Social information and spontaneous emergence of leaders in human groups

Abstract

Understanding the dynamics of social networks is the objective of interdisciplinary research ranging from animal collective behaviour to epidemiology, political science and marketing. Social influence is key to comprehending emergent group behaviour, but we know little about how inter-individual relationships emerge in the first place. We conducted an experiment where participants repeatedly performed a cognitive test in a small group. In each round, they were allowed to change their answers upon seeing the current answers of other members and their past performance in selecting correct answers. Rather than following a simple majority rule, participants granularly processed the performance of others in deciding how to change their answers. Toward a network model of the experiment, we associated a directed link of a time-varying network with every change in a participant's answer that mirrored the answer of another group member. The rate of growth of the network was not constant in time, whereby links were found to emerge faster as time progressed. Further, repeated interactions reinforced relationships between individuals' performance and their network centrality. Our results provide empirical evidence that inter-individual relationships spontaneously emerge in an adaptive way, where good performers rise as group leaders over time.

1. Introduction

Many animals use social information [1,2], and humans are no exception [3]. The use of social information is often regarded as an adaptive strategy that is pursued to improve decision accuracy when personal information is uncertain [4,5]. Social information is favoured over personal information when the utility of social information outweighs the cost associated with obtaining knowledge from the direct interaction with the environment [6,7]. Therefore, social information is an essential commodity that might influence individual fitness [8,9] and foster social and cultural evolution [10–13]. However, little is known about the mechanisms governing the use of social information over time [14], let alone how individual differences in the use of social information might influence human response.

In groups, individuals can capitalize on social information to improve decision accuracy [15–18]. The underlying mechanism of collective intelligence lies in the wisdom of the crowd [19], where a group mean or median is close to the truth. Individuals can improve decision accuracy by adjusting their opinion toward the majority and counterbalancing judgement errors among individuals [20]. For example, experimental evidence supports that human groups improve accuracy in navigation to a target by pooling directional uncertainty among individuals [21]. In small groups, however, individuals may exploit social information in a more complex way than simply conforming to the majority, if they could remember the information utility of each member over repeated interactions. This may also apply to large groups when the use of social information is supported by local interactions with the same neighbours. In such cases, individuals could discriminate social information based on information utility, and consequently, the premise of the wisdom of the crowd might not hold.

The use of social information is advantageous when individuals copy good performers [22,23]. In this sense, it is possible that social information is selectively used based upon information utility, thereby shaping the adaptation of social influences in the group. In humans, for example, young children trust information provided by accurate speakers more than that provided by inaccurate ones in language learning [24], and physicians follow research-active peers in the prescription of new drugs [25]. By contrast, the interaction may be masked if social influences are mediated by other factors, such as familiarity [26], homophily [27], dominance [28,29], boldness [30] and social responsiveness [31,32].

The phenomenology of social influence among group members may be viewed as a network, with individuals and social influences mapped into nodes and directed links, respectively. In these social networks, individual differences in the use of social information reverberate in the network topology, where more influential individuals have higher degrees [33]. For large social networks, the degree distribution is often found to follow a power law [34], whereby individuals with high degrees tend to exert disproportionate influence on the whole group. The study of topological properties is often leveraged to identify critical individuals to vaccinate for epidemic prevention and support the rapid spreading of new ideas [35,36].

The presence of influential individuals may constitute an advantage or a burden, depending on their information accuracy. Social influence would lead to better group performance if influential individuals spread accurate information in the group, whereas group performance would be hampered if their information is inaccurate. However, in contrast to burgeoning research on the role of network properties on group performance [35–38], we lack empirical evidence about the mechanisms that underlie the process of network formation and temporal evolution. For example, we presently cannot explain the emergence of group leaders, which lies at the heart of understanding social networks. How do individuals decide whom to follow over interactions in the first place?

In general, the study of network evolution is a rather unexplored field of investigation, with the vast majority of research endeavours focusing on static networks, whose topology is constant in time [39–41]. Here, we investigated the emergence and evolution of a functional network from a simple all-to-all pristine network. Our approach is analogous to seeking how neural circuits function in the brain, rather than how they are anatomically connected [42]. Specifically, we examined how individuals would use social information of others over repeated interactions in making decisions on unfamiliar subjects, given no constraint on the communications among individuals. We hypothesized that: (i) individuals would take into account the performance of others to decide whom to follow in making decisions, rather than adopting a simple majority rule; (ii) with an increase in the accuracy of performance over repeated interactions, individuals would rely more on social than personal information and (iii) as a consequence, good performers would emerge as group leaders, exerting a stronger influence on others over time.

To test our hypotheses, we conducted experiments on small groups of humans where participants repeatedly chose one among multiple answers in a simple cognitive test. In each round, we provided participants social information about current answers of each other group member, along with their own past performance in selecting correct answers at the end of each round. During each round, participants were allowed to change their answers after receiving the information, and these changes were reflected in their performance in the next round. Through the lens of time-varying networks, we analysed the dynamics of the group answers to investigate potential relationships between individual performance and pairwise interactions between individuals. We considered individual performance as a combination of personal information (associated with the individual skill to perform the task) and the ability to use social information, considering that individual fitness would be determined by the combination of the two. To isolate the role of personal information, we conducted an additional experiment where participants were presented only with the performance of others based on their initial answers before seeing the answers of others, thereby removing their ability to correctly use social information from the performance.

2. Material and methods

2.1. Experimental set-up

The experimental set-up consisted of a computer, a screen and custom-made clickers. Each clicker housed a microcontroller (LightBlue Bean+, Punch Through, Minneapolis, MN, USA) in a three-dimensional printed case (15.7 × 4.6 × 3.8 cm, length × width × height), with five pushbuttons labelled as A, B, C, D and E. The clicker was wirelessly connected to the computer through Bluetooth, and the computer recorded clicker identity, button label and time (in ms) when a button was pressed. The computer was able to receive and record multiple signals without data collision. A 55-inch screen mounted on the wall was used to display a cognitive test, followed by visualization of the button press via multiple clickers in real time. The test was programmed in Python.

Social influence was examined through a subitizing test, a type of cognitive test to estimate the number of objects in a flash [43]. On a screen, we displayed a number of dots ranging from 8 to 12 for 0.5 s (figure 1). Immediately after the image disappeared, we displayed on the screen the multiple answers, each of which corresponded to a button label on the clicker. The multiple answers were generated such that the correct answer was in either the second, third or fourth smallest number of five consecutive numbers. The number of dots and the order of the multiple answers were randomized to avoid a predictable pattern of the correct answer.

Figure 1.

Screen display during the experiment. (a) Subitizing test, where an image of dots is flashed on the screen for 0.5 s, followed by the display of multiple choices on the bottom. (b) Social information. Bar graph indicates the past performance of each participant (%), with the current answer selection on the top. Horizontal bar indicates the remaining time to change the answer. (Online version in colour.)

2.2. Experiment procedure

We recruited volunteers from university students. Upon consent, participants were randomly assigned to a group of five and escorted together as a group to a room. Each participant was handed a clicker with a unique number and a colour name on the back to help identify own performance displayed in a bar graph on the screen while keeping anonymity of other participants.

We instructed participants to estimate the number of dots and press the corresponding button based on their estimation. When the last participant pressed the button, the answers of all participants were displayed on the screen. Then, participants were allowed to change their answers as many times as desired within 10 s by pressing buttons, without verbally communicating with one another. Changes of the answers were displayed on the screen in real time, and a countdown timer was visualized through a decreasing horizontal bar displayed at the bottom of the screen. In addition to the current answers, we displayed on the screen a cumulative performance of each participant in a bar graph, whose colour corresponded to the colour name written on the back of the clicker (figure 1). Individual performance was quantified as the percentage of correct answers over the past rounds, based on the last answer the participant selected during the 10-s time window in each round.

After two practice trials, each group performed 10 rounds consecutively. We explained to participants that the objective of the experiment was to increase individual performance with respect to the entire population tested, not to the other participants in the same group. Each group was presented with the same set of images in the same order. A total of 17 groups (n = 85) were tested.

To compare our results with those from the classic wisdom of the crowds [44], we performed an additional experiment in which participants were presented with the cumulative performance of each participant over the past rounds based on their initial answers, before the start of the 10-s window, instead of the last ones. Therefore, in this setting, individual performance was simply based on the ability to guess the correct number of dots without using social information. We tested 10 groups (n = 50) in the additional experiment.

2.3. Social influences on answer choices

We tested whether participants were influenced by social information in changing their answers during the experiment. In each round, we recorded each participant's initial answer (that is, the answer chosen before all participants' answers were displayed on the screen) and all the changes after all participants’ answers were displayed, within the 10-s window when they could all see the answers of the others and change theirs. We counted the instances where participants changed their answers to those of others. When one participant changed the answer to that of two or more participants with the same answer, we counted the instances by tallying these cases.

To test whether participants changed their answer to those of specific others, we counted the instances in the same way after randomly shuffling the group members. The simulated groups modelled the hypothetical scenario in which participants did not see others' answers. We compared the observed mean number of changes per group with the simulated groups with 1000 permutations.

2.4. Influence of performance on leadership

To explore the influence of displaying participants’ past performance on changing their answers, we investigated the probability of a participant being copied by others in relation to the current answers and past performance. Specifically, we fitted a generalized linear mixed model (GLMM) to the occurrence of being copied. As explanatory variables, we used the numerical majority score and the weighted majority score and we also examined their interaction. These majority scores were computed with respect to each participant, by removing cases in which all the participants had the same answer, which could not be conducive to an instance of copying behaviour.

In each round, for the generic participant i (i = 1, 2, … , 5), the numerical majority score was calculated as the cardinality of Sⁱ, where Sⁱ is the subset of participants (including participant i) whose current answers are the same as the participant i. Thus, it ranged from 0.2 when all participants had a different answer from participant i, to 0.8 when three other participants shared the same answer of participant i. The weighted majority score accounted for previous performance. With respect to participant i, the weighted majority was calculated as ${\sum }_{\hspace{0.17em}j\in S^i}{X}_j/{\sum }_{\hspace{0.17em}j=1}^5{X}_j$, where X_j is the cumulative performance of participant j. Thus, it ranged from 0 when participant i (and any other who presently shared the same answer) made all wrong answers in the past, to 1 when the answer of participant i was presently supported by all the participants with nonzero performance.

The model was specified with binomial errors and a logit link function, and participant nested within the group as a random effect. Both explanatory variables were standardized by subtracting the mean and divided by the standard deviation. The first round of the experiment was removed from the analysis because participants had no information with regard to performance. Statistical significance of the interaction term was ascertained using a likelihood ratio test by comparing the model with no interaction term.

2.5. Evolution of the social network

We investigated the dynamics of social influence from a network perspective. Specifically, we constructed a network where the participants were the nodes and links were consequences of social influence. In each round, we generated a directed link from participant i to participant j when participant i changed the answer to that of participant j. Here, links determine how social networks should function, rather than a structure that constrains communication between nodes. Multiple links were generated from a single node when a participant changed the answer to one of multiple participants. Thus, the network generated at the end of each round describes how participants used the social information during the round.

We tested the rate of growth of the network over time using a linear mixed model. In the model, we specified round as an explanatory variable, the number of links generated in a group in the corresponding round as a response variable, and group as a random effect. Statistical significance was ascertained using a likelihood ratio test by comparing the model with a null model.

2.6. Network centrality and performance

We investigated relationships between participants' performance and their social influence over the rounds. To that end, we constructed an integrated network by including all links that were generated over the rounds and weighting them with the number of occurrences. As a measure of network centrality, we adopted PageRank [45]. Initially proposed to determine the ranking of web pages for a search engine, PageRank is widely used to quantify the nodes’ influence in networks. The advantage of PageRank compared to other centrality measures lies in its ability to accurately quantify the importance of a node by taking into account not just the local links occurring on the node but the whole network topology [46]. A node has a high PageRank score if it influences other nodes that are strong influencers.

The implementation of PageRank relies on a damping factor q, which models a noise effect. In its original incarnation, q represents the probability of jumping to a random web page. In our case, the damping factor defines a probability of spontaneous changes of answers in the absence of social influence. Through trials where a different set of participants performed the same experiment while being alone in a room (n = 14), we estimated q = 0.036. From the adjacency matrix A, where the element a_ij is the number of occurrences that participant i changed the answer to that of participant j, we calculated a modified adjacency matrix A′ = (1 – q)A + qB, where B is a matrix with 1 for all elements. Then, A′ was converted to a random walk matrix by normalizing the elements such that elements on each row sum up to 1, and PageRank of each node was computed through a power iteration method [45].

To test whether the relationships between participants' performance and their social influence changed over the rounds, we obtained a weighted network by integrating the 2nd–5th rounds, 6th–10th rounds and all rounds, and tested a significance of Pearson's correlation coefficient between performance and PageRank score using a t-test.

2.7. Simulation study

To support the emergence of correlation between performance and network centrality in the experiment, we simulated the behaviour of participants using a simple decision rule. In the simulation, we formed a group of five individuals (i = 1, 2, … , 5) whose probabilities of choosing the correct initial answers (P_i) were randomly drawn from a beta distribution fitted to the observed data (α = 2.91, ß = 3.09). In each round, every individual chose the initial answer from five possible answers. The correct first answer was chosen with probability P_i, while any of the other answers had a probability of being chosen (1 – P_i)/4. After selecting their first answer, they used social information with probability P_social to adjust their answers and ignored social information with probability 1 − P_social. When they opted to use social information, they changed their answers with a probability proportional to a weighted majority of each answer. The weighted majority of the answer was calculated as the proportion of the number of individuals who chose the answer, where each individual's weight was multiplied by the past performance of the individual. To attain a number of copying instances similar to experimental observations (approximately nine instances per group over all rounds), we set P_social = 0.35. We also included a spontaneous change of answers with a probability of 0.04, based on observed data of single-user experiments. Each group repeated this process for 10 rounds.

Through simulated data, we investigated the correlation between individuals' performance and their influence in a network in the same way we analysed the observed data. We obtained networks by integrating the 2nd–5th rounds and 6th–10th rounds and calculated a correlation coefficient between individuals’ performance and their PageRank scores, respectively. We tested from 10 to 30 groups, with each group simulated 100 times.

3. Results

3.1. Social influence on decision making

Participants in a group of five performed 10 consecutive rounds of a cognitive test to estimate the number of dots displayed on a shared screen for 0.5 s. In each round, participants were asked to choose one from multiple answers using a custom-made clicker, without verbally communicating with one another. When all participants chose their initial answers, the screen displayed the current answers of all members along with their past performance in selecting correct answers (%). The presentation of the past performance differed between the main experiment and the additional one: in the main experiment, it reflected the final answer after the 10-s window when each participant sees the answers of others and can change their answer, while in the additional experiment, the displayed performance was based only on the initial answers before the 10-s window.

In the main experiments (17 groups, n = 85), participants chose their initial answers in 4.3 ± 2.4 s (mean ± s.d.), after the dots disappeared on the screen. When they changed the answers, the change took place in 5.9 ± 2.5 s after seeing the answers of others. In the additional experiment (10 groups, n = 50), participants chose their initial answers in 4.5 ± 2.7 s, and the first change took place in 6.7 ± 3.1 s after seeing the answers of others.

In each group, there were on average 9.1 instances (ranging from 0 to 24) over all rounds of the main experiment where participants changed the answers to those of others, and 0.6 instances (ranging from 0 to 3) where they changed the answers to those no one had selected at that time. The observed mean value of copying instances was significantly higher than the mean values obtained by chance if participants would have changed their answers without knowing the answers of others (95% intervals: 5.4–7.0; figure 2a), indicating that participants copied the answers of specific others when they changed answers. In the additional experiment, we observed on average 12 instances of answer changes (ranging from 0 to 58), which was significantly higher than in the main experiment (generalized linear model with Poisson errors, ${\chi }_1^2$ = 5.029, p = 0.025). There were 0.9 instances (ranging from 0 to 5) where they changed the answers to those no one had selected at that time. Again, the observed mean value was significantly higher than random (95% intervals: 7.9–10.4; figure 2b).

Figure 2.

The observed mean number of instances where participants changed their answers to those of others, compared with the distribution of mean values that would be obtained by chance if individuals did not see the answers of others. (a) When participants were shown the cumulative performance of others based on the last answers at each round in the main experiment, (b) when participants were shown the cumulative performance of others based on the first answers at each round in the additional experiment. An arrow represents the observed mean number of instances per group over all rounds, and grey bars indicate the probability density estimated from 1000 permutations that randomly swap group members to estimate the lack of social information use. The significantly higher observed mean value indicates that participants copied others in changing their answers. (Online version in colour.)

Over all rounds, participants in the main experiment chose correct answers 47.8 ± 20.9% (mean ± s.d.) based on their answers before seeing those of others, and 50.5 ± 20.5% after seeing them. Although the increase in performance was small, participants significantly increased their performance by changing their answers (paired t-test, t = 2.50, d.f. = 84, p = 0.014). In the additional experiment, participants chose correct answers 43.3 ± 22.7% based on their initial answers, and 47.3 ± 22.4% based on their final ones. Again, participants significantly increased their performance by changing their answers (paired t-test, t = 2.70, d.f. = 49, p = 0.009). There was no significant interaction between the experiments and the increase in performance (linear mixed model with the participant as a random effect, ${\chi }_1^2$ = 0.617, p = 0.432).

At a group mean level, changing answers resulted in only a weak increase in the probability of choosing correct answers in the main experiment (paired t-test, t = 2.11, d.f. = 16, p = 0.051). Similarly, in the additional experiments, where participants were presented with the performance of others based only on their initial answers, there was no significant increase in group mean performance (t = 1.77, d.f. = 9, p = 0.111).

3.2. Rules on social information use

We tested whether participants changed their answer to those of specific others by simply following the numerical majority of the group or granularly taking into account individuals' performance. In a GLMM, we specified numerical majority, weighted majority and their interaction as explanatory variables, and the number of instances in which participants were copied by others as the response variable. The numerical majority was measured as the proportion of the number of participants with the same answers of the participant, and the weighted majority was measured as a majority vote weighted by individuals’ performance.

We found a significant interaction between the numerical majority and the weighted majority, both in the main and additional experiments (binomial GLMM with individual nested within group as a random effect, likelihood ratio test against a model without the interaction, ${\chi }_1^2$ = 4.074, p = 0.044 in the main experiment; ${\chi }_1^2$ = 27.941, p < 0.001 in the additional experiment), indicating that the numerical majority alone did not explain the probability of participants being copied by others (figure 3). For example, participants were more likely to be copied if their performance were good, even if their answers were the minority of the group (figure 3).

Figure 3.

Probability of being copied as functions of the numerical majority (x-axis) and the weighted majority (y-axis). (a) When participants were shown the cumulative performance of others based on the last answers at each round in the main experiment, (b) when participants were shown the cumulative performance of others based on the first answers at each round in the additional experiment. A significant interaction between the two explanatory variables indicates that individuals did not simply use a numerical majority rule in changing their answers. (Online version in colour.)

3.3. Evolution of social networks

We associated a directed link of a time-varying network with every change in a participant's answer that mirrored the answer of another group member in each round. In the main experiment, the network grew over time with a varying rate (figure 4), whereby links were found to emerge faster as time progressed (LMM with the group as a random effect, likelihood ratio test against a null model, ${\chi }_1^2$ = 5.509, p = 0.019; figure 5). By contrast, we did not find a network growth over time in the additional experiment (${\chi }_1^2$ = 0.107, p = 0.743).

Figure 4.

An example of network evolution. The directed links were generated when one individual changed their answer to that of another. (a) When participants were shown the cumulative performance of others based on the last answers at each round in the main experiment, (b) when participants were shown the cumulative performance of others based on the first answers at each round in the additional experiment. Arrow width identifies the number of such instances, while the node size and colour represent network centrality and performance as a cumulative score, respectively. (Online version in colour.)

Figure 5.

The number of links generated in each group in each round. (a) When participants were shown the cumulative performance of others based on the last answers at each round in the main experiment, (b) when participants were shown the cumulative performance of others based on the first answers at each round in the additional experiment. Points and vertical lines are means and standard errors, respectively. Lines indicate significant (solid) and non-significant (dashed) trends. (Online version in colour.)

Social influence in the network was quantified through a PageRank score by integrating the network over the rounds [45]. In the main experiment, there was an overall significant correlation between individuals' performance and their network centrality (r² = 0.242, t = 2.268, d.f. = 83, p = 0.026; figure 6). The correlation was weak in the first half of the trials (r² = 0.182, t = 1.685, d.f. = 83, p = 0.096), while it became stronger in the second half (r² = 0.251, t = 2.336, d.f. = 83, p = 0.021). That is, good performers emerged as group leaders over time, exerting stronger influence on others. Similarly, in the additional experiment, the correlation between individual performance and network centrality became stronger over time (r² = 0.011, t = 0.074, d.f. = 48, p = 0.942 in the first half; r² = 0.301, t = 2.184, d.f. = 48, p = 0.034 in the second half). However, there was no overall significant correlation (r² = 0.027, t = 0.184, d.f. = 48, p = 0.855).

Figure 6.

Correlation between individual performance and network centrality in the first half of the trials (left), the second half of the trials (centre) and all trials (right). Closed circles indicate the estimates when participants were shown the cumulative performance of others based on the last answers at each round, and open circles indicate the estimate when participants were shown the cumulative performance of others based on the first answers at each round. Vertical lines indicate standard errors, and a dashed horizontal line indicates r² = 0. (Online version in colour.)

To explain the observed trend, we simulated the network evolution using a simple behavioural rule. In the simulation, individuals probabilistically changed their answers proportional to those of others weighted by their performance. We simulated 10–30 groups of five, with 100 times each, and calculated a correlation coefficient between performance and network centrality in the same way. The results confirmed the observed trend, where a stronger correlation between performance and network centrality emerged over time through the use of social information (see electronic supplementary material).

4. Discussion

We presented empirical evidence of the evolution of social networks in small groups of humans, where group leaders spontaneously emerge over repeated interactions. Individuals used social information at a greater extent over time, and the accuracy of social information played a role in modulating the selective use of social information. Consequently, we observed stronger relationships between individuals’ performance and their social influence over time, where individuals with higher performance emerged as group leaders.

The rate of growth of the network was not constant in time, whereby links were found to emerge faster as time progressed. This may indicate the adaptive use of social information, considering that social information of others could become more reliable over repeated interactions. That is, starting with no prior belief in the performance of others, individuals could gauge more accurate posterior distributions on the performance of others through Bayesian updating, which often underlies decision-making rules in humans [47]. Consequently, individuals could differentiate the utility of social information of others and incorporate the differences in decision making, rather than simply applying a majority rule [48]. Similarly, individuals might have gauged more accurate information about their own performance over repeated trials. Therefore, leaders and followers might spontaneously emerge in groups through a trade-off between social and personal information [6].

The selective use of social information reinforced relationships between individuals' performance and their social influence over the course of the network evolution. Such relationships could not only enhance individual performance but also stabilize the emergent group response against erroneous information. A theoretical study demonstrated a similar phenomenon in network evolution under a repeated Prisoner's Dilemma game, where cooperators emerge as group leaders and stabilize group dynamics [49]. In addition to individual behaviour, simulation studies have demonstrated enhanced group behaviour through dynamic reinforcement of the relationships between network centrality and individual attributes, such as reputations and trustworthiness [50,51]. In our experiments, however, we observed a significant improvement in the performance at an individual level, but at a group level, we only registered a weak trend. This could indicate that social information about the performance of others might lead to improvement in individual performance, but not necessarily to a wisdom of the crowd.

Additionally, we explored a case in which participants were presented with the performance of others, only based on their ability to correctly identify the number of dots on the screen without using social information. In such a case, we still observed the coevolution of network topology and individual attributes, where good performers emerged as group leaders over time. While participants in the main experiment used social information more often over time, in the additional experiment, more links were created in early rounds and the rate of growth of the network did not change over time. Thus, in the main experiment, use of social information was associated with its utility, whereby it was accessed when it reflected more accurately the fitness of group members. Although the mechanisms that caused the difference were unclear, it is interesting to observe that such contrasting behavioural responses were elicited by a difference in social information.

Although our results demonstrate the evolution of social networks through repeated interactions, other factors may explain the emergence of social networks. In general, individuals may be able to discriminate the utility of social information of others through proxy traits that could correlate with it. For example, children trust information from familiar adults compared to non-familiar ones [52], and in bottlenose dolphins, Tursiops spp., social networks in a companionship are largely explained by age- and sex-related homophily [27]. It is possible that social information of familiar or similar others would be more pertinent and have a higher utility. Similarly, in guppies, Poecilia reticulata, females copy the mate choice of older [53] and larger females [54], which likely indicate more experience in decision making. In our experiment, however, participants interacted with one another anonymously, and the only social information provided was their current answers and past performance. This allowed us to mitigate the effect of other personal traits that may interfere with the process of network evolution.

The premise of a coevolution of network topology and individual attributes, empirically demonstrated in our work, is also at the core of computational models of opinion dynamics, in which individuals with similar opinions are linked to each other [55]. However, in our study, the emergence of links is triggered by differences rather than similarities. More specifically, social influence is manifested through individual differences in performance, thereby creating a positive feedback loop between individual performance and social influence. This adaptive mechanism should be related to the utility of social information, which potentially pertains to the probability distribution of fitness [56] and contrasts a mere attitude to conform to others. While we show that this adaptive mechanism positively contributes to individual performance, we cannot exclude the possibility that, in other settings that are more prone to changes in environmental factors, social information might adversely affect individual performance [57,58]. In such cases, reinforcement between network topology and individual attributes could steer individuals toward suboptimal or even detrimental trajectories.

We studied network evolution by treating multiple answers as mutually exclusive. Owing to the numerical nature of the multiple answers we provided, individuals could have changed their answers toward those of others by compromising between social information and personal beliefs [59]. We analysed only the drastic instances where participants changed their answers to those of others, which may becloud our ability to detect the selective use of social information. Nonetheless, we were able to unveil network evolution and highlight reinforced relationships between individuals' performance and their social influence, supporting the robustness and generality of our findings.

We presented empirical evidence of network evolution and spontaneous emergence of group leaders. The relationships between individuals’ performance and their social influence were reinforced over time, which can be underpinned by an adaptive mechanism through eco-evolutionary dynamics [60]. In reality, however, the utility of social information could be multidimensional or frequency-dependent. Further, different from a pristine network like the one analysed herein, it may be more common that new individuals will join existing networks. In such a case, it is tenable that the existing network topology will shape the emergence of group leaders. Understanding how these additional layers of complexity would steer the network evolution is our next step.

Ethics

The experiment was approved by the New York University Institutional Review Board (IRB-FY2017-898).

Data accessibility

Data are available in the electronic supplementary material.

Authors' contributions

S.N. and M.P. designed research. E.K. performed experiments. All authors contributed to data analysis. S.N. wrote the initial draft, and S.N., L.Z. and M.P. contributed to writing the final manuscript.

Competing interests

The authors declare no conflict of interest.

Funding

This study was supported by National Science Foundation CMMI 1561134 and CBET 1547864.