator Model (GLAM; Molter et al., 2019; Sepulveda et al., 2020; Thomas et al., 2019). GLAM belongs to the family of race models with an additional modulation by visual attention (Figure 5A). It is an approximation of a widely used class of models – the attentional Drift Diffusion Model (aDDM; Krajbich et al., 2010; Krajbich and Rangel, 2011) in which the full dynamic sequence of fixations is replaced by the percentage of time spent fixating the choice alternatives. Even-numbered trials were used to fit the model while odd-numbered trials were used to test it. See the Materials and methods section for further details.

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GLAM is defined by four free parameters: ν (drift term), γ (gaze bias), τ (evidence scaling), and σ (normally distributed noise standard deviation). The model correctly captured the reaction times (RT) and choice behaviour of the participants at group-level both in the free-sampling (Figure 5B) and fixed-viewing conditions (Figure 5C). More specifically, we found that the model predicted faster RTs when trial difficulty was low (|ΔDots| is high; Figure 5B–C, top left). The model also reproduced overall choice behaviour as a function of the number of dots in the patches (ΔDots = Dots_Left – Dots_Right) in both conditions (Figure 5B–C, top right). Furthermore, we found gaze allocation (ΔGaze = g_Left – g_Right) predicted the probability of choosing the correct patch in the free-sampling condition (Figure 5C, bottom left). However, to properly test how predictive gaze allocation is of choice, we must account for the effect of evidence (ΔDots) on choice. As such, we used the gaze influence (GI) measure (Thomas et al., 2019), which reflects the effect of gaze on choice after accounting for the effect of evidence on choice. GI is calculated taking the actual choice (0 or 1 for right or left choice, respectively) and subtracting the probability of choosing the left item as predicted by a logistic regression with ΔDots as a predictor estimated from behaviour. The averaged residual choice probability reflects GI. We found GI estimated purely from participant’s behaviour was higher in the free-sampling than in the fixed-viewing condition (comparing average GI by participant, free-sampling condition: Mean = 0.148, SD = 0.169; fixed-viewing condition: Mean = 0.016, SD = 0.14; t₁₇ = 2.708, p < 0.05). This suggests the effect of visual attention on choice was higher in the free-sampling condition. In line with this, the model also predicted a higher GI on corrected choice probability in the free-sampling condition (comparing average GI by individual model predictions, free-sampling condition: Mean = 0.112, SD = 0.106; fixed-viewing condition: Mean = 0.033, SD = 0.028; t₁₇ = 2.853, p < 0.05; Figure 5B–C, bottom right).

We then tested whether attention affected information integration more when information was actively sought (i.e. the free-sampling condition) compared to when information was given to the participants (i.e. the fixed-viewing condition). We compared the parameters obtained from the individual fit in the free-sampling and fixed-viewing conditions (Figure 5D). We found a significant variation in the gaze bias parameter (Mean γ _Free = 0.81, Mean γ _Fixed = 0.98, t₁₇ = –3.934; p < 0.01), indicating a higher influence of gaze on choice in the free-sampling condition. Note that during the fixed-viewing condition, the parameter γ ≈ 1 indicates that almost no gaze bias was present on those trials. Conversely, there was no significant difference for the other parameters between the conditions (Mean τ_Free = 1.44, τ_Fixed=1.13, t₁₇ = 1.003; p = 0.32, n.s.; Mean σ_Free = 0.0077, Mean σ_Fixed=0.0076, t₁₇ = 0.140; p = 0.89, n.s.; ν_Free=8.07x10^–5, ν_Fixed=8.70x10^–5, t₁₇ = −1.201; p = 0.24, n.s.). These results suggest that gathering information actively (i.e. free-sampling condition) does not affect the overall speed at which information is integrated, but it specifically modulates the likelihood of choosing the gazed-at option. Finally, to test that the identified effect did not depend on a less variable gaze time range we resampled the data from the free-sampling condition to match the gaze time range in the fixed-viewing condition, and fitted the GLAM again. We replicated our finding even when the gaze time range in the free-sampling condition was reduced to match that in the fixed-viewing condition (Figure 5—figure supplement 1). For more in-depth analyses including model comparisons please see Figure 5—figure supplements 1–4.

Finally, we explored the idea that a sampling bias could arise from the use of previous choice as evidence in its own right, in addition to previously acquired information. Formalizing this idea, we developed an economic model that makes behavioural predictions aligned with our findings (see Appendix 3). In this model, after the first choice, the prior that feeds into the subsequent active sampling phase is not the belief after the first sampling phase, but rather it is a convex combination of this with the belief that the individuals would hold if they only knew of the previous choice. Subsequent active sampling then varies as a strictly increasing function of this prior. As a result, a sampling bias in favour of the initially chosen option arises, and this bias varies as a function of confidence in the initial choice, as seen in our data. This economic model provides a formal description of the behaviour we observed. At the same time, it suggests that seeking for confirmatory evidence might not arise from a simple low-level heuristic, but is rooted in the way information is acquired and processed (for more details, see Appendix 3).

In this work, we have demonstrated that a form of confirmation bias exists in active information sampling, and not just in information weighting as previously shown. Using two novel experiments we showed that this effect is robust for simple perceptual choice. Critically we show that this sampling bias affects future choice. Furthermore, we demonstrated that this effect is only present in the free-sampling condition, showing that agency is essential for biased sampling to have an effect on subsequent choice.

Preference for confirmatory evidence has previously mostly been studied in the context of strongly held political, religious or lifestyle beliefs, and not in perceptual decision-making (Bakshy et al., 2015; Hart et al., 2009; Lord et al., 1979; Nickerson, 1998; Stroud, 2007; Wason, 1960, Wason, 1968). Our results, together with the recent work of others (Talluri et al., 2018; Palminteri et al., 2017b; Lefebvre et al., 2020), show that confirmation bias in information search is present even in decisions where the beliefs formed by participants are not meaningful to their daily lives. This suggests that confirmation bias might be a fundamental property of information sampling, existing irrespective of how important the belief is to the agent.

Recent findings suggest that biases in information sampling might arise from Pavlovian approach, a behavioural strategy that favours approaching choice alternatives associated with reward (Hunt et al., 2016; Rutledge et al., 2015). Furthermore, the number of hypotheses an individual can consider in parallel is likely to be limited (Tweney et al., 1980). As such, it may be advantageous to first attempt to rule out the dominant hypothesis before going on to sample from alternative options. In this vein, the sampling bias we see could be the solution to an exploit-explore dilemma in which the decision-maker must decide when to stop ‘exploiting’ a particular hypothesis (on which stimulus has the most dots) and instead ‘explore’ different ones.

A key novel feature of this task is that participants were able to freely sample information between choice phases, providing a direct read-out of confirmation bias in the active sampling decisions made by the participants. Previous accounts of confirmation bias in perceptual choice have instead focused on altered weighting of passively viewed information as a function of previous choice (Bronfman et al., 2015; Rollwage et al., 2020; Talluri et al., 2018). However, from these findings, it remained unclear to what extent this bias manifests in the processing of information compared to active sampling of information. Our findings show that active information sampling plays a key role in the amplification of beliefs from one decision to the next, and that changes in evidence weighting likely only account for part of observed confirmation bias effects.

We exclude some alternative explanations for our main findings. Firstly, it could have been possible for participants’ biased sampling to have been driven by a need to reduce uncertainty determined by numerosity (Scott et al., 2015). It is unlikely that this was the case in this task, as neither total numerosity or numerosity of the chosen option significantly predicted sampling bias. Another possibility is that sampling bias is simply a measure of internal confidence, whereby sampling bias towards the initially chosen stimulus reflects the likelihood of it being chosen again. However, if this were the case a strong relationship between sampling bias and confidence in the second choice would be expected. We only see such a relationship in the first experiment, but not in the second experiment. This suggests sampling bias on this task cannot be fully attributed to an expression of endogenous confidence.

We show that confidence modulated the confirmation bias effect, such that choices made with higher confidence, led to increased sampling of the chosen option and an increased likelihood of choosing the same option again in the second choice phase. This shows that the strength with which a belief is held determines the size of the confirmation bias in active information sampling. Confidence has previously been shown to affect the integration of confirmatory evidence as reflected in MEG recordings of brain activity during evidence accumulation (Rollwage et al., 2020). Furthermore, recent work in economics and neuroscience have given theoretical and experimental proof of a relationship between overconfidence, and extreme political beliefs (Ortoleva and Snowberg, 2015; Rollwage et al., 2018). Our results suggest altered information sampling could be the missing link between these two phenomena. Specifically, given that we have shown that increased confidence leads to increased confirmation bias, it follows that overconfidence in a belief would lead to increased sampling of confirmatory evidence in line with that belief, which in turn would lead to even higher confidence.

We also show that it is not sufficient that agents freely make a choice for that choice to bias future decisions. When participants were presented with their chosen option for longer in a fixed sampling condition, this did not affect subsequent choice as it did in the free sampling condition, where a sampling bias in favour of the chosen option made changes of mind less likely. This suggests that integration of evidence into beliefs is dependent on whether the agent has actively chosen to sample this information. In other words, a sense of agency appears to impact the extent to which new information influences future choice (Hassall et al., 2019; Chambon et al., 2020; Doll et al., 2011; Cockburn et al., 2014), and making a choice may not necessarily lead to confirmation bias if it is not followed by active decisions to sample evidence in line with that choice. Our results are in line with Chambon et al., 2020, in which confirmation bias in learning rates was only present when participants were able to freely choose between stimuli and not when these choices were fixed by the experimenter. In their task, though, choice and information gain were not separated by design, meaning information sampling was only possible from outcome feedback after a choice was made. Our results expand on these findings, by showing that choice commitment also affects subsequent decisions to sample, and that the resulting biased sampling influences future choices. This means that active information sampling is likely to play a central role in the propagation of confirmation bias across decisions, as seen in our descriptive economic model (see Appendix 3). It is less clear, however, to what extent the ability to freely sample and any resulting confirmation bias might be beneficial or detrimental to choice accuracy, as in our task there was no clear difference in accuracy between the free and fixed sampling conditions.

Additionally, the results from the GLAM model show that, in line with previous studies (Krajbich et al., 2010; Krajbich et al., 2010; Sepulveda et al., 2020; Tavares et al., 2017; Thomas et al., 2019), a specific boost in the accumulation of evidence of the visually attended items was found in the free sampling condition. Conversely, a disconnection between an item’s sampling time and evidence accumulation was found in the fixed condition (i.e. the absence of gaze bias in GLAM implies that visual fixations did not affect evidence integration when the sampling was not controlled by the decision-maker). One explanation for this result is that attentional allocation itself is directed towards the options that the participants reckon more relevant for the task to be performed (Sepulveda et al., 2020). In our experiment, the goal of the task was theoretically identical for the first and second choice (i.e. to find the patch with more dots). However, in agreement with the ideas of our descriptive economic model, it could be that participants perceived the goal of the second choice to be slightly different from the goal of the first: in the second case they had to verify whether their initial choice was correct, as well as finding the patch with the most dots. This immediately bestowed the chosen option with higher relevance and then more attention (consequently boosting evidence accumulation). On the other hand, since in the fixed sampling condition participant’s attention allocation is not necessarily associated with their goals, the difference in display time of the items is ignored or cannot be consistently integrated in their decision process. A complementary perspective has been given in recent work by Jang et al., 2021 and Callaway et al., 2021. Their models characterize attention’s role as lowering the variance of the accumulated evidence towards the attended option, which in turn updates the internal belief. Crucially, they have characterized attention as an internally generated factor that is allocated following optimal sampling policies, unlike other models that take attention as an exogenous factor (Krajbich et al., 2010; Krajbich et al., 2010; Thomas et al., 2019). Perhaps, in a similar way to the proposition above in relation to internal goals, it could be the case that the exogenous sampling pattern we imposed in our experiment is not aligned with the optimal evolution of the internal beliefs of participants, therefore, the ‘offered’ evidence is misaligned and therefore does not impact choice. Further modelling work testing Jang and Callaway proposals in regimes where attention is exogenously controlled can give insight on the relevance of attentional agency. An alternative hypothesis is that gaze allocation itself is used as additional evidence in favour of a choice alternative in a way similar to previous choice as in our descriptive model (see Appendix 3). This would mean that when an agent has previously attended to a choice alternative, this is used as evidence in favour of that option in and of itself. Therefore, when gaze allocation is not under the agent’s control, as in the fixed-viewing condition, it is not used to inform choice.

Our findings imply that agency plays a clear role in evidence accumulation, and consequently in confirmation bias. It also suggests that common experimental designs in which information is provided by the experimenter and passively sampled by the participant might not be an ecological way to study decision-making. These tasks mask the potentially large effect of active information search on belief formation and choice. Pennycook et al., 2021 recently showed that people were less likely to share false information online if they had been asked to rate the accuracy of a headline just previously. It may therefore be possible to reduce confirmation bias in information search in a similar way by priming participants to attend more to accuracy instead of confirmatory evidence. More complex behavioural tasks are required to improve our understanding of the different drivers of information sampling and how sampling in turn guides future choice (Gottlieb and Oudeyer, 2018).

To summarise our findings, we observed that participants sampled more information from chosen options in a perceptual choice paradigm and that this sampling bias predicted subsequent choice. Asymmetric sampling in favour of the chosen alternative was stronger the higher participants’ confidence in this choice. Furthermore, the effect of information on subsequent choice was only seen in a version of the task where participants could sample freely, suggesting agency plays an important role in the propagation of strongly held beliefs over time. These findings suggest that confirmatory information processing might stem from a general information sampling strategy used to seek information to strengthen prior beliefs rather than from altered weighting during evidence accumulation only, and that active sampling is essential to this effect. Biased sampling may cause a continuous cycle of belief reinforcement that can be hard to break. Improving our understanding of this phenomenon can help us better explain the roots of extreme political, religious and scientific beliefs in our society.

All data is available on the lab GitHub page (https://github.com/BDMLab).

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Author details

1. Paula Kaanders

   1. Department of Experimental Psychology, University of Oxford, Oxford, United Kingdom
   2. Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, United Kingdom

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing - original draft, Writing - review and editing

   For correspondence

   paula.kaanders@psy.ox.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5068-1946

2. Pradyumna Sepulveda

   Institute of Cognitive Neuroscience, University College London, London, United Kingdom

   Contribution

   Formal analysis, Methodology, Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0159-6777

3. Tomas Folke

   1. Department of Mathematics and Computer Science, Rutgers University, Newark, United States
   2. Centre for Business Research, Cambridge Judge Business School, University of Cambridge, Cambridge, United Kingdom

   Contribution

   Formal analysis, Software, Writing - review and editing

   Competing interests

   No competing interests declared

4. Pietro Ortoleva

   Department of Economics and Woodrow Wilson School, Princeton University, Princeton, United States

   Contribution

   Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5943-6621

5. Benedetto De Martino

   1. Institute of Cognitive Neuroscience, University College London, London, United Kingdom
   2. Wellcome Centre for Human Neuroimaging, University College London, London, United Kingdom

   Contribution

   Conceptualization, Funding acquisition, Methodology, Resources, Supervision, Writing - review and editing

   For correspondence

   benedettodemartino@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3555-2732

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