Stimulus reliability automatically biases temporal integration of discrete perceptual targets yielding suboptimal decisions

Decision making is a ubiquitous cognitive process that determines choice behaviour. In recent years there has been increased interest in how information about multiple discrete sensory events are combined in support of single, integrated decisions. Previous studies have shown that integrative decision-making is biased in favour of more reliable stimuli. As reliability-weighted integration typically mimics statistically optimal integration, it remains unclear whether reliability biases are automatic or strategic. To dissociate reliability-weighting and optimal decisions, we developed a task that required participants to monitor two successive epochs containing brief, suprathreshold coherent motion signals which varied in their reliability. Rather than judging the individual target motion directions, however, participants had to reproduce the average motion direction of the two targets. Using mixture distribution modelling and linear regression to model behavioural data, we found robust biases in favour of the more reliable stimulus, despite the fact that unbiased responses were optimal in our paradigm. Using population-tuning modelling to characterise feature specific brain activity recorded using electroencephalography, we observed robust and sustained feature-specific responses to target signals in both epochs. Using the same method, we were able to capture the temporal dynamics of integrated decision-making by characterising tuning to the average motion direction. Critically, the tuning profiles to the average motion direction exhibited biases in favour of the more reliable signal, in keeping with the modelled behavioural responses. Taken together, our findings reveal that temporal integration of discrete sensory events is automatically and suboptimally weighted according to stimulus reliability.


Introduction
Decision-making is a ubiquitous cognitive process involved in any form of choice behaviour, from choosing to cross a busy street to choosing a life partner. Sequential-sampling evidenceaccumulation models have had great success in modelling both choice behaviour and the neural correlates of decision-making, from single cell firing to the activity of large neuronal populations (1)(2)(3)(4)(5)(6). According to these models, evidence in support of one or more choices accumulates in time toward a decision criterion, and the decision is made once the accumulated value reaches a criterion threshold. This architecture can account for response-time distributions of correct and error responses in a variety of behavioural tasks, from simple detection of sensory events to memory retrieval (7)(8)(9). Importantly, the neural activity recorded in both humans (10)(11)(12) and in animal models (13)(14)(15) closely mimics the time-course of the hypothetical decision variable, thereby lending neurobiological support to the idea that the brain accumulates evidence toward a decision threshold.
In recent years there has been increased interest in the cognitive and neural mechanisms underpinning more complex decision making (15)(16)(17)(18)(19). One pertinent issue is how multiple sources of evidence might be combined in support of a single decision. For example, to safely cross a busy street, one should consider the traffic coming from both sides of the road. This decision presumably engages at least two evidence-accumulation processes, each of which should converge on the same decision, namely, whether to cross or to wait. While much has been learned about decision making in relation to single stimuli -in our example, monitoring cars on just one side of the street -little is known about how the brain integrates two (or more) distinct sources of evidence into one decision.
Here we characterised the cognitive and neural mechanisms underpinning such 'integrative' decision-making.
To investigate integrative decision-making, most studies to date have used a variant of the 'redundant signals' paradigm (17,18,(20)(21)(22) in which a stream of multisensory stimuli -typically auditory and visual pulses -are concurrently presented and observers have to discriminate whether the number of pulses in either stream is lower or higher than an arbitrary criterion. The pulse counts in the two streams vary independently, so that, at the end of trial, the streams can either support the same decision (i.e., congruent trials), or different decisions. Importantly, the streams are temporally jittered so that they cannot be integrated into a single multisensory event at the level of initial sensory encoding. Instead, each stream should engage a separate evidence accumulator and yield two decisions that are integrated at later stages of the processing hierarchy. Following this rationale, a comparison between single-signal trials (unimodal) and redundant-signals trials (multimodal) can reveal mechanisms of integrative decision-making. Typically, participants are more accurate in congruent multimodal than in unimodal trials suggesting that the two decisions are indeed integrated at some stage. Critically, the higher accuracy in multimodal trials scales with stimulus reliability of the individual streams, suggesting that the integration process is biased in favour of the more reliable sensory stream. In fact, biases in integrative decision-making closely resemble statistically optimal signal integration (23,24) in which the contributions of individual signals are weighted by their reliability so as to yield statistically optimal decisions.
While previous research has demonstrated that integrative decision-making is subject to biases based on factors such as stimulus reliability, it remains unclear whether these biases are automatic or strategic. One ubiquitous finding in the literature on integrative decision-making is that some observers do not integrate decisions at all, but rather rely exclusively on signals of higher reliability (17,18,20,22). This finding suggests that integrating decisions may be subject to higher order influences such as a trade-off analysis of increased accuracy at the expense of increased effort.
It is important to note that the redundant signals paradigm, in which deciding on the basis of a single stream already affords accurate decisions, is especially vulnerable to such higher order effects.
While characterising higher order biases is an important open issue (25), it remains unclear whether integrating several discrete decisions automatically favours sources of higher reliability in tasks where the integration is essential, rather than opportunistic.
To address this important issue, we developed a task which required explicit integration of two simple visual decisions on brief periods of coherent motion in successive stimulus displays (Fig.   1a). On every trial, we presented two epochs of coherently moving dots separated by 1 s of randomly moving dots. At the end of the trial the task was to reproduce the direction of the average target motion. To illustrate, if a trial contained successive motion directions toward 10 o'clock and 2 o'clock, participants should indicate an average motion direction of 12 o'clock. Participants made their decisions without time constraints by adjusting the orientation of a response dial. To manipulate stimulus reliability, motion coherence in the first and second epoch could either be low (40% of coherently moving dots) or high (80%). Critically, as we explain below, these motion coherence values were deliberately chosen to be well above normal motion coherence thresholds.
Target reliability across the two epochs of each trial was factorially combined so that different combinations (low/low, low/high, high/low, and high/high) were presented equally often and in a random order. The main goal was to characterise the effects of stimulus reliability on cognitive and neural mechanisms of integrative decision-making.
To adjudicate between automatic versus strategic reliability-weighted biases in integrative decision-making, it is important to demonstrate that unbiased integration is, in principle, the optimal strategy. If a motion direction is particularly difficult to discern at low coherence and very easy at high coherence, for example, then unbiased averaging of a very noisy and a very precise representation would yield relatively poor performance. In other words, the specific combination of low and high coherences will determine the optimality of unbiased integration. For this reason, we used motion coherence levels that were well above threshold (40% and 80%) as opposed to threshold-level stimuli, which are typically around 6-7% for most observers (26). The suprathreshold coherence levels we used should afford the best possible motion discrimination for both low and high coherence signals, thus permitting unbiased source integration. Any bias in favour of signals of higher reliability would strongly suggest that reliability-weighted integration of discrete decisions is automatic. To ensure that different coherence levels afforded similar response precision, in Experiment 1 we compared error magnitudes for reproducing single motion directions of low and high coherence.
In contrast to commonly used forced-choice paradigms (1,2,4), which are optimised for characterising the temporal dynamics of decision-making, the reproduction task provided us with a continuous, feature-specific read-out of integrated decisions. In that sense, our paradigm is complementary to forced-choice paradigms; by measuring the difference between the expected and the reproduced average-motion direction on each trial, we could use mixture distribution modelling (27,28) and linear regression (16,29,30) to characterise behavioural biases in integrative decisionmaking. To characterise the neural correlates of decision-making, we recorded brain activity using electroencephalography (EEG). We were primarily interested in measuring feature-specific brain responses to presented motion signals using population-tuning modelling of brain activity (31)(32)(33)(34)(35)(36).
Critically, our experimental design also permitted us to use the same method to decode featurespecific brain responses to the average motion direction. This quantity must be internally computed by integrating the representations of the two target signals and, as such, must be closely related to the mechanisms of integrative decision-making. If stimulus reliability affects integration processes, then population-tuning responses to the average motion direction should depend on the combination of motion coherence levels across target epochs within a trial.
Using a similar analytical approach, previous studies (35,37) have successfully characterised feature-specific brain responses to both task-relevant and task-irrelevant stimuli. Although weaker than neural responses to relevant stimuli, robust responses to irrelevant stimuli suggest that the population-tuning analyses have a strong sensory component. To gauge the degree to which decoded motion-specific responses reflect sensory processing, on every trial of the motionaveraging task we presented two overlaid patches of dots in different, distinctive colours. At the beginning of every trial, a colour cue indicated the dot-patch that would contain the target-motion direction; the other dot-patch served as a concurrent distractor which could be ignored. Different, uncorrelated motion signals were briefly (500 ms) and concurrently presented in both target and distractor patches. Introducing distractor signals enabled us to dissociate sensory responses -which should be comparable for target and distractor signals -and decision-related brain responseswhich should be more prominent for targets than distractors.
Unlike commonly used decision-making paradigms in which all stimuli are task-relevant, contrasting target and distractor processing should elucidate the role of selective attention in integrative decision-making. On the basis of the vast literature on selective attention (38), we expected target motion signals to influence behavioural measures of integrative decision-making more strongly than distractor signals. What is less clear, however, is whether and in what way selective attention might affect feature-specific brain responses to distractor signals. While unlikely, it is possible that the brain represents both relevant and irrelevant sensory input with equal fidelity, predicting a comparable degree of population tuning to target and distractor signals. A more likely outcome (39,40) is that selective attention modulates the temporal dynamics of tuning to target and distractor motion, predicting suppression of distractor-related responses following an initial, sensory response to both target and distractor signals. By presenting both target and distractor signals and using population-tuning modelling, we could adjudicate between these two alternatives.

Results
In Experiment 1 (Fig. 1a, upper panel), we presented only one epoch containing a motion stimulus, and participants had to ascertain the target motion direction while ignoring a concurrently presented distractor motion event. By presenting a single epoch of coherent motion, we could test whether participants' ability to discern motion direction was comparable across low (40%) and high (80%) coherence levels. By presenting both target and distractor motion signals within each singleepoch trial, we could also ask whether selective attention operates differently at different coherence levels. Importantly, on every trial the strength of motion coherence of the concurrently presented target and distractor signals was the same, either both high coherence or both low coherence. To quantify overall task performance, we used mixture distribution modelling of error magnitudes (see Methods) to separately analyse the response precision (K) of noisy target responses and the proportion of random guesses (Pg). To quantify the degree to which individual target and distractor motion signals influenced the responses, we used linear regression (ordinary least squares; OLS) with complex-valued data. The absolute value of the regression coefficients associated with individual signals will reflect the degree to which target and distractor signals influenced the decision, or decision weights. A coloured cue indicating the task-relevant colour (fixed per participant) was followed by a patch of grey dots moving randomly. After 1 s buffer periods, the colour saturation increased gradually to reveal two intermingled fields of distinctly coloured target and distractor dots. Coherent motion signals were presented for .5 s in both fields, jittered relative to the maximum saturation onset (.25-.5 s). In Experiment 1, only one epoch was presented and participants reproduced the target motion direction. In Experiment 2, two epochs were presented and participants reproduced the average motion direction of the two target motion stimuli. To summarise, Experiment 1 showed that participants were able to discern target motion direction with comparable precision at both low and high coherence values. Similarly, the efficiency of selective attention, as indexed by the difference between target and distractor weights, was comparable across low and high coherence trials. These results suggest that the low and high coherence levels we chose were both close to the asymptote of the psychometric curve.
Consequently, unbiased integration of signals with low and high reliability should permit accurate integrative decisions.
In Experiment 2, we examined how temporally discrete perceptual decisions are integrated into a single decision. To this end, two epochs of coherent motion, rather than a single epoch as in Experiment 1, were presented in each trial. Participants had to reproduce the average motion direction of the two target signals while ignoring the concurrently presented distractors. We were primarily interested in characterising biases in behavioural decision weights as a function stimulus reliability. In addition, we recorded brain activity using EEG. To characterise the temporal dynamics of individual perceptual decisions, we quantified a well-documented neural correlate of decisionmaking (11,12,41), the centro-parietal positivity (CPP), time-locked to the onsets of both coloursaturation modulation and coherent motion signals (see Methods and Fig. 1a). Further, we characterised feature-specific neural responses to the presented motion using population-tuning modelling. Finally, using the same method, we quantified feature-specific brain activity related to the average motion direction. The average-motion responses should be closely related to the integration of the two target signals and, as such, are a good candidate for the neural correlate of integrative decision-making.
Similar to Experiment 1, the mixture distribution modelling of error magnitudes in The fact that the variance of single signals was additive when averaging them indicates that participants performed the two tasks in a qualitatively similar way.
We next analysed the effect of dot coherence in different epochs on response precision and guessing rates. Consistent with Experiment 1, response precision was comparable for low and high coherence in the first epoch (K = 8.12 and 8.19, respectively, F < 1). By contrast, response precision was significantly lower for low than high coherence targets in the second epoch (  Similar to Experiment 1, decision weights were significantly larger for target than distractor motion signals (.56 and .09, respectively, F1,21 = 2,028, p < .001, η " # = .99, Fig. 2b). Unexpectedly, however, both target and distractor weights were higher in the first epoch than in the second (.63 and .53 for targets, respectively, F1,21 = 24.28, p < .001, η " # = .54; .10 and .09 for distractors, F1,21 = 4.60, p = .044, η " # = .18). As the trials were relatively long (5 s), one might expect memory decay (29,43) to affect the first target more than the second, more recent target. The primacy bias we observed in Experiment 2 is opposite to what one might expect from simple memory decay, and might be indicative of how participants represented individual signals prior to integrating them.
Most importantly, this order bias was further qualified by two-way interactions with motion coherence in both the first epoch and the second (Fig 2b, right  .17). The interaction of dot coherence with order bias indicates that averaging two signals was biased in favour of the signal of higher reliability. Importantly, this bias arose despite the fact that, consistent with the task instructions to average the two target signals, unbiased averaging should be the optimal response strategy. Moreover, the results of Experiment 1 confirmed that participants could perform equally accurate motion judgements on both high and low coherence signals when they were presented in single-epoch trials (see Fig. 1b).
To characterise the time-course of evidence accumulation in the motion-averaging task, we next analysed the CPP (Fig. 3), a positive deflection over centro-parietal electrodes that has been shown to closely mimic temporal dynamics of evidence accumulation (11,12,41). Visual inspection of the ERP topographies ( We next analysed shorter segments (500 ms) time-locked to the onsets of colour modulation and coherent motion ( Fig. 3c and 3d, respectively). For both colour-and motion-locked epochs, the CPP deflection started at around 200 ms after the onset, consistent with the notion that the CPP is not merely a sensory-evoked response, but rather reflects higher level processes following sensory encoding (see the Intercept line in Fig. 3c and 3d, bottom panel). The colour-locked CPP was modulated only by the epoch, with a steeper rise and higher peak amplitude in the first epoch than the second (Fig. 3c). Analyses of the motion-locked CPP revealed a robust effect of motion coherence, with a steeper rise and higher peak amplitude for high coherence relative to low in both epochs (Fig. 3d). Importantly, only the coherence for the currently presented motion stimulus affected the CPP, as evidenced by a significant interaction between epoch (first/second) and the motion coherence per epoch (First coherence x Epoch and Second coherence x Epoch lines, bottom panel). This finding suggests that the motion-locked CPP reflects evidence accumulation in support of discriminating the currently presented motion target (i.e., a simple perceptual decision), rather than the averaging process (i.e., an integrated decision). Whereas analyses of behavioural decision weights revealed robust interactions between the order bias and motion coherence across the two epochs, the ERP analyses suggest that the order effect and the coherence effects might have separable neural correlates. The order bias, evident in the colour-locked CPP, appears to reflect the process of selecting the target patch against the distractor patch -and, potentially, staying focused on the target patch -whereas the coherence effect, evident in the motion-locked CPP, appears to reflect the strength of the subsequently presented motion signals.
We next characterised time-resolved motion-specific responses to target and distractor signals (Fig. 4a) using population-tuning modelling (31)(32)(33) of the motion-locked EEG signals (see Methods for details). Inspection of tuning to target signals revealed a robust and sustained motionspecific response. The onset of significant motion-tuning coincided with the peak latency of the motion-locked CPP, suggesting that motion-tuning reflects the decision about the currently presented motion stimulus. There was no such tuning to distractor signals, which further supports the notion that motion tuning captures the dynamics of deciding about task-relevant signals, rather than stimulus-driven responses regardless of task relevance. Importantly, tuning to the target motion direction was sustained well after motion offset (indicated by dotted vertical lines), suggesting that representations of individual signals were maintained until both targets had been presented.  To match the number of trials in the same-coherence and different-coherence trials and to maximise the signal-to-noise ratio in the different-coherence conditions, the channels were flipped for the High®Low trials so that the direction of a potential order bias would be the same as for the Low®High trials. Small inset panel: the average shift of the tuning profiles computed as the difference between the mean response for channels tuned to -p -0 and 0 -p intervals. Whiskers denote ±1 within-participants SEM.
In a final analysis, we characterised the temporal dynamics of integrated decision-making by estimating neural tuning to the average motion direction (Fig. 5a). For the first epoch, there was no significant motion tuning. This finding was expected, as neural representations of average motion direction can only be determined after presentation of the second motion target within the trial. By contrast, there was robust and sustained tuning to the average motion direction in the second epoch, starting from the offset of coherent motion. Note that during this period only random motion was actually presented on the screen, so tuning to the average motion direction could not have been stimulus-driven.
To investigate how the brain integrates two discrete decisions, we next quantified the tuning profiles for the average motion direction (Fig. 5b). We focused on quantifying potential shifts in the profile that might reflect the first and the second target bias. To do so, the motion channels on each trial were re-coded so that negative channels were closer to the first presented target, and positive channels were closer to the second. Thus, a leftward shift would indicate a first-target bias, and a rightward shift would indicate a second-target bias. The channels' responses were then averaged across trials separately for different combinations of stimulus reliability across epochs. Motivated by the first-target bias we observed in behavioural decision weights (Fig. 2b), we expected to see a leftward shift for trials with the same coherence across epochs (Fig. 5b, upper panel). To increase signal-to-noise ratio, we averaged the tuning profiles for High®High and Low®Low coherence trials. The observed tuning profiles (Fig. 5b, lower panel) confirmed our expectation, as we observed a statistically significant leftward shift consistent with a first-target bias (M/SEM = -.16 /.06, t21 = 2.32, pFDR-corrected = .046, Fig. 5b, inset panel). This result mimics the first-target bias in behavioural decision weights, and it suggests that the brain integrates two target signals in a biased way, with the first signal contributing more strongly than the second.
In contrast to the same-coherence trials (High®High, Low®Low), for the differentcoherence trials we expected to observe effects of signal reliability on the tuning profile shifts. For the High®Low sequence, in which the order bias and the reliability bias both favoured the first target, we expected to see an even stronger leftward shift relative to the same-coherence trials (Fig.   5b, upper panel). For the Low®High sequence, on the other hand, in which the order bias and the reliability bias favoured different targets, we expected to see weaker shifts in the tuning profile relative to the same-coherence trials (Fig. 5b, upper panel). To match the numbers of trials in the same-and different-coherence conditions and to increase signal-to-noise ratio in the differentcoherence condition, we flipped the tunning profiles for High®Low trials so that the expected shift direction was the same for High®Low and Low®High trials. Confirming our predictions, the firsttarget bias for different-coherence trials was not significantly different from zero (.05/.06, t21 = .66, pFDR-corrected = .519, Fig. 5b, inset panel), and it was significantly smaller than the bias for same-coherence trials (t21 = 2.35, pFDR-corrected = .046). Taken together, analyses of shifts in tuning profiles revealed that the brain relies more on signals with high reliability than low when integrating the two.
Across two experiments in which we combined behavioural testing and whole-brain recording, we have shown that behavioural decision weights and population-tuning profiles to the average motion direction exhibit qualitatively similar biases in favour of stimuli of higher reliability.
These findings demonstrate that temporal integration of discrete perceptual decisions is biased even when the bias is suboptimal and unbiased, optimal integration is possible. Our findings suggest that the brain encodes the reliability of sensory inputs and that the encoded reliability is used automatically to weight respective inputs during integrative decision-making.
The relatively narrow distributions of error magnitudes and high response precision suggest that participants were able to successfully select target signals and ignore concurrently presented distractors. This finding was further corroborated by very low decision weights for distractors, which were five to nine times lower than the respective target weights. Perhaps most interestingly, and contrary to expectations, the population-tuning modelling of distractor motion signals revealed no distractor-specific neural activity. As participants were given some preparation time (500-750 ms) before the motion onset, it is likely that this time was sufficient for attentional resources to be engaged exclusively on the target-motion stimulus. By contrast, the motion decoding for target signals was robust and sustained well after signal offset, suggesting that the population-tuning modelling primarily captured decision-making processes as opposed to purely sensory-evoked activity patterns. With this in mind, it is likely that decoding of the average motion direction also reflected the dynamics of integrated decision making. One might ask whether it is possible that tuning to the average motion direction simply reflects tuning to the second target, given that the two directions were not entirely uncorrelated. This seems unlikely, however, as comparable tuning to the average motion direction should also have been observed in the first epoch (for which target signals were likewise not uncorrelated with the average), but this was clearly not the case.
Moreover, if tuning to the average motion direction was driven by the second target then the time course of average motion tuning should have been similar to that of the second target, which, again, clearly was not the case. We therefore conclude that the robust tuning to the average target motion observed in Experiment 2 reflects the temporal dynamics of integrative decision making.
An unexpected finding in Experiment 2 was a reliable order bias, with higher decision weights for the first epoch than the second. Additionally, the colour-locked CPP had a steeper slope and a higher peak in the first epoch than the second. By contrast, the motion-locked CPPs did not differ much between epochs, at least prior to the peak of the CPP response. These findings suggest that the order bias originates from processes related to selecting the task-relevant dot patch, rather than from processing of the motion signals themselves. Perhaps most compellingly, the order bias was also evident in tuning to the average motion direction, with robust shifts in favour of the first target-motion direction. This order effect was independent of reliability-weighted source integration, as we observed the shift in population tuning for epochs that were matched in coherence. Additionally, as the stimuli across the two epochs were matched for low-level properties, the order bias cannot be stimulus-specific. Finally, the first-target bias speaks against a simple memory decay explanation, which instead would predict a recency effect (29,43). Taken together, the most parsimonious explanation for the primacy bias is that the effectiveness of attentional selection decreases from the first epoch to the second. Characterising attentional selection dynamics in relation to integrated decision-making was not in the focus of the present study, and follow-up studies will be needed to address this issue in more detail. For the interested reader, we have recently conducted a study (44) that focused on the relationship between selective attention and decision-making using a similar experimental paradigm but a different analytical approach.
The reproduction task we employed enabled us to probe the nature of the representations underlying integrated decision-making. In typical decision-making paradigms (4), the response is a categorical decision, for example, whether motion direction is to the left or to the right. While forced-choice paradigms lend themselves to speeded responding, and permit use of computational modelling to characterise different aspects of decision making, they do not capture the precision of the sensory and memory representations that underlie evidence accumulation processes. A wellknown property of the brain's responses to sensory input (18,(45)(46)(47) is that they are graded, forming a probabilistic stimulus representation in feature space. In the case of motion signals, the large-scale neural representation of a given motion direction should resemble a bell-shaped curve with a peak over the actual direction which gradually decreases for motion directions further away from the peak. Classical decision-making paradigms would be sensitive to the location of the peak, but would have difficulty characterising the variability of the probabilistic representation -and that variability seems to play a critical role in integrated decision-making. Using mixture distribution modelling for behavioural measures, and population tuning modelling for neural measures, we were able to characterise both the peak and the variance of the underlying probabilistic representations.
A key question regarding reliability-weighted integrated decision-making concerns how two discrete representations get combined in support of an integrated decision. Using the redundant signals paradigm, previous research on signal integration at both sensory (23,24) and decisionmaking (17,22,48) stages has suggested that a simple multiplication of two probabilistic representations could drive reliability-weighted integration. The multiplication, however, predicts lower variability (18,23) of the integrated representation relative to the variability of individual sources. By contrast, the variability of integrated decisions in our study was higher than that of single decisions, following the summation rule for two random variables. Therefore, it appears that for tasks such as the one employed here the two probabilistic representations are summed rather than multiplied.
As both the behavioural and neural results of Experiment 2 depended more strongly on high-reliability events than on low, the summation process appears to be biased, with higher weights for high-reliability representations. It is unlikely that these weights reflect learning processes, as in our paradigm the coherence of individual signals was unpredictable. Rather, the summation weights were likely encoded in parallel with encoding of the motion direction signals.
One possibility is that the weights directly reflect the variability of the probabilistic signal representations: a simple combination of two probabilistic representations of differing variances would be shifted in favour of the representation of higher reliability. Another possibility is that the weights reflect a belief about the accuracy of the respective representations. In this scenario, even though the two reliability levels afforded comparable accuracy (as confirmed in Experiment 1), the strong perceptual differences between low-and high-reliability signals would have resulted in different beliefs about signals of different coherence. While at present we cannot adjudicate between the two potential correlates of the summation weights, the absence of strong coherence effects in our study suggests that the representations of the high and low reliability signals were comparably accurate, speaking in favour of the latter, beliefs-as-weights alternative. Further studies, most likely in combination with hierarchical computational modelling (49), would be necessary to address this issue conclusively. At present, computational models of decision-making in reproduction tasks are just beginning to appear (50,51), and more research will be needed before applying these models to integrative decision-making tasks.
In summary, here we have shown that combining two discrete, temporally separated signals in support of a single, integrated decision is biased in favour of higher reliability signals. Unlike previous studies in which reliability-weighted integration was statistically optimal, in the present study biased integration was suboptimal. These findings suggest that reliability-weighted integrated decision-making is automatic, taking place even when it is detrimental for performance.

Methods
Participants. 25 neurotypical adults (mean age 22 years, 14 females) participated in Experiment 1. All had normal or corrected-to-normal visual acuity and normal colour vision confirmed by Ishihara colour plates. The sample size was selected with the aim to achieve high power (b = .9 at a = .05) to detect a medium to large effect size (Cohen's dz = .65) for a one-tailed, one-sample t-test between response error magnitude for low-and high-motion coherence. Due to corrupted data acquisition, one participant was immediately removed from further analyses. The aim of Experiment 2 was to investigate integration of target signals across two epochs.
Experiment 2 was identical to Experiment 1, with two exceptions. First, two epochs of coloured dots, rather than one, were presented in every trial and participants had to reproduce the average motion direction of the two target signals while ignoring distractor motion events. Second, target motion in the first epoch was selected randomly from 0-360 degrees range in 1 degree steps. The target motion in the second epoch was selected from a ±30-150 degree range relative to the first target.
The dot coherence across the two epochs was selected pseudo-randomly so that all four combinations (low/high in the first epoch ´ low/high in the second) were presented equally often.
Both behavioural and electroencephalography data were recorded.

Apparatus.
The experiments were conducted in a dark, acoustically and electromagnetically shielded room. The stimuli were presented on a 24" monitor with 1920´1080 resolution and a refresh rate of 144 Hz. The experimental software was custom-coded in Python using the PsychoPy toolbox (52,53). EEG signals were recorded using 64 Ag-AgCl electrodes (BioSemi ActiveTwo) arranged in the 10-20 layout, and sampled at 1,024 Hz.

Behavioural analyses.
To identify outlier participants, the distributions of error magnitudes (i.e., the angular difference between the response and the correct answer) were compared to a uniform distribution (i.e., pure guessing) using the Kolmogorov-Smirnov test. Participants for whom the probability of the null hypothesis (i.e., a uniform distribution of error magnitudes) exceeded .001 were removed from further analyses. The remaining distributions per experimental condition and per participant were fitted to a theoretical model (54), and responses were separated into noisy target responses and random guesses. To quantify decision weights, a multiple-regression (OLS) model with a term for each of the presented motion directions, expressed as complex numbers, was fitted to the responses, separately per participant and experimental condition. The absolute value of the resulting regression coefficients reflects the influence of each of the presented coherent motion signals on the response, i.e., its decision weight.
EEG analyses. EEG signals were analysed using the MNE-Python toolbox (55). The data were offline re-referenced to the average electrode, low-pass filtered at 99 Hz and notch-filtered at 50 Hz to eliminate line noise. The recorded signal was pre-processed using the FASTER algorithm for automated artefact rejection (56). The pre-processed signal was down-sampled to 256 Hz, segmented into 4 s periods between the onset of the first epoch and the response-display onset, baseline-corrected relative to -.1-0 s pre-trial and linearly de-trended. Outlier trials and participants were identified using the FASTER algorithm and removed from further analyses.
Next, whole-trial time-traces were further segmented into shorter (.5 s) periods time-locked to the onset of colour-saturation increase and the onset of coherent motion in the first and second epoch, and baseline-corrected relative to .1-0 s pre-onset interval. To characterise the temporal dynamics of evidence accumulation, we quantified an ERP known as the central-parietal positivity (CPP). Previous research has shown that the time-course of the CPP closely resembles the timecourse of evidence accumulation: specifically, its amplitude builds up gradually, the build-up slope is proportional to stimulus quality, and it is observed even in the absence of overt responses (11,12,41). Visual inspection of the ERP topographies revealed a positive deflection in a cluster of central-medial electrodes (FCz, C1, Cz, C2, and CPz) consistent with the CPP ERP -to improve signalto-noise-ratio, the average of these electrodes was used in further analyses. Next, the CPP voltage per time-sample, trial and participant was submitted to a stepwise linear mixed-effects model with epoch (first/second) and motion coherence (low/high) per epoch as fixed effects, and participant as a random effect. A likelihood ratio test between models of higher and lower complexity was used to assess the significance of each main effect and interaction terms. To control for multiple comparisons, the p-values for all time-samples and all model terms were jointly corrected using the false discovery rate algorithm (57).
To recover feature-specific information about motion signals from the EEG signals (Fig. 6), we used a population tuning curve model (31)(32)(33). To that end, the first and the second epochs (1 s