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The authors have declared that no competing interests exist.

Information sampling can reduce uncertainty in future decisions but is often costly. To maximize reward, people need to balance sampling cost and information gain. Here we aimed to understand how autistic traits influence the optimality of information sampling and to identify the particularly affected cognitive processes. Healthy human adults with different levels of autistic traits performed a probabilistic inference task, where they could sequentially sample information to increase their likelihood of correct inference and may choose to stop at any moment. We manipulated the cost and evidence associated with each sample and compared participants’ performance to strategies that maximize expected gain. We found that participants were overall close to optimal but also showed autistic-trait-related differences. Participants with higher autistic traits had a higher efficiency of winning rewards when the sampling cost was zero but a lower efficiency when the cost was high and the evidence was more ambiguous. Computational modeling of participants’ sampling choices and decision times revealed a two-stage decision process, with the second stage being an optional second thought. Participants may consider cost in the first stage and evidence in the second stage, or in the reverse order. The probability of choosing to stop sampling at a specific stage increases with increasing cost or increasing evidence. Surprisingly, autistic traits did not influence the decision in either stage. However, participants with higher autistic traits inclined to consider cost first, while those with lower autistic traits considered cost or evidence first in a more balanced way. This would lead to the observed autistic-trait-related advantages or disadvantages in sampling optimality, depending on whether the optimal sampling strategy is determined only by cost or jointly by cost and evidence.

Children with autism can spend hours practicing lining up toys or learning all about cars or lighthouses. This kind of behaviors, we think, may reflect suboptimal information sampling strategies, that is, a failure to balance the gain of information with the cost (time, energy, or money) of information sampling. We hypothesized that suboptimal information sampling is a general characteristic of people with autism or high level of autistic traits. In our experiment, we tested how participants may adjust their sampling strategies with the change of sampling cost and information gain in the environment. Though all participants were healthy young adults who had similar IQs, higher autistic traits were associated with higher or lower efficiency of winning rewards under different conditions. Counterintuitively, participants with different levels of autistic traits did not differ in the general tendency of oversampling or undersampling, or in the decision they would reach when a specific set of sampling cost or information gain was considered. Instead, participants with higher autistic traits consistently considered sampling cost first and only weighed information gain during a second thought, while those with lower autistic traits had more diverse sampling strategies that consequently better balanced sampling cost and information gain.

Information helps to reduce uncertainty in decision making but is often costly to collect. For example, to confirm whether a specific tumor is benign or malignant may require highly invasive surgery procedures. In such cases, it can be more beneficial to tolerate some degree of uncertainty and take actions first. To maximize survival, humans and animals need to balance the cost and benefit of information sampling and sample the environment optimally [

However, autism spectrum disorder (ASD)—a neurodevelopmental disorder characterized by social impairments and repetitive behaviors [

The autistic traits of the whole population form a continuum, with ASD diagnosis usually situated on the high end [

The present study is aimed to understand how autistic traits in typical people may influence their optimality of information sampling. In particular, we focused on the situation where information can be used to improve future decisions (e.g. [

Possible suboptimality may arise from a failure of evaluating sampling cost or information gain, or improper trading off the two, or a greater noise [

What cognitive processes in information sampling are particularly affected by autistic traits? Through computational modeling, we further decomposed participants’ sampling choices into multiple sub-processes and found that the influence of autistic traits was surprisingly selective and subtle. In particular, participants’ sampling choices could be well described by a two-stage decision process: When the first decision stage does not reach the choice of stopping sampling, a second decision stage is probabilistically involved to arbitrate, which offers a second chance to consider stopping sampling. The two stages were independently controlled by cost and evidence and neither stage showed autistic-trait-related differences. What varied with levels of autistic traits was the strategic diversity: Participants with higher autistic traits were more likely to always consider cost in the first stage and evidence in the second, while those with lower autistic traits had a larger chance to use the reverse order as well. As a consequence, the former would perform better when the optimal strategy does not depend on evidence, while the latter would do better when the optimal strategy is determined jointly by cost and evidence.

One hundred and four healthy young adults participated in our experiment, whose autistic traits were measured by the self-reported Autism Spectrum Quotient (AQ) questionnaire [

(a) Time course of one trial. “Preview” informed the participant of the pink-to-blue ratios of the two jars (80%:20% vs. 20%:80% in this example, corresponding to the high-evidence condition). Then the participant could sample beads from the unknown pre-selected jar one at a time up to 20 beads (“sampling”) or quit sampling at any time. Afterward, the participant judged which jar had been selected (“judgment”). Feedback followed, showing the correctness of judgment and winning of the current trial. Feedback was presented for 1 s, whereas preview, sampling, and judgment were self-paced. During sampling, the remaining bonus points (green bar), as well as the array of bead samples, were visualized and updated after each additional sample. (b) Optimal sampling strategy vs. participants’ performance for each of the six cost-by-evidence conditions. On a specific trial, the expected probability of correctness (dashed lines) and the remaining bonus points (dotted lines) are respectively increasing and decreasing functions of the number of bead samples. The expected gain (solid lines), as their multiplication product, first increases and then decreases with the number of samples. Note that the sample size that maximizes expected gain varies across different cost and evidence conditions. Each circle represents a participant with the color indicating their AQ score.

We computed efficiency—the expected gain for participants’ sample sizes divided by the maximum expected gain—to quantify the optimality of participants’ sampling choices and used linear mixed model analyses to identify the effects of AQ and its interactions with sampling cost and information gain (LMM1 for efficiency, see _{2,100.98} = 65.38, _{1,101.88} = 124.95, _{2,202.89} = 123.20,_{2,203.45} = 5.60, _{137.82} = −3.16, _{151.58} = −2.64, _{136.08} = 2.11, _{121.32} = −2.51,

(a) Sampling efficiency varied with cost (abscissa) and evidence (different colors) conditions. Participants’ efficiency was on average 94% (i.e. close to optimality) but decreased with increasing cost or decreasing evidence, and decreased more dramatically when high cost and low evidence co-occurred. (b) The mean number of bead samples participants drew in a condition (solid lines) decreased with increasing cost or increasing evidence. Compared to the optimal number of samples (dashed lines), participants undersampled in the zero- or low-cost conditions while oversampled in the high-cost conditions. (c) Sampling variability (standard deviation of the numbers of samples drawn across trials) varied with cost and evidence conditions. Error bars in (a)–(c) denote between-subject standard errors. (d)–(f) Effects of AQ levels on participants’ sampling performance in different cost (different colors) and evidence (abscissa) conditions. Β_{AQ} is the unstandardized coefficient of AQ indicating how much the efficiency (d), number of samples (e), and sampling variability (f) would change when AQ increases by one unit. Error bars represent standard errors of the coefficients. Orange asterisk:

The overall high efficiency was accompanied by adaptive sampling behaviors that were modulated by both sampling cost and information gain: Participants drew fewer samples in costlier or more informative conditions as the optimal strategy would require (_{s})).

A linear mixed model analysis on _{2,100.93} = 752.65, _{1,101.98} = 177.48, _{2,202.97} = 546.59, _{2,101.13} = 3.99, _{101.90} = 2.61, _{110.02} = 2.67, _{107.86} = 1.68,

According to a similar linear mixed model analysis on _{s}) (LMM3, see _{2,100.86} = 57.13, _{1,101.89} = 161.78, _{2,203.43} = 33.51, _{2,204.09} = 5.27, _{172.54} = −2.43, _{188.90} = −3.51, _{140.52} = −2.22, _{154.23} = 2.50,

Taken together, participants with different levels of AQ differed in both the mean and SD of sample sizes. Participants with higher AQ had higher efficiency in the zero-cost, low-evidence condition, which was associated with less undersampling and lower sampling variability. Meanwhile, higher AQ corresponded to lower efficiency and higher sampling variability in the high-cost, low-evidence condition.

Decision time (DT) for a specific sample—the interval between the onset of last bead sample (or, for the first sample, the start of the sampling phase) and the key press to draw the sample—provided further information about the cognitive process underlying sampling choices. Though decision or response times usually have a positively skewed unimodal distribution and are close to Gaussian when log-transformed [

(a) The distributions of DTs aggregated over all participants (main plot) and for each cost and evidence condition (insets). In the main plot, the distribution of DTs (histogram) was clearly bimodal, well fitted by a Gaussian mixture (gray curve) with two Gaussian components (black curves). Such bimodality was also visible in most inset plots, though the relative weights of the two components varied with experiment conditions. (b) Mean DTs varied with cost (abscissa) and evidence (different colors) conditions. Error bars represent between-subject standard errors. (c) Effects of AQ levels on participants’ DTs in different cost (different colors) and evidence (abscissa) conditions. Β_{AQ} is the unstandardized coefficient of AQ indicating how much the mean DT in a condition would change when AQ increases by one unit. Error bars represent standard errors of the coefficients.

Linear mixed model analysis (LMM4) showed that the mean DTs (_{2,101} = 120.62, _{1,102} = 165.85, _{2,204} = 14.65, _{2,101} = 6.22, _{102} = 3.45,

The DTs within the same trial changed with sample number (LMM5, _{19,10805525.21} = 24.5, _{4323568} = −12.26, _{19,11498809.98} = 1.66, _{4628456} = 3.62,

A straightforward explanation for the bimodal DT distribution would be a probabilistic mixture of two cognitive processes. Next, we used computational modeling to explore the possibility of two decision stages and showed that it could quantitatively predict the effects of cost and evidence as well as the bimodal distribution of DTs.

We considered a variety of models for sampling choices, which fell into two categories: one-stage models and two-stage models (

(a) Schematic of one-stage and two-stage models. One-stage models only consist of the steps on the left-hand side: Each time a participant decides whether to stop or continue sampling, the probability of stopping is a sigmoid function of a linear combination of multiple decision variables. Two-stage models assume that participants may probabilistically have a second thought to reconsider the choice (the coral dashed arrow). The second stage (on the right-hand side) works in the same way as the first stage but the two stages are controlled by different sets of decision variables. (b) Results of model comparison based on the joint fitting of choice and DT. The ΔAICc for a specific model was calculated for each participant with respect to the participant’s best-fitting model (i.e. lowest-AICc) and then summed across participants. Both fixed-effects (summed ΔAICc: lower is better) and random-effects (estimated model frequency: higher is better) comparisons revealed that the best-fitting model was a two-stage model with cost-related variables considered in the first stage and evidence-related variables in the second stage (i.e.

In two-stage models of sampling choices, we assumed that deciding whether to stop or continue sampling may involve two consecutive decision stages, where the decision in the first stage can either be final or be re-evaluated in an optional second stage. Whether to enter the second stage is probabilistic, conditional on the decision reached in the first stage. The decisions in the two stages are independent and controlled separately by the cost- and evidence-related factors and are subject to evidence decay. In other words, the decision in each stage is similar to that of a one-stage model. We considered 12 different two-stage models whose assumptions differ in three dimensions (see

We fit all the models to participants’ sampling choices separately for each participant using maximum likelihood estimates. For each fitted choice model, with some additional assumptions, we were able to model participants’ DTs and fit the additional DT parameters using maximum likelihood estimates as well (see

When two-stage models were fit to participants’ DTs, the second-thought probabilities were estimated exclusively from choices and not free parameters adjustable by DTs (see

As additional evidence for the link between two-stage decisions and bimodal RTs, the mean DT—as a proxy for the proportion of slow decisions—increased with the probability of using the second stage (_{S} = .60,_{S} = .44,_{S} = .35,_{S} = .22,_{1,78.06} = 47.74,_{1,284.99} = 25.76,_{2,73.75} = 2.43,_{2,233.83} = 2.59,

According to two-stage models, mean DT—as a proxy for the proportion of slow decisions—should increase with the probability of using the second stage. Indeed, mean DT and second-thought probability were positively correlated, separately for each cost condition (the first three panels) and when aggregated across all cost conditions (the last panel), thus providing additional support for the two-stage decision process. Each dot is for one participant in one specific cost condition. Lines and shaded areas respectively represent regression lines and standard errors. The _{S} refers to Spearman’s correlation coefficient.

What individual differences in the decision process may relate to the autistic-trait-related effects on the optimality of sampling choices? We first examined the estimated parameters of the best model (_{S} = −.22,_{S} = −.02,

Next we tested whether participants’ autistic traits influenced the decision strategies they used. As shown in our results of model comparisons, participants may have used a variety of different two-stage decision processes: Among the 104 participants, 52 participants were best fit by the _{cost→evidence}−_{evidence→cost} and referred to as cost-evidence strategy index) was negatively correlated with AQ (_{S} = −.23,

(a) Correlation between AQ and cost-evidence strategy index (_{cost→evidence}−_{evidence→cost}). More negative cost-evidence strategy index indicates stronger preference for cost-first over evidence-first decision processes, while more positive cost-evidence strategy index indicates the reverse. Each dot is for one participant. The blue line and the shaded area respectively represent regression line and standard error. (b) Correlation coefficients between cost-evidence strategy index and efficiency for each cost and evidence condition. C:0 = zero-cost, C:0.1 = low-cost, C:0.4 = high-cost, E:0.6 = low-evidence, E:0.8 = high-evidence. Error bars represent FDR-corrected 95% confidence intervals. All these correlations were consistent with what we would expect if AQ influences sampling efficiency through its influence on the use of cost-first vs. evidence-first decision processes. For example, given that AQ was negatively correlated with cost-evidence strategy index, and cost-evidence strategy index was negatively correlated with the efficiency in the zero-cost, low-evidence condition, we would expect AQ to be positively correlated with the efficiency in the zero-cost, low-evidence condition, and indeed it was. (c) Correlation between AQ and cost-evidence strategy index varied with the value of cost-evidence strategy index. We ranked all participants by cost-evidence strategy index in ascending order, that is, from the strongest preference for cost-first to the strongest preference for evidence-first, and plot the Spearman’s correlation coefficient between cost-evidence strategy index and AQ as a function of the number of participants included in the correlation analysis. The observed overall negative correlation and the stronger correlation given only the cost-first-dominated participants were included supports the cost-first vs. balanced-strategy hypothesis (see text): Participants with higher AQ tended to always consider cost first, while those with lower autistic traits considered cost or evidence first in a more balanced way. Statistical significance marked on the plot was based on cluster-based permutation tests (see

We assured that such differences in decision process could cause the observed autistic trait-related effects in sampling optimality by computing the correlation between cost-evidence strategy index and efficiency for each cost and evidence condition (corrected for 6 comparisons). The correlation (_{S} = −.66,_{S} = −.55,_{S} = −.34,_{S} = .48,_{s})) (

Given that all participants were either much better modeled by cost-first models (i.e. cost-evidence strategy index ≪ 0) or almost equivalently well by cost-first and evidence-first models (i.e. cost-evidence strategy index ≈ 0) (

In the two-stage decision process we modeled, because the second stage is only probabilistically recruited, factors considered in the first stage would effectively leverage a greater influence on the sampling choice than those of the second stage. In other words, always being cost-first means the sampling choice is mainly determined by cost-related factors, while sometimes cost-first and sometimes evidence-first means the sampling choice is more of a tradeoff between cost- and evidence-related factors. Neither strategy is necessarily optimal but may approximate the optimal strategy in different situations: The former is closer to optimal when the optimal strategy does not depend on evidence, while the latter is closer to optimal when the optimal strategy varies with both cost and evidence. Participants’ differences in strategic diversity thus explain the autistic trait-related differences we observed in efficiency.

Humans must sample the environment properly to balance the advantage of gaining additional information against the cost of time, energy, and money [

Previous ASD studies that had used similar bead-sampling tasks yielded inconclusive results: One study found that adolescents with ASD sampled more than the control group [

The autistic-trait-related differences in sampling decisions we found through computational modeling are surprisingly selective. Participants with different levels of autistic traits were indistinguishable in their ability to weigh sampling cost or evidence gain in the two decision stages. What distinguished them was the strategic diversity across choices concerning whether to consider cost or evidence in the first stage. Participants with higher autistic traits were less diverse and stuck more to evaluating cost first.

Studies using autistic traits as a surrogate for studying ASD have revealed congruent and converging autistic-trait-related effects as those of ASD [

In our task, information sampling is instrumental—additional information would increase the probability of correct judgment. There are also situations where information is non-instrumental, for example, the information that is gathered after one’s decision and that would not change the outcome of the decision. Both humans [

To summarize, we find that people with different levels of autistic traits differ in the optimality of information sampling and these differences are associated with their strategic diversity in the decision process. Recent studies suggest that autistic traits may influence an individual’s ability of adaptively using her own information processing capability while not influencing the capability itself. For example, autistic traits may only influence the flexibility of updating learning rate but not probabilistic learning itself [

The experiment had been approved by the Institutional Review Board of School of Psychological and Cognitive Sciences at Peking University (#2016-03-03). All participants provided written informed consent and were paid for their time plus performance-based bonus.

One hundred and fourteen college student volunteers participated in our experiment. Ten participants were excluded. Six of them were IQ outliers, one misunderstood instructions, one had a strong judgment bias towards one type of stimuli, one did not draw any bead in 286/288 of the trials, and one had a poor judgment consistency. This resulted in a final sample size of 104 participants (42 males, aged 18–28).

We estimated effect size a priori based on a mini meta-analysis of previous literature [

Combined Raven Test (CRT) was used to measure participants’ IQ for control purpose. Raw CRT scores of all 114 participants averaged 67.69 (s.d., 4.71) and ranged from 41 to 72. Six of the participants (scoring from 41 to 58) fell out of two standard deviations of the mean and was excluded from further analyses along with four other participants (as mentioned above). The remaining 104 participants had a mean CRT score of 68.65 (s.d., 2.82; ranging from 61 to 72), corresponding to a mean IQ score of 117.68.

Autism Spectrum Quotient (AQ) questionnaire [

The AQ scores of the 104 participants were normally distributed (Shapiro-Wilk normality test, _{s} = −.01,_{s} = −.08,

All stimuli of the bead-sampling task were visually presented on a 21.5-inch computer screen controlled by MATLAB R2016b and PsychToolbox [

On each trial of the experiment (

The pink-dominant jar was pre-selected on half of the trials and the blue-dominant jar on the other half. Their left/right positions were also counterbalanced across trials. In the formal experiment, the two evidence (i.e. bead ratio) conditions (60/40 and 80/20) were randomly mixed within each block and the three cost conditions (0, 0.1, and 0.4) were blocked. Besides being visualized by the green bar on each trial, cost for each block was also informed at the beginning of the block. The order of cost blocks was counterbalanced across participants. We further confirmed that block order (6 permutations) had no significant effects on participants’ sampling choices (efficiency: _{5,97.90} = 2.06,_{5,97.99} = 1.51,_{s}): _{5,97.97} = 1.53,_{5,98} = 0.60,

All statistical analyses (except for group-level Bayesian model comparison) were conducted in R 3.5.3 [

Linear mixed models were estimated using “afex” package [

LMM1: decision efficiency is the dependent variable; fixed effects include an intercept, the main and interaction effects of AQ, cost, and ratio (evidence); random effects include correlated random slopes of costs and ratios within participants and random participant intercept.

LMM2: sampling bias (mean number of actual sampling minus optimal number of sampling;

LMM3: standard deviation of the number of sampling (_{s})) is the dependent variable; the fixed and random effects are the same as LMM1.

LMM4: mean decision time (DT) across all sampling choices of a condition is the dependent variable; the fixed and random effects are the same as LMM1.

LMM5: DT of each sample number (1 to 20 samples) averaged over all trials is the dependent variable; fixed effects involve an intercept, the main and interaction effects of AQ and sample number, and random effects include a random participant intercept. The model also incorporated weights on the residual variance for each aggregated data point to account for the different number of raw DTs for each sample number of each participant.

LMM6: the dependent variable is the same as LMM4; in addition to the fixed and random effects of LMM1, the linear effect of second-thought probability is included in the fixed effects, and a random slope of the second-thought probability that is uncorrelated with the random intercept is included in the random effects.

Following Jones et al. [

To examine possible non-linear effects of AQ, we constructed LMMs that included AQ^{2} and its interaction with cost and ratio as additional fixed-effects terms separately for LMM1–6. We found that adding the second order terms of AQ did not significantly improve the goodness-of-fit of any LMM.

Because stopping sampling involved a different key press, only DTs for continuing sampling were analyzed. Before any analysis of DTs, outliers of log-transformed DTs were excluded based on nonparametric boxplot statistics, with data points lower than the 1st quartile or higher than the 3rd quartile of all the log-transformed DTs by more than 1.5 times of the interquartile range defined as outliers.

Spearman’s rank correlations (denoted _{s}) were computed between AQ and model measures (model parameter or model evidence), and between model measures and behavioral measures (efficiency, _{s})). Except for the statistics in

To test whether the curve of correlation coefficients between cost-evidence strategy index and AQ in _{s} was defined as the cluster size. We randomly shuffled the values of cost-evidence strategy index across participants to generate virtual data, calculated the correlation curve and recorded the maximum size of its clusters for the virtual data. This procedure was repeated for 10,000 times to produce a distribution of chance-level maximum cluster sizes, based on which we calculated the

For the test against the overall correlation of 104 participants, we randomly shuffled the order of inclusion across participants and identified points that were significantly different from the overall correlation at the uncorrected significance level of .05 using Monte Carlo methods. Otherwise the permutation test was identical to that described above.

Given a specific sequence of bead samples, an ideal observer would always judge the preselected jar to be the one whose dominant color is the same as that of the sample sequence. In the case of a tie, the observer would choose the two jars with equal probability. Suppose the sample size is

The expected gain is E[

We modeled participants’ each choice of whether to continue or stop sampling (i.e. whether to press the space bar or Enter key) as a Bernoulli random variable, with the probability of stopping sampling determined by cost- or evidence-related factors. Pressing the Enter key after 20 samples was not included as a choice of stopping sampling, because participants had no choice but to stop by then.

We considered two families of models: one-stage and two-stage models. The description for each model is summarized in

Different one-stage models differed in whether cost-related variables, evidence-related variables, or both served as DVs (

Cost-only one-stage model (denoted

Evidence-only without decay one-stage model (denoted

Cost + evidence without decay one-stage model (denoted

Cost + evidence with decay one-stage model (denoted

In models with decayed evidence, cumulative information (CI) is modulated by a decay parameter

The DVs of absolute value of cumulative information and total log evidence in the models with decay are modulated by the decay parameter accordingly.

In two-stage models, sampling choices may involve two decision stages, with the probability of reaching the decision of stopping sampling in each stage being

Whether to enter the second stage is probabilistic, conditional on the decision reached in the first stage. For models where the second stage is triggered by the decision of continuing sampling in the first stage, the overall probability of stopping sampling can be written as:

Here

Each stage works in the same way as one-stage models do (Eqs

Cost-first two-stage models (models denoted by

Evidence-first two-stage models (models denoted by

Continue-then-2nd-thought two-stage models (models denoted by

Stop-then-2nd-thought two-stage models (models denoted by

Cost-controls-2nd-thought two-stage models (models denoted by _{C-zero}, _{C-low}, and _{C-high} are free parameters.

Evidence-controls-2nd-thought two-stage models (models denoted by _{E-low} and _{E-high} are free parameters.

Flexible-2nd-thought two-stage models (models denoted by

The intuition behind this form of second-thought probability is that participants should be likely to use the second stage to stop sampling when they are reluctant to continue but end up with choosing continue in the first stage, and likewise for the reverse case.

For both one- and two-stage models, given that the probability of stopping sampling on the _{ij}, the likelihood of observing a specific choice _{ij} (0 for continue and 1 for stop) is

Evidence-accumulation models are the common practice to model the response time (RT) of human decision-making, which can capture the three properties of the observed RT distributions [

Therefore, we modeled participants’ decision time (DT) for each sampling with a simplified form that is able to capture the three properties summarized above. For one-stage models or the first stage of two-stage models, we have

The expected total DT of reaching the decision of continuing sampling in the second stage equals to the time required by the first stage plus that of the second stage and has the forms

Thus, for one-stage models, the likelihood of observing a specific _{ij} for drawing the

For two-stage models, where _{ij} is a mixture of _{ij}) and _{ij}) respectively refer to the probabilities that the choice is finalized at Stage 1 and Stage 2, given that continuing sampling is the choice. These probabilities are computed based on the corresponding choice model, which are

The

For a specific sampling choice modeled by two-stage models, the likelihood of the joint observation of _{ij} and _{ij} is

That is, the joint likelihood is equivalent to the product of the likelihoods of choice (

Therefore, we used the sum of the log likelihoods of the choice and DT models for model comparisons.

Each one- or two-stage model consists of two parts: choice and DT. We first fit each choice model separately for each participant to the participant’s actual sampling choices using maximum likelihood estimates. As an example, if the participant samples 5 beads on a trial, she has a sequence of 6 binary choices on the trial (000001, with 0 for continue and 1 for stop). Different models differ in how the likelihood of generating a specific choice (0 or 1) varies with the cost or evidence observed before the choice. For one-stage models, where all decision variables control the choice in one stage, the influence of cost- or evidence-related variables is fixed across experimental conditions. In contrast, for two-stage models, the decision variables that control the second stage exert variable influences on the choice, because the probability for the second stage to be recruited varies with experimental conditions. The observed choice patterns in the experiment thus allowed us to discriminate different models, including one- and two-stage models.

For a specific fitted choice model, we could compute the second-thought probability, whenever applicable, as well as the probabilities of choosing to stop sampling at each stage. With this information, we then fit the corresponding DT model to the participant’s DTs to estimate the DT-unique parameters.

We chose to optimize the parameters of choice and DT models in this way instead of optimizing them simultaneously to avoid the computational intractability of fitting a large number of parameters. In addition, choices and DTs can serve as independent tests for the two-stage decision process we proposed.

All coefficients _{k} of decision variables, second-thought probabilities _{1}, and _{2} of DT models were bounded to (0, Inf). Optimization was implemented by the

The Akaike Information Criterion corrected for small samples (AICc) [

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(a) Similar to what we have found for the linear effect of AQ on efficiency, we have found a significant three-way interaction of AQ groups, cost and evidence conditions (_{4,200.83} = 11.03, _{2,132.62} = 4.27, _{132.62} = 0.53, _{132.62} = -2.23, _{132.62} = -2.77, _{2,117.67} = 8.18, _{118.45} = -1.60, _{117.29} = 2.42, _{117.25} = 4.02, _{cost→evidence}−_{evidence→cost}; _{2,101} = 5.96, _{101} = -2.81, _{101} = -3.175,

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Gray, blue, and red lines respectively denote data, the best one-stage model predictions, and the best two-stage model predictions. Each panel is for one participant, with each of its sub-panels for one cost and evidence condition. Panels are arranged by participants’ AQ (marked at the top-left corner) ascendingly from left to right and from top to bottom. For most participants, the observed DT distributions were bimodal and were better predicted by the best-fit one-stage model than by the best-fit one-stage model. C: Cost, E: Evidence.

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The observed decision times had a significant decreasing trend with the increase of sample number (

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(a-b) Mean ΔAICc and ΔBIC for every model. ΔAICc or ΔBIC for a specific model was calculated for each participant with respect to the participant’s best-fitting model (i.e. lowest AICc or BIC) and then averaged across participants. Error bars denote standard errors. Model comparisons based on AICc and BIC led to almost the same results. (c-d) Individual participants’ ΔAICc and ΔBIC for every model. In the heatmaps, each column is for one participant, arranged in ascending order of AQ from left to right. Each row is for one model, arranged in the same order as in a-b.

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Gray, blue, and red lines respectively denote data, the best one-stage model predictions, and the best two-stage model predictions. Each panel is for one participant, with each of its sub-panels for one cost and evidence condition. Panels are arranged by participants’ AQ (marked at the top-left corner) ascendingly from left to right and from top to bottom. For most participants, the observed sample size distributions were better predicted by the best-fit one-stage model than by the best-fit one-stage model. C: Cost, E: Evidence.

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There were little correlations between cost-evidence strategy index (_{cost→evidence}−_{evidence→cost}) and participants’ age (a) or IQ score (b); cost-evidence strategy index did not differ between genders either (c).

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Correlations between cost-evidence strategy index (_{cost→evidence}−_{evidence→cost}) and sampling bias (signed deviation from the optimal number of sampling, denoted _{s})) under different cost and evidence conditions were consistent with what we would expect if AQ affects these measures through cost-first vs. evidence-first preference in decision process. See

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Each circle denotes one participant.

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Following Jones et al. [

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