How conformity can lead to polarised social behaviour

Folco Panizza1,2*, Alexander Vostroknutov3, Giorgio Coricelli4,5,

1 Center for Applied and Experimental Epistemology, Vita-Salute San Raffaele University, Via Borromeo, 41, 20811 Cesano Maderno (MB), Italy 2 Center for Mind/Brain Sciences, University of Trento, Via delle Regole 101, Mattarello (TN), Italy 3 Department of Economics (MPE), Maastricht University, Tongersestraat 53, 6211LM Maastricht, The Netherlands 4 Department of Economics, University of Southern California, 3620 South Vermont Ave. 300, Los Angeles, CA 90089, USA 5 LaPsyDE´ - UMR CNRS 8240, La Sorbonne, 46 rue Saint-Jacques, 75005 Paris, France

* Corresponding author: [email protected]

Abstract

Learning social behaviour of others strongly influences one’s own social attitudes. We compare several distinct explanations of this phenomenon, testing their predictions using computational modelling across four experimental conditions. In the experiment, participants chose repeatedly whether to pay for increasing (prosocial) or decreasing (antisocial) the earnings of an unknown other. Halfway through the task, participants predicted the choices of an extremely prosocial or antisocial agent (either a computer, a single participant, or a group of participants). Our analyses indicate that participants polarise their social attitude mainly due to normative expectations. Specifically, most participants conform to presumed demands by the authority (vertical influence), or because they learn that the observed human agents follow the norm very closely (horizontal influence).1

Author summary

What drives people to extreme acts of generosity? What causes behaviour that is unduly spiteful? This study explored how our social decisions polarise. Participants chose whether to spend money to increase or decrease the earnings of an unknown person. Halfway through this task, they observed another agent playing. The agent took participants’ choices to the extremes: if for instance the participant was moderately generous, it spent considerable sums to help the other. Participants conformed regardless of whether the agent was a computer algorithm, a person, or a group of people. We tested several competing explanations of why this happened with the help of cognitive modelling. Our analyses identify two factors behind polarisation: willingness to comply with the experimenter expectations (social desirability), and concern about appropriate behaviour (norm conformity). Our approach provided insight into how social choices are influenced by others, and could be applied in the study of conformity in other types of decisions.

1A first preregistered version of this study is available at osf.io/th6wp, all changes to the original protocol are listed in S1 Methods.

September 7, 2021 1/36 Introduction 1

Recent years have seen a growing concern with online discourse promoting violence, 2

such as cyber-bullying or hate speech [1]. Increasing exposure to uncivil commenting, 3

besides taking substantial psychological and societal toll [2], is thought to reinforce 4

users’ toxic behaviours [3, 4], political polarisation [5], or their perception of political 5

divide [6]. Conversely, viral trends can also lead to pro-social outcomes: learning about 6

others’ donation choices increases individuals’ willingness to give to charity [7, 8]. 7

Evidence suggests that fund-raising success of charitable initiatives is predicted by how 8

much they are shared by social network users [9], or by how concerted the network 9

structure is [10]. If people’s attitude becomes more charitable or more malevolent in 10

these contexts, this is at least partly due to social conformity [11–13]. 11

Insights on the cognitive mechanisms behind anti- and prosocial conformity come 12

from the literature on attitude alignment and preference learning [14, 15]. These studies 13

have spanned a variety of domains such as attractiveness ratings [16], food [17], risk 14

preferences [18–20], moral behaviour [21], effort [20], and inter-temporal 15

decisions [20, 22–25]. At a brain level, learning about others’ attitudes or preferences 16

appears to alter the value representation of choices [16, 21, 22, 24] or even reward 17

signals [19], while not necessarily affecting one’s private preferences [18]. In addition, 18

features such as choice variability [23] or attitude extremeness [25] seem to be significant 19

predictors of conformity. 20

Recent studies have also brought attention towards the behavioural aspects of social 21

conformity [8, 26–29]. The work by Dimant and colleagues shows for instance how 22

anti-social models beget a higher degree of conformity compared to pro-social models, 23

and that social proximity to the model is also a strong predictor of conformity. 24

While this research helps untangling the brain bases and behavioural ramifications of 25

preference conformity, it remains largely unclear why exactly people shift their attitude 26

in the direction of others’ behaviour in general, and their social attitude towards other 27

individuals in particular. In this paper we test several competing mechanisms that were 28

proposed as explanations of attitude conformity. We consider five competing hypotheses. 29

The time-dependence hypothesis predicts that people change their social attitude even 30

in the absence of any observation. Indeed, there is preliminary evidence that during 31

strategic interactions, participants’ behaviour becomes more self-oriented with 32

time [30–33]. The contagion hypothesis [19, 34] posits that attitude conformity is the 33

result of some kind of automatic imitation of an agent’s behaviour, irrespective of its 34

nature or relationship with the observer. This hypothesis predicts that conformity will 35

occur regardless of whether the observed agent is human or non-human. The compliance 36

hypothesis states that participants could change attitude due to the mere presence of an 37

authority, in our case the experimenter [35]. This hypothesis predicts that a portion of 38

participants would change their attitude in any context where they think they are 39

expected to, rather than actually reacting to others’ behaviour. The preference learning 40

hypothesis [23] posits that people are unsure about what their own preferences are, but 41

they can learn them from the behaviour of others, assuming that the agent’s and 42

observer’s preferences come from a common distribution. Other people’s choices can 43

thus be used to learn how one wants to behave, rather than how one ought to behave. 44

Since preference learning should decrease in the process of learning others’ choices, a 45

second prediction of this hypothesis is that participants’ behaviour should become more 46

consistent after learning. 47

The last hypothesis that we test, norm learning, states that attitude conformity 48

stems from learning what behaviour is socially appropriate or how much social 49

appropriateness matters in a given context. We conjecture that in many real life 50

situations there is a considerable amount of uncertainty about what constitutes a social 51

norm or how salient it is [36]. Furthermore, many studies have shown that people have 52

September 7, 2021 2/36 a strong preference to follow norms conditional on others following them as well [37, 38]. 53

Thus, observing other people’s behaviour should reveal either information about what 54

others believe is ”the right thing to do” or at least how frequent or infrequent deviations 55

from the norm are [33, 39]. This hypothesis makes two separate predictions: that 56

participants conform after changing their beliefs about which norms are in place (norm 57

uncertainty), or rather that participants are aware of the existing norms, but conform 58

after learning how strictly the norm is followed (norm salience). 59

To our knowledge of the various literatures surveyed, these five hypotheses exhaust 60

the list of tested explanations of conformity in decision making. Therefore, our 61

approach is to falsify as many hypotheses as we can, and attribute the behaviour to the 62

hypotheses that we cannot reject. To disentangle the predictions of these five 63

hypotheses, we use a series of between-subjects experimental conditions. In all 64

conditions participants play a resource-allocation game where in each round they choose 65

between two money allocations to themselves and another unknown participant. 66

Halfway through the game, participants are asked to predict and learn the choices made 67

by another agent in the same task. Depending on the condition, the agent is either a 68

computer, a previous participant, or a group of previous participants (in the Baseline 69

condition participants do not observe anyone). After the main part of the experiment, 70

we administer another task measuring the normative beliefs of participants. 71

We use a series of cognitive models of participants’ decisions to analyse behaviour in 72

the resource-allocation game. These models link behaviour to the mental processes 73

associated with the different hypotheses. Testing of the competing mechanisms behind 74

social conformity is then performed by comparing social attitudes before and after the 75

manipulation phase, and using additional evidence collected during and after the main 76

task. Model estimation is essential for distinguishing different sources of attitude 77

variability, as for instance participants’ own variability in behaviour and attitude 78

changes induced by learning. 79

Materials and methods 80

Participants were recruited through the recruitment system of the Cognitive and 81

Experimental Economics Laboratory (CEEL) at the University of Trento and contacted 82

via e-mail. The local Ethical Committee of the University of Trento approved the study 83

and subjects provided written informed consent prior to their inclusion. No particular 84

exclusion criteria were defined, with the only exception that participants should not 85

have taken part in other experiments involving a similar task. Payments were made in 86

cash and varied depending on participants’ choices. 87

To determine the sample size necessary to detect a change in social attitude, we 88

conducted a power analysis using G*Power [40] aiming to obtain .95 power, .05 α 89

probability, and at least a small-to-medium effect size (Cohen’s d = 0.35 for all tests). 90

This effect size figure was recently proposed as a plausible mean prior for experiments in 91

social psychology [41]. As the original hypotheses were directional (i.e., participants’ 92

attitudes shift towards the agent’s attitude), tests considered were one-tailed one-sample 93

t-tests against constant, and two-tailed two-sample t-tests (for post-hoc pairwise 94

comparisons between conditions, uncorrected). Calculation yielded a sample size of 90 95

participants in order to achieve the required power across all conditions. Due to an 96

unforeseen limit in the size of the recruitment pool however, the samples of the last two 97

conditions in order of acquisition were smaller than this pre-specified size (74 and 66 98 2 participants). 99

2The unbalance in sample size across experimental conditions is not particularly concerning for our analyses, as the tests that we run in the results to compare conditions are non-parametric and therefore do not require the assumptions typically achieved with samples of similar size such as homoscedasticity.

September 7, 2021 3/36 376 participants (age M = 22, SD = 2, 167 males) took part in the experiment. 100

Data from four participants had to be excluded due to failures in the software, as well 101

as the data from three other participants who already participated in a pilot version of 102

the study. Analyses were thus conducted on 369 participants. 103

Resource-Allocation Game 104

During each trial of the task, participants observed an allocation of points (1 point = 105 0.10€) distributed between themselves and an unknown other participant, the recipient. 106 Participants were then asked whether they preferred the current allocation of points or 107

a default allocation (100 points to oneself, 50 points to the recipient, Fig 1B). 108

Participants played the game twice, with different allocations, before and after the 109

manipulation phase. At the end of the experiment, participants were randomly paired, 110

and one participant in each pair was randomly selected: one of the selected participant’s 111

decisions was randomly sampled and implemented for payment (i.e. the selected 112

participant earned the points for herself and the non-selected participant received the 113

points for the other). 114

101 alternative allocations (102 for Baseline condition) and the default allocation 115

were drawn from the set of integer allocations closest to the circumference of radius 50 116

centred at (50, 50) (Fig 1A). Compared to the default allocation, these alternatives 117

provided less points to the participant, but could in exchange affect the recipient’s 118

payoffs: half of the alternative allocations were more advantageous for the recipient 119

than the default allocation (“prosocial” trials), whereas the other half left the recipient 120

worse off (“antisocial” trials). In addition, 9 alternative allocations were more profitable 121

for the participant (making her earn more than 100 points) whereas the recipient gained 122

50 points, as in the default allocation. 123

To define the allocations around the circumference, we first considered all integer 124

coordinates within one point tolerance from the circumference (i.e., all values between a 125

circumference of radius 49 and a circumference of radius 51). Second, only points 126 ◦ ◦ between 112.5 and −112.5 were included for the analyses; this range excluded 127

allocations that were too extreme (e.g. (15, 15) or (0, 50)). Third, we excluded 128

allocations with more points to oneself than the default option, because gains for the 129

player risk to overshadow the difference in points for the other. Likewise, we excluded 130

allocations with the same points to the other as the default option. Finally, we 131

eliminated allocations that give more than 100 or less than 0 to the other player. This 132

procedure yielded 406 allocations in total; these were then divided in four subsets, two 133

of 101 and two of 102 trials, all evenly distributed around the arc of the circle. The two 134

subsets of 102 trials were used in the Baseline condition (in the choice parts of the task), 135

whereas the remaining subsets of 101 trials were used in the other conditions (S1 File 136

contains a full list of trials). 137

The use of the circumference as a way to select trials was based on two 138

considerations. First, the circumference has been used in the previous literature as a 139

measure of social orientation ( [42] is the seminal paper), and should yield comparable 140

results. Second, many models have been adopted in the literature to describe how 141

people value options in social decision-making (e.g., [43–46]); by using allocations 142

around a circumference, most of these models make the same predictions. Agreement in 143

model predictions allowed us to use a very simple utility model (Eq 1), with only one 144

variable defining the attitude of the decision-maker. A simple model greatly simplifies 145

computations and thus helps testing our cognitive predictions concerning attitude 146

conformity and choice consistency. 147

September 7, 2021 4/36 B

A default allocation prosocial allocations antisocial allocations

100 B

o 75 112.5�

50 C

25 points to other �

0 C 50 75 100 points to self �y

Fig 1. Trials in the experiment. The complete list of trials is available at osf.io/th6wp. A: Participants chose between a default allocation (black rhombus) and an alternative allocation, which could be either prosocial (light blue) or antisocial (orange). Allocations were limited to a certain arc of the circumference and to a certain range, with the exception of 9 allocations giving more points to the participant (not shown in the figure). B: resource-allocation game. Participants observed the current alternative allocation and had a maximum of 10 seconds to respond. Decision cues (‘yes’/‘no’) indicated which button to press for each decision (up/down arrows). Points for self and for the other were colour-coded (points for self: red; points for the other: blue) and were presented on the left and on the right of the decision cues. Both cues and points (self/other) switched position randomly across trials. If participants did not answer within 10 seconds, the trial ended, and they were automatically assigned the default allocation. Unanswered trials were considered missing data. After the decision, an inter-stimulus interval of 1 second divided the decision and the feedback. Feedback lasted for 1.5 seconds and displayed the allocation preferred by the participant. The trial ended with an inter-trial interval of 2 seconds. C: manipulation phase. Participants were presented with an alternative allocation, and indicated whether they believed the agent preferred the alternative over the default allocation (‘yes’) or not (‘no’). The choice could be made within 10 seconds, after which it would no longer be valid. After an inter-stimulus interval of 1 second, participants received feedback about their answer. If the prediction was correct, the feedback message ‘correct prediction’ appeared on the screen for approximately 1.5 seconds (minimum 1, maximum 2). If the prediction was wrong or not given in time, a similar feedback message (‘wrong prediction’ or ‘no answer’) appeared on the screen for about the same time, followed by the actual choice of the agent, lasting 1.5 seconds. The name of the agent varied between conditions (Group condition: ‘majority’; Individual condition: ‘participant’; Computer condition: ‘computer’). After the feedback, the trial ended with an inter-trial interval of 2 seconds.

September 7, 2021 5/36 To estimate attitude towards others, we assume that participants can attribute to 148

each allocation of points a unique subjective value. Value of an allocation is computed 149

according to Eq 1: 150

V (πy, πo) = πy + tan(α) · πo, (1)

where πy and πo are respectively the amount of points for oneself (you) and for the 151 other, and α represents the “social value orientation” or social attitude of the 152

participant [47, 48]. The attitude defines how much and in what way the amount of 153

points for the other plays a role in the participant’s decisions; in fact, tan(α) represents 154

how much one point for the other person is worth in terms of one’s own points (e.g., 155 ◦ when α = 30 one point for the other is roughly equal to 0.58 points for oneself). If α is 156

positive (negative), then the higher (smaller) amount of points for the other makes the 157

player better off. A participant with a positive α is said to be prosocial, whereas a 158

participant with a negative α is said to be antisocial. 159

Social attitude—together with other parameters relevant to the decision process—is 160 estimated twice, for choices before (αbefore) and choices after (αafter) the manipulation 161 phase. A separate estimation allows measuring any change in attitude that ensues from 162

the manipulation phase (Cognitive Modelling and Model Comparison). 163

Manipulation Phase 164

In the Computer, Individual, and Group conditions, after the first part of the 165

resource-allocation game, participants were asked to predict the choices of an agent in a 166

different set of alternative allocations (Fig 1C). Participants played 63 trials of the 167

manipulation phase in all conditions except Baseline. Correct predictions were 168

incentivised to ensure that participants paid attention to the task. Participants received 169

immediate feedback after each prediction, so that they could correctly learn about the 170

agent’s attitude. 171 The attitude of the observed agent (αobs) was controlled experimentally 172 unbeknownst to participants. Specifically, if participants displayed a prosocial attitude 173 in the first part of the game (αbefore > 0), they observed an agent with an extremely 174 ◦ prosocial attitude (αobs ≈ 45 , one point for the other equals one point for the self); and 175 vice versa: if participants displayed an antisocial attitude (αbefore < 0), they observed 176 ◦ an agent with an extremely antisocial attitude (αobs ≈ −45 , one point for the other 177 equals negative one point for the self). 178

The behaviour of the observed agents were based on real choices of participants in 179

the Baseline condition taken from either the first or second part of the 180

resource-allocation game. In the Individual condition, the agent was a single previous 181 ◦ ◦ participant, with an estimated α value close to 45 (prosocial agent) or −45 (antisocial 182

agent). In the Group condition, the agent consisted of a group of five previous 183

participants (the size of the group was not mentioned in the instructions). The choices 184

shown to participants referred to the allocation preferred by the majority of the group, 185

that is the modal response. Lastly, in the Computer condition, participants were told 186

that the agent was a computer selecting options according to a predefined criterion. 187

The criterion of the computer agent was in fact to choose exactly as the group in the 188

Group condition. 189

We chose to display extreme agents in order to distinguish attitude conformity from 190

a gradual increase in selfishness that was observed by [30] and [32]. Hence, if 191

participants with a moderate attitude conformed to the agent’s attitude, this change 192

could not be attributed to an increase in selfishness. In addition, if participants did 193

learn about decision makers who were less extreme than themselves, the attitude change 194

September 7, 2021 6/36 would push them in the same direction as the regression to the mean. Any movement of 195

the attitude away from the mean cannot then be obfuscated by this effect. In addition 196

to experimentally manipulating agents’ attitudes, we also carefully calibrated the 197

consistency of choices. This procedure ensured that agents displayed consistent patterns 198

of choice, so that their attitudes could be easily predicted by participants. 199 We calibrated αobs based on the participant’s attitude in the first part of the 200 resource-allocation game, before the manipulation phase (αbefore). Since we could not 201 tell a priori which cognitive model would fit participants’ data best (Cognitive 202 Modelling), we determined whether participants had an αbefore greater or less than zero 203 (prosocial or antisocial) using the following formula 2: 204

  X πot − 50 1t,A · atan , (2) q 2 2 t (πot − 50) + (πyt − 50) + πyt − 50

where πyt and πot are the points in the alternative allocation for self (you) and the 205 other in trial t of the resource-allocation game, and 1t,A is an indicator variable that 206 equals 1 when the participant preferred the alternative allocation in trial t and 0 when 207

the participant preferred the default allocation in trial t. 208

The dependent variable that we use to measure conformity is attitude convergence, 209 denoted by δdiff. To compute its value, we use Eq 3 (coincidentally similar to the 210 Contagion Gap of [26]): 211

δdiff = δbefore − δafter = |αbefore − αobs| − |αafter − αobs|, (3)

where δbefore and δafter are the distances between the attitude of the observed agent 212 αobs and participant’s attitude estimated respectively before and after the manipulation 213 phase. In order to have comparable results with the other conditions, we use this 214

measure also for Baseline participants as if they were predicting choices of an agent 215

from the Group or the Computer condition. As an exercise of parameter recovery for 216

this variable, see S2 Analyses. 217 We have chosen δdiff as a measure of attitude conformity because it has two critical 218 advantages over previous measures used in the literature [22, 24]. First, δdiff depends on 219 the original distance from the model: if a participant’s starting attitude is very close to 220 that of the observed agent, then δdiff can only be small. As this is a conservative 221 measure, it prevents close participants from biasing the estimate at sample level. 222 Second, by taking into account the attitude distances from αobs of both αbefore and 223 αafter, δdiff differentiates between participants who shift attitude closer to the agent, 224 and those who overshoot and become more extreme than the agent. It is indispensable 225

to distinguish between these two types of attitude change, as the hypotheses that we 226

test–with the exception of time-dependence–are concerned only with the former kind 227

(moving closer to the agent). 228

Attitude convergence unambiguously predicts participants’ attitude to converge 229

towards the observed agent’s attitude, hence this measure also penalises attitude 230

changes that lead the participant to become more extreme than the observed agent. As 231

a robustness check, we show that all the main results hold using an alternative measure 232

that accounts for polarisation (see S6 Analyses): 233

δα = sgn αobs(αafter − αbefore), (4)

Predictions regarding attitude convergence for each of the five hypotheses are 234

summarised in the left part of Table 1. Notice that the predictions of the 235

September 7, 2021 7/36 time-dependence hypothesis have an opposite direction compared to all other hypotheses. 236

Moreover, the two versions of the norm learning hypothesis (norm uncertainty and norm 237

salience) make no specific prediction about attitude change in the Individual condition. 238

Hypotheses Conditions Other Measures Baseline Computer Individual Group

Time-dependence ↓ ↓ ↓ ↓ Contagion – ↑ ↑ ↑ Compliance – ↑ ↑ ↑ Compliance Index (only ≥ 25%) Preference learning – – ↑ ↑ Consistency increase (in human conditions) Norm uncertainty – – – /↑ ↑ Different norms (human vs. computer) Norm salience – – – /↑ ↑ Same norms (human and computer) Table 1. The predictions of the five hypotheses. “↑” refers to increasing extremeness of the attitudes. “–” means no change predicted. “↓” refers to the shift towards selfishness.

Other Measures 239

While attitude convergence is the main measure that we use to distinguish among the 240

hypotheses, we also need to test ancillary predictions that these hypotheses make to 241

distinguish between the contagion and compliance hypotheses, and between the 242

preference learning and norm learning hypotheses. For this purpose, we adopt a series of 243

additional measures. The right-hand side of Table 1 summarises the related predictions. 244

Compliance 245

The contagion and compliance hypotheses make identical predictions in terms of 246

attitude change. To distinguish between them, we assess participants’ tendency to 247

comply with the experimenter’s expectations [49,50]. If the contagion hypothesis is true, 248

we should observe attitude convergence in the Computer condition even after controlling 249

for participants’ compliance tendencies. If instead attitude convergence in the Computer 250

condition depends on compliance tendency, this result should support the compliance 251

hypothesis. 252

Compliance to experimenter demand in standard Dictator Games has been 253

associated with an increase in prosocial behaviour (see for instance [51]). In the 254

resource-allocation game, however, participants can make both prosocial and antisocial 255

decisions, making prosocial behaviour a less obvious choice to appease the 256

experimenter [52]. Moreover, such demand by the experimenter is explicitly ruled out in 257

the instructions, where we specify that we do not expect any particular behaviour, 258

neither prosocial nor antisocial. Evidence for what might constitute compliance in the 259

resource-allocation game comes from an experiment adopting a similar paradigm [53]. 260

This study suggests that when presented with conflicting choices during a task, such as 261

behaving prosocially and antisocially, complying participants think they should 262

demonstrate both types of behaviour to meet the experimenter’s expectations, even if 263

these choices yield paradoxical outcomes. Critically, such pattern of behavior has been 264

associated with compliance with experimenter expectations and a personality index 265

measuring social desirability [53, 54]. If a participant displays such behaviour in the 266

resource-allocation game, then it is plausible that authority compliance—rather than 267

September 7, 2021 8/36 conformity to the observed agent—explains her attitude change. To measure authority 268

compliance, we consider separately the proportion of prosocial alternatives and the 269

proportion of antisocial alternatives chosen over the default allocation: we define our 270

index of compliance as the smallest of these two numbers in percentage terms. 271

To distinguish between compliant and non-compliant participants, we use a 272

preregistered threshold set to 25% (osf.io/th6wp; see S1 Table for the robustness of 273

results adopting different thresholds). In other words, a participant is said to be 274

compliant if she chose both prosocial and antisocial alternatives at least once out of 275

every four choices made. We use the compliance index to test attitude convergence in 276

the Computer condition. If compliant participants change attitude but non-compliant 277

participants do not, we interpret this evidence in favour of the compliance hypothesis. If 278

instead participants change attitude regardless of the compliance index, we interpret 279

this evidence in favour of the contagion hypothesis. As an exploratory analysis, we also 280

treat compliance index as a continuous variable, to test whether attitude convergence is 281

linearly associated with compliance. 282

Preference Learning 283

The preference learning hypothesis predicts that participants change their attitude 284

because they learn their own social preferences from others. Since learning in this case 285

should reduce participants’ uncertainty about how they want to behave, we should 286

observe a corresponding increase in choice consistency after the manipulation phase in 287

human (Individual, Group) relative to non-human (Baseline, Computer) conditions. In 288

other words, consistency (variability) between choices should reflect how certain 289

(uncertain) a person is about her social attitude, and consistency should increase after 290

learning about the preferences of others. 291

While increased consistency is a precondition for preference learning, participants 292

might also become more consistent if the norm learning hypothesis is true. Contrary to 293

preference learning, however, norm learning does not exclude that participants already 294

follow a social norm even before observing the agent. If this is the case, the information 295

obtained from the observed agent might add knowledge about the norm without 296

necessarily increasing choice consistency. Therefore, if our analyses fail to confirm a 297

differential increase in consistency between human and non-human conditions, we will 298

interpret this evidence as being against the preference learning hypothesis but not 299

against the norm learning hypothesis. 300

We can test for changes in consistency by looking at the cognitive model used to 301

understand participants’ choices, and in particular at the parameter representing 302

variability in participants’ choices. Depending on the winning cognitive model, this 303

parameter is either τ or σ (see Variability Parameters τ vs. σ): a small τ (σ) 304

corresponds to very consistent choices and vice versa. Hence, to test the preference 305

learning hypothesis we measure whether participants’ variability decreases after the 306 manipulation phase (e.g., for σ, σafter < σbefore). If participants do become more 307 consistent after the manipulation, we will further test whether consistency increase is 308

significantly different between conditions, and particularly between the human and 309

non-human conditions. 310

Norm Following 311

The norm learning hypothesis assumes that participants’ behaviour is influenced by 312

beliefs about what constitutes a socially appropriate or inappropriate action. 313

Accordingly, we should expect that prosocial and antisocial participants have different 314

beliefs about what choices are considered appropriate in the resource-allocation game. 315

To measure appropriateness perception, participants in the Computer, Individual, and 316

September 7, 2021 9/36 Group conditions completed the norm elicitation task [55] at the end of the experiment. 317

In this task, participants rated on a 4-point Likert scale the degree of social 318

appropriateness of choosing the alternative allocation over the default option in a 319

selection of choices from the resource-allocation game. If one of these ratings, randomly 320

chosen, matched that of the majority of other participants in the experimental session, 321 then the participant was rewarded with 3.00€. This procedure ensured that 322 participants reported their true beliefs about what the majority thought was socially 323

appropriate, namely what constituted a social norm. Using the norm elicitation task, we 324

test whether prosocial and antisocial participants have different perceptions of the social 325

norms in the game. This is done in the Computer condition where no social information 326

can be acquired from the agent. We expect that any difference in appropriateness 327

ratings is due to participants’ original beliefs before the task. If prosocial and antisocial 328

participants do indeed report different normative beliefs, this could explain their 329

differences in social attitudes, in accordance to the norm learning hypothesis. 330

Norm Uncertainty and Norm Salience 331

If the results of the elicitation task support the hypothesis of norm learning, we also use 332

appropriateness ratings to explore what kind of information participants learn about the 333

norm. Indeed, observing a social agent allows learning distinct features of a social norm. 334

First, if participants are uncertain about what is appropriate and what is not, 335

observation can provide useful information about the norm itself (norm uncertainty). If 336

there is norm uncertainty, we expect observation of a human agent with very prosocial 337

or antisocial behaviour to polarise the perception of what constitutes a right or wrong 338

choice. Polarisation in turn should lead to more extreme appropriateness ratings in the 339

Group and Individual conditions than in the Computer condition, where participants 340

simply predict the choice patterns of a computer (and therefore learn nothing about 341

social norms). 342

In addition to learning about the norm itself, observing the behaviour of others 343

reveals whether a norm is actually followed or not (norm salience). The norm 344

elicitation task, however, is not designed to measure norm salience, and we are unaware 345

of any other task that could possibly elicit this feature of a norm. We therefore test for 346

norm uncertainty by computing differences in appropriateness ratings between the 347

Computer and human conditions, for prosocial and antisocial participants separately. If 348

the ratings differ between the conditions, we interpret this as evidence of norm 349

uncertainty. If ratings do not differ between conditions, we conjecture that norm 350

learning occurred through a change in norm salience. 351

Cognitive Modelling 352

Bias Parameter κ 353

We associate participants’ choices to their social attitude via Eq 1. Yet this estimate or 354

that of other parameters could be biased by the participant’s tendency to comply to 355

authority (see Other Measures). To control for compliance, we allow for the possibility 356

that participants prefer an alternative allocation even when it should be on a par with 357

the default allocation, or vice versa. To represent this change in subjective value of the 358

alternative allocation, we define for each participant a bias parameter κ 5: 359

V (D) = V (100, 50) = 100 + tan α · 50 − κ, (5)

where κ is equivalent to an amount of penalty or bonus points for the default 360

allocation: The higher (lower) κ is, the higher (lower) the propensity to choose the 361

September 7, 2021 10/36 alternative over the default allocation. In other words parameter κ captures the bias, 362

unexplained by other parameters, according to which participants choose between the 363

alternative allocation and the default allocation as if the default allocation was missing 364 3 or having additional κ points. 365

Variability Parameters τ vs. σ 366

During the allocation game, participants might show variability in the way they choose, 367

such as being more or less prosocial (or antisocial) from choice to choice. Not 368

accounting for this variability within each part of the game (before or after prediction) 369

could bias the estimation of the change in attitude due to the manipulation. To 370

estimate choice variability, we compare two types of cognitive models that also give 371

different interpretations about the nature of social attitude. 372

The first model type, Stable Attitude, assumes that attitudes are a stable personal 373

trait, and that any variability in participants’ choices is due to cognitive mistakes when 374

comparing different options. If for instance a person occasionally shows a more 375

prosocial (or more antisocial) attitude than usual, this fluctuation is interpreted by the 376

model as a miscalculation on how to behave. Comparisons errors are modelled through 377

the parameter τ: the smaller (larger) τ is, the higher (lower) the probability of choosing 378

consistently with one’s own attitude. Stable Attitude models compare alternatives using 379

a softmax function (Eq 6, [56]): 380

V − V Λ(Pr(D = 1)) = D A , (6) τ

where Λ is the logit link function, Pr(D = 1) is the probability of choosing the 381 default allocation, VD and VA are the estimated values for the default and alternative 382 allocations, as in Eq 1 and 5. 383

The second model type, Variable Attitude, assumes instead that attitude is a 384

variable mental state. If for instance people behave more or less prosocially, this is 385

interpreted as a natural fluctuation of attitude. Participants choices are modelled using 386

random preference [57–59]: every time the participant has to make a decision, her social 387

attitude α is sampled from a normal distribution with centre µ and standard deviation 388

σ. The parameter σ represents variability in the way participants behave: the smaller 389

(larger) σ is, the more (less) consistent the participant will be across her choices. The 390

model is defined as 7: 391

( Tα−µ , if π > 50 σ o , (7) µ−Tα σ , if πo < 50

where Φ is the probit link function, Pr(D = 1) is the probability of choosing the 392 default allocation, and threshold Tα is the value of α for which the default and 393 alternative allocations have equal subjective value (VD = VA, Eq 8): 394

  πy − 100 + κ Tα = atan , (8) 50 − πo

If the sampled α > Tα, an allocation is preferred and consequently taken, otherwise 395 the other option is chosen. 396

3Although we acknowledge that this parameter could capture phenomena other than authority compliance, we were unable to provide any other interpretation of κ. In addition, κ and the original compliance index strongly correlate (see Cognitive Modelling), suggesting a common variance between the two measures.

September 7, 2021 11/36 Error Parameter ε 397

The error parameter ε defines the probability with which participants make a mistake in 398

implementing their choice (e.g., mistyping or inattention). The probability of choosing 399

the default allocation is expressed as Eq 9: 400

1 Pr(D = 1) = (1 − ε) · Pr + ε · , (9) model 2

where Prmodel represents the probability of choosing the default allocation according 401 to the model under consideration (Eq 6 for Stable Attitude or Eq 7 for Variable 402

Attitude). The error parameter thus allows to assume that participants’ answers are a 403

mixture between model-based choices and random errors. 404

Model Estimation 405

We estimate three versions of each model type. In the full version of a model, all 406

parameters are estimated twice, before and after the manipulation phase. A second, 407

simpler version of the models assumes that social attitude α is fixed for the whole task, 408

as if it could not change with the manipulation; α is thus estimated only once across all 409

choices. In the third version of the models instead, it is the variability parameter (σ for 410

Variable Attitude or τ for Stable Attitude) to be estimated once for the whole task, as if 411

participants could not get more or less self-consistent in their choices after the 412

manipulation phase. Models thus vary based on two factors: 2 (Stable Attitude / 413

Variable Attitude) × 3 (fixed attitude / fixed variability / both vary). Consequently, we 414

estimate and compare 6 unique models. 415

Models are estimated in JAGS [60] using the rjags [61] and R2jags [62] packages. 416

Parameters are fitted using Hierarchical Bayesian Analysis (HBA, [63]) on two levels: a 417

sample level (by subject) and a subject level (by time: before/after prediction). For 418

each model, we ran 4 Markov chains for 100,000 iterations, with a burn-in period of 419

5,000 iterations and a thinning rate of 4. The model with the lowest Deviance 420

Information Criterion (DIC) is selected and used for the statistical analyses. We use the 421

maximum a posteriori (MAP) estimate to derive the most likely value for each 422 parameter, including attitude convergence δdiff. 423

Results 424

Cognitive Modelling 425

Model Comparison 426

The cognitive model that describes participants’ behaviour best is the full version of the 427

Variable Attitude model in which both α and σ vary before/after the manipulation 428 phase (DICVA = 32997.4, Fig 2). Model comparison thus suggests that both attitude 429 and attitude variability change after the manipulation phase, and that α varies across 430

trials rather than being stable. This latter finding is further supported by the generally 431

lower DIC values of Variable Attitude models as compared to all Stable Attitude models. 432

Despite our original attitude categorisation of participants was agnostic with respect 433

to the winning cognitive model, 346 participants out of 369 (93.8%) were classified in 434 the same categories when using αbefore estimates from the Variable Attitude model. 435 Mismatch affects only participants with a moderate social attitude (mean 436 ◦ ◦ |αbefore| = 2.12 , max = 12.91 , NBaseline = 10, NComputer = 5, NIndividual = 3, 437 NGroup = 5). 438

September 7, 2021 12/36 Variable Attitude fixed s fixed a

full model

Stable Attitude fixed t fixed a

0 1000 2000 3000 D DIC Fig 2. Model comparison. The difference ∆DIC between the Deviance Information Criterion (DIC) of a model and the full version of the winning Variable Attribute model. The Variable Attitude models are in blue, and the Stable Attitude models are in red.

Compliance and κ relation 439

We test whether the bias parameter κbefore estimated before the manipulation phase 440 correlates with the compliance index. If correct, the bias parameter could be then used 441

as an improved measure of authority compliance, in that it could integrate compliance 442

effects directly within the computation of the decision process, and improve the 443

estimates of other parameters. Splitting participants below and above the compliance 444

threshold, we observe that the two groups have significantly different estimated values 445 of κbefore (Wilcoxon rank-sum test with continuity correction, log(V ) = 7.65, p < .001, 446 r = .51[.42,.61]), with participants below threshold with average 447 κbefore = 1.14[0.85, 1.43] and participants above threshold with average 448 κbefore = 11.48[8.78, 14.19]. We then measure the association between the two measures 449 using a Spearman’s rank correlation, and find a significant association (ρ = .62[.55,.67], 450

p < .001). These results support the hypothesis that the bias parameter κ in our model 451

also captures a significant portion of the effect of authority on participants. 452

Attitude Convergence 453

Preliminary results. 454

Based on choices before the manipulation phase, 75% (25%) of participants were 455

categorised as having a prosocial (antisocial) attitude. When presented with prosocial 456

alternatives, prosocial participants chose them over the default allocation 40% of the 457

time, while antisocial participants did the same with antisocial alternatives around 54% 458

of the time. According to our model estimates, mean social attitude before prediction 459 ◦ ◦ ◦ ◦ αbefore was 20 (SD = 14 ) for prosocial and −22 (SD = 20 ) for antisocial 460 participants (see Supplementary Fig A for a comparison across experimental conditions). 461

However, for a significant portion of participants (21% of the sample), 1 point for the 462 ◦ ◦ other player was worth less than one tenth of a point for oneself (−5 < αbefore < 5 ), 463 meaning that many participants showed a moderate, if not selfish, social attitude. 464

In the manipulation phase, prediction accuracy was relatively high: the average 465

number of correct predictions in the last 20 trials was 18.6 (SD = 2.2; Computer: 466

19.1,SD = 1.8, Individual: 17.9,SD = 2.8, Group: 18.7,SD = 1.8). This result 467

suggests that participants had successfully learned the attitude of the observed agent. 468

September 7, 2021 13/36 Time dependence 469

If the time-dependence hypothesis is true, participants should become more selfish in all 470

experimental conditions. We first test whether participants chose more often the 471

default, selfish allocation in the second part of the resource-allocation game (after and 472

despite the manipulation phase) than in the first part. Contrary to this prediction, 473

prosocial (antisocial) participants chose more prosocial (antisocial) alternatives when 474

learning about the agent’s choices (Baseline (no agent): -4.0%, Computer: +0.7%, 475

Individual: +5.3%, Group: +6.9%; S5 Analyses). 476 These results are mirrored by changes in social attitude, where we find that αafter 477 ◦ ◦ was on average more polarised than αbefore (Baseline: 0 , Computer: +4 , Individual: 478 ◦ ◦ +7 , Group: +5 ). Bayes Factor analyses suggest that the data are overwhelmingly 479 more likely under the alternative hypothesis (H1 : δα 6= 0) than under the null 480 hypothesis (all BF10 > 100) with the exception of Baseline, where there is substantial to 481 strong evidence in favour of the null (BF01 = 10.2; see S5 Analyses for a full report of 482 the analyses). These results suggest that time dependence is not present even in the 483

Baseline condition, indicating that this mechanism is not an important factor at play. 484

Contagion 485

If the contagion hypothesis is true, attitude convergence δdiff should be significant and 486 positive in all conditions excluding Baseline. Given that the normality assumption does 487

not hold (Shapiro-Wilk test, all p < .001), we test this prediction using a one-tailed 488

Wilcoxon signed-rank test. Indeed, participants, in all conditions except Baseline shifted 489

attitude towards that of the observed agent (Fig 3; Baseline: log(V ) = 8.40, p = .457, 490 ◦ ◦ ◦ δdiff = −1 [−2 , 0 ], r = .01[−.17,.18], BF0+ = 12.32; Computer: log(V ) = 7.64, 491 ◦ ◦ ◦ p < .001, δdiff = 4 [2 , 6 ], r = .43[.23,.63], BF+0 = 786.20; Individual: log(V ) = 7.51, 492 ◦ ◦ ◦ p < .001, δdiff = 6 [3 , 8 ], r = .57[.41,.75], BF+0 > 10000; Group: log(V ) = 8.28, 493 ◦ ◦ ◦ p < .001, δdiff = 5 [4 , 7 ], r = .58[.43,.72], BF+0 > 10000). 494

Baseline

Computer ***

Individual ***

Group ***

-30° -20° -10° 0° 10° 20° 30° 40° attitude convergence d diff Fig 3. Mean attitude convergence by condition. Error bars indicate t-adjusted, 95% Gaussian confidence intervals. *: p < .05; **: p < .01; ***: p < .001.

September 7, 2021 14/36 A B

-110.6°,-43° ← *** Baseline 75 Computer Individual Group *** 50

-217.8°,-80.6°,-59.2° ← ***

25

123.3° *** →

0 0% 10% 20% 30% 40% 50% 60% 70% -30° -10° +10° +30° +50° +70° +90° compliance index consistency increase sbefore - safter Fig 4. Compliance index and consistency increase. A: Distribution of the compliance index across all participants. The vertical line shows the threshold value (25%) beyond which a participant is considered to be susceptible to authority compliance. B: Consistency increase across conditions. Participants become more consistent after the manipulation phase (σafter < σbefore), but the increase is not significantly different across conditions. Error bars indicate t-adjusted, 95% Gaussian confidence intervals. Arrows indicate outliers. *: p < .05; **: p < .01; ***: p < .001.

We also measure the difference in convergence across conditions. A Kruskal-Wallis 495

test reveals that there is a significant effect of condition on attitude convergence 496 2 2 (χ (3) = 42.22, p < .001, ε = .11[.07,.19]). Post-hoc pairwise comparisons reveal that 497

attitude convergence differs between the Baseline and Group conditions (z = 5.87, 498 p < .001, r = −.39[−.51, −.27], BF10 > 10000), between the Baseline and Individual 499 conditions (z = 4.68, p < .001, r = −.33[−.46, −.17], BF10 = 717.97), and between the 500 Baseline and Computer conditions (z = 3.56, p = .005, r = −.24[−.38, −.10], 501 BF10 = 33.55). Bayes Factor analyses additionally suggest no difference in attitude 502 convergence between the Group and Individual conditions (BF01 = 5.78, substantial 503 evidence). 504

Compliance 505

The above results are compatible with the contagion hypothesis, but also with the 506

compliance hypothesis. To study the influence of the experimenter on attitude 507

convergence, we categorise participants using the compliance index. We find that 63 508

participants (Baseline: 23, Computer: 13, Individual: 16, Group: 11), around 17% of 509

the sample, are above the 25% preregistered threshold (Fig 4A). We thus focus on the 510 4 remaining participants below threshold. While the results in the Group and Individual 511

conditions hold, attitude convergence in the Computer condition is still significant but 512 ◦ ◦ ◦ weakened (Baseline: log(V ) = 8.06, p = .323, δdiff = 0 [−1 , 1 ], r = .04[−.15,.23], 513 ◦ ◦ ◦ BF0+ = 7.16, nobs = 109; Computer: log(V ) = 7.11, p = .015, δdiff = 3 [0 , 5 ], 514 r = .30[.06,.53], BF+0 = 6.27, nobs = 60; Individual: log(V ) = 6.96, p < .001, 515 ◦ ◦ ◦ δdiff = 5 [2 , 7 ], r = .57[.36,.77], BF+0 = 958.61, nobs = 50; Group: log(V ) = 8.02, 516 ◦ ◦ ◦ p < .001, δdiff = 5 [3 , 7 ], r = .55[.39,.71], BF+0 = 6652.22, nobs = 86). 517 In support of this observation, we find that Baseline and Computer conditions are no 518 more significantly different (z = 2.06, p = .058, r = −.15[−.30,.01], BF10 = 1.08; 519

4One participant did not respond in any antisocial trial before manipulation. Without these responses we could not compute a compliance index and the participant was consequently excluded for analyses about compliance.

September 7, 2021 15/36 2 2 Kruskal-Wallis test: χ (3) = 31.72, p < .001, ε = .10[.05,.19], nobs = 305). Instead, 520 Baseline and Group conditions are still significantly different (z = 5.20, p < .001, 521 r = −.37[−.51, −.24], BF10 = 2117.44), and so are Baseline and Individual conditions 522 (z = 3.90, p = .001, r = −.31[−.45, −.15], BF10 = 54.87). 523 To explore the relation between compliance and attitude convergence, we run a 524

robust linear regression [64] with attitude convergence as dependent variable, and with 525

experimental condition and the interaction between compliance and experimental 526

condition as predictor variables (Fig 5A). We compare the deviance of the regression 527

against a simpler model using only experimental condition as an independent variable: 528 2 the full model has a better fit on the data ((χ (4) = 19.70, p < .001, adjusted 529 2 R = .241). In support of the compliance hypothesis, we find that the weights for the 530

main effect of Group and Individual conditions are significant, whereas that of the 531

Computer condition is not (Fig 5B; Baseline: β = .170[−1.02, 1.36], t = .279, p = .780; 532

Computer: β = .176[−1.50, 1.85], t = .206, p = .837; Individual: β = 3.69[1.89, 5.50], 533

t = 4.011, p < .001; Group: β = 4.67[3.29, 6.03], t = 6.67, p < .001). Furthermore, the 534

interaction term with compliance is only significant in the Computer condition 535

(β = 25.31[14.75, 35.87], t = 4.70, p < .001) and not in the other experimental conditions 536

(all p > .05). These findings suggest that attitude convergence in the Computer 537

condition is mainly driven by experimenter compliance, rather than contagion. 538

Baseline Computer Individual Group A B b = 0.17, t= 0.28, p= 0.78 Baseline 40° b = 0.18, t= 0.21, p= 0.837 Computer

b = 3.69, t= 4.01, p£ 0.001 diff Individual 20° b = 4.66, t= 6.67, p£ 0.001 Group

b = - 2.64, t=- 0.74, p= 0.46 0° Baseline × compliance

b = 25.31, t= 4.7, p£ 0.001 Computer × compliance

attitude convergence d b = 1.07, t= 0.23, p= 0.819 -20° Individual × compliance

b = - 0.82, t=- 0.18, p= 0.856 Group × compliance

0% 20% 40% 60% -10° 0° 10° 20° 30° compliance index attitude convergence d diff Fig 5. Robust regression results. A: Robust regression on attitude convergence with experimental condition and the interaction between compliance and experimental condition as predictor variables. Shaded areas indicate 95% confidence intervals. B: Coefficients of the regression. Labels report unstandardised effect size, t-value, and p-value. Error bars indicate t-adjusted, 95% Gaussian confidence intervals.

September 7, 2021 16/36 Preference Learning 539

If compliance could explain attitude convergence in the Computer condition, and given 540

that we tend to exclude the presence of contagion in our experiment, attitude 541

convergence in the Group and Individual conditions could be explained instead by either 542

the preference learning or the norm learning hypotheses. We first test the second 543

prediction of the preference learning hypothesis, namely that learning about others’ 544

attitude should significantly increase participants’ consistency. We thus test whether 545

choice consistency increased, and if this increase is higher after observing a human agent 546

(Individual, Group conditions) than after predicting a computer’s choices or nothing at 547

all (Computer and Baseline conditions). Shapiro-Wilk test for normality is significant 548

(all p < .001), therefore we adopt non-parametric tests. Wilcoxon signed-rank tests show 549 that σafter was indeed significantly smaller than σbefore in all conditions (p < .001; 550 Fig 4B). 551

When we compare consistency increase across conditions, we find that participants 552

become more consistent in the Group condition than in the Baseline condition (z = 2.85, 553 2 p = .026, r = .20[.06,.33], BF10 = 6.83; Kruskal-Wallis test: χ (3) = 8.50, p = .037, 554 2 ε = .02[0,.07]). Despite this significant result, Bayes Factor analyses for most 555

comparisons favour the null hypothesis (no differential increase; Baseline-Computer: 556 BF01 = 6.07; Baseline-Individual: BF01 = 4.48; Computer-Individual: BF01 = 4.53; 557 Individual-Group: BF01 = 3.44). We question then that the preference learning 558 hypothesis does adequately explain our data. 559

Norm Learning 560

We use the data from the norm elicitation task to test the plausibility of the norm 561

learning hypothesis and to distinguish between norm uncertainty and norm salience. 562

We first compare appropriateness ratings between prosocial and antisocial 563

participants in the Computer condition using a series of Kruskal-Wallis tests (one test 564

for each rating; Fig 6, top). Appropriateness ratings are statistically different for every 565

rating, even after correcting for multiple comparisons (all p < .004). These ratings link 566

norm perception to social attitude: prosocial participants seem to consider it very 567

appropriate to give money to the other and very inappropriate to take money, while the 568

opposite is true for antisocial participants. Thus, it appears that participants’ social 569

attitudes are influenced by normative beliefs. 570

Given this evidence in support of the Norm Learning hypothesis, we proceed to 571

testing norm uncertainty. To check this, we test whether the distribution of 572

appropriateness ratings differ across conditions by participant type, which would 573

happen if norm uncertainty was present. Two Kruskal-Wallis tests out of twenty-four 574

are statistically significant, but do not survive the correction for multiple comparisons 575 (all p > .153). We also perform Bayes Factor analyses, but given the large number√ of 576 pairwise comparisons we choose to adopt a wider Cauchy prior, with spread r = 2. 577

Results show that the null hypothesis is favoured by 67 tests out of 72 (Fig 7). Similar 578

ratings in human (Group/Individual) and Computer conditions are thus not compatible 579

with the norm uncertainty hypothesis, leaving norm salience as the only available 580

explanation. Thus, authority compliance and norm salience are the only hypotheses 581

that we failed to reject. 582

September 7, 2021 17/36 choose over 100/50? antisocial prosocial

Very Appropriate Computer Individual

Appropriate

Inappropriate

Very Inappropriate

Very Appropriate

Appropriate

Inappropriate

Very Inappropriate

Very Appropriate

Appropriate Group

Inappropriate

Very Inappropriate 50/0 69/4 85/15 95/28 98/39 99/47 99/53 98/61 95/72 85/85 69/96 50/100 alternative allocation Fig 6. Norm elicitation task. Appropriateness ratings for prosocial and antisocial participants in the Computer (top), Individual (centre), and Group (bottom) conditions. Only participants below threshold are plotted. Square size is proportional to the number of participants, whereas the lines connect the median ratings for each alternative allocation.

Discussion 583

Drivers of Social Conformity 584

In this study, we identified and estimated the contributions of several competing 585

explanations to attitude conformity in social decision making. Attitude conformity was 586

assessed using a series of cognitive models coupled with several experimental conditions 587

and complementary measures, which helped to test the predictions of these hypotheses. 588

Participants’ attitude became more prosocial or antisocial when they learned about the 589

choices of an extremely prosocial or antisocial agent, regardless of whether the agent 590

was a group of people, one person, or a computer. We found, however, that attitude 591

compliance in the Computer condition was primarily driven by those participants who 592

were more likely to conform to authority demands, suggesting that attitude change in 593

this condition was primarily driven by compliance with the experimenter’s expectations 594

September 7, 2021 18/36 41 H0 H1

26

4

1

-3 -1 -1 0 1 1 3 very strong10 2 strong10 substantial 10 2 anecdotal10 anecdotal102 substantial 10 strong 102 BF10 Fig 7. Norm comparison between conditions. Histogram of Bayes Factor values for the 72 pairwise comparisons of appropriateness ratings for each allocation, for each pair of experimental conditions, binned by strength of evidence. Evidence in favour of the null hypothesis (H0) increases from right to left, and vice versa.

rather than conformity to the observed agent. Once we had accounted for authority 595

compliance, computational modelling helped us to disentangle the surviving hypotheses, 596

preference learning and norm learning. We first tested the prediction of the preference 597

learning hypothesis that participants should have become more self-consistent in their 598

choices after observing human agents. Since results disconfirmed this prediction, we 599

proceeded to test one prediction of the norm learning hypothesis, namely that the 600

behaviour of participants in the game is reflected by their beliefs about what is 601

considered appropriate or not. Results from a norm elicitation task [55] confirmed this 602

prediction, adding evidence in favour of the hypothesis that participants conform mainly 603

because of social expectations. As an exploratory analysis, we additionally tested the 604

norm uncertainty hypothesis, which posits that participants are uncertain about the 605

norm underlying the game and learn about it by observing other human agents. Results 606

from the norm elicitation task however suggest that participants do not change their 607

norm perceptions upon observing human agents. Based on this finding, we speculate 608

that social conformity in the experiment occurs because participants learn how salient 609

following the norm is (i.e. how unlikely it is for someone to deviate from the norm). 610

Given the exploratory nature of this result, we cannot exclude other interpretations: a 611

broader set of responses in the norm elicitation task paired with a properly powered 612

study design should be able to assess what mechanisms underlie norm learning. 613

A number of findings support the idea that norms and the beliefs related to them 614

are at the basis of social attitudes. Social appropriateness has been shown to play a role 615

in decisions in various economic games [38, 55, 65–68]. More relevantly to our study, it 616

September 7, 2021 19/36 was found that anonymity, and therefore reduced accountability, appears to have clear 617

effect on allocation choices. Experiments with increased anonymity—also with respect 618

to the experimenter, i.e. double blind paradigms—show plummeting contributions in 619

economic games such as the Dictator game [51, 69]. At the same time, even subtle cues 620

of being observed seem to increase contributions [70] (although see [71] for a recent 621

failed replication). The impact of reputation can also account for attitude change driven 622

by compliance. Authority compliance is indeed a phenomenon analogous to conformity, 623

as it links attitude change to vertical influences, as opposed to peer observation. 624

Participants who have a strong tendency to choose the alternative option, regardless of 625

whether it is beneficial or detrimental for the other and regardless of the identity of the 626

observed agent, may think that this is what authority wants, and that this is the norm 627

in the experiment [38, 72, 73]. The complementary result, that participants who are not 628

influenced by authority only change their attitude when learning about other humans’ 629

behaviour, works in a similar fashion. By learning to predict the agent’s behaviour, 630

participants deduce how salient following the norm is for others, and change their 631

behaviour to be more consistent with them. Therefore, we can conclude that the two 632

effects that we observe—authority compliance and attitude conformity in human 633

conditions—are both in line with the general social norms explanation. 634

The results of this study prompt some additional thoughts about the process of 635

learning social norms. First, we observe that information about norms can spread 636

through indirect transmission [74]. During the experiment participants cannot interact 637

in any way with the observed human agent—who is not physically present—but 638

participants can nevertheless extract some information about the norm from the 639

observed behaviour in the manipulation phase. Indirect transmission thus highlights how 640

adherence to social norms can be pervasive in dispersed and loosely regulated groups 641

such as online communities. Second, the fact that participants conform by learning how 642

salient a norm is implicates that if a norm is already salient among a group of 643

individuals then such group should be more resilient to conformity influences. If future 644

studies do confirm that norm perception prior to observation does predict conformity, 645

this could suggest new measures to countervail polarisation in social discourse. 646

Our contribution not only fosters and provides better characterisation of the norm 647

learning hypothesis, but also systematically devalues the several competing explanations 648

that we tested, that to our knowledge were not yet properly compared in one framework. 649

These non-social hypotheses include time-dependence, contagion, and preference 650

learning. The social/non-social distinction is crucial here as it gives an insight into how 651

to interpret conformity dynamics in interpersonal relations: if a person changes her 652

attitude we suggest that this change has to be primarily social in nature, and linked to 653

the changes in social context in which the decision maker is placed. This idea can have 654

profound implications for studying any social learning mechanisms and social decision 655

making in general. Specifically, many non-social explanations of the change in behaviour 656

can be ruled out. 657

Whereas the experimental design focused on some of the most prominent hypotheses 658

in the literature, it is also possible that further mechanisms may guide participants’ 659

social conformity. Social mimicry for instance suggests that participants change attitude 660

in order to increase ties within a group [14, 75, 76]. The need to belong [77] could 661

represent an alternative explanation to norm compliance, although it is not able to 662

explain why prosocial and antisocial participants display different appropriateness 663

beliefs. It is also by all means possible that several mechanisms contribute together to 664

the present results; our main conclusion is that they probably operate on a social level. 665

Concurrently, we do not claim that results on social behaviour directly apply to other 666

domains of decision-making, such as risk or temporal preferences. Our research method, 667

however, could be applied to other types of preferences to test whether these results 668

September 7, 2021 20/36 extend to other types of choices. 669

Cognitive modelling 670

Cognitive modelling does not only play a fundamental role in testing the predictions of 671

the different hypotheses, but is also inherently connected to two additional contributions 672

of this paper. First, we add to the series of studies challenging the conceptualisation of 673

preference as a stable trait of people, and thus the use of the softmax function as the 674

privileged method to model value-based choices. Studies on both risk [78, 79] and 675

inter-temporal preferences [23, 80] have in fact highlighted how choice variability can be 676

better explained by fluctuations of subjective preferences rather than “errors” in 677

comparing different alternatives. This is in line with our finding that the Variable 678

Attitude model explains behavioural data better than the Stable Attitude model. While 679

we do not claim that computational distortions are absent during the estimation of 680

value, we nonetheless support the idea that this mechanism cannot be the only one, nor 681

can it be the main cause for choice inconsistencies in value-based decision making. 682

This interpretation finds additional support in recent perspectives on brain 683

architecture, which hold that value representation is less specifically defined and is more 684

distributed than current thinking suggests [81–84]. Assuming that preferences vary 685

across contexts and across time requires a network of resources that not only keeps 686

track of the current internal state, but that takes also into account the situational 687

factors and the different scopes within which the choice is considered. For instance, a 688

decision to act prosocially would require the integration of the tendency of an individual 689

to help others, considerations related to the nature of the interaction and of the other 690

person, the general goals of the decision maker, as well as the history of choices 691

preceding that particular choice. Considering the complexity of a choice and of the 692

neural substrates that make it possible, it seems hard to postulate the stability of 693

subjective value as a justifiable premise for studying personal preferences and attitudes. 694

While we stand by the current findings, future research could improve the Variable 695

Attitude model by accounting for some of its limitations. One way to do this could be 696

to integrate both types of choice variability (errors in comparison and variability in 697

attitude) under a common cognitive model to test whether these mechanisms co-exist 698

and what are their individual contributions (see for example [85–88]). Such a model, 699

however, requires either a prohibitive number of trials per participant, or the integration 700

of some other type of information. This problem could possibly be overcome by 701

integrating temporal information to simple choice data: several studies have successfully 702

analysed subjective choices with this method before using so-called sequential sampling 703

models (SSM, see for instance [21, 89]). While this approach would require challenging 704

improvements, such as disentangling variability both within and between trials, it could 705

also promote the analysis of other decision components, such as the trade-off between 706

fidelity with one’s preferences and speed in making a decision. 707

A second contribution of cognitive modelling is the use of a computational 708

parameter to directly measure the impact of authority compliance on the decision 709

process (Bias Parameter κ and Compliance and κ relation). This parameter correlates 710

with the compliance index that we used in the present study to categorise participants. 711

We propose that this parameter can be used independently to measure compliance to 712

authority demands. Directly including the effect of compliance in the computational 713

model has the advantage that other estimates, such as the person’s attitude or its choice 714

consistency, are corrected for the presence of this effect. We also consider this 715

estimation procedure as more reliable than alternatives in the literature: while other 716

methods indeed exist, they are based on ad hoc tasks to quantify authority demand 717

(e.g., [50, 90]), whereas the measures we use work within the main task of the 718

experiment, thus reducing the risk that results in one task do not extend to another. As 719

September 7, 2021 21/36 a limitation of our approach, it could be argued that using a default option might seem 720

too unequivocal; we argue however that this feature of the task design actually 721

simplifies the expression of attitude by participants as it makes value comparison less 722

challenging also from a computational point of view (see for instance [91, 92]). We thus 723

think that our computational parameter could be of value to researchers who need to 724

control for the influence of the experimenter when fitting decision models. 725

Limitations 726

Our study does not come without some limitations. The experimental design is 727

between-subjects, and it is thus not possible to compare directly the effect of the various 728

manipulations, nor does it allow to exclude the possibility that multiple mechanisms are 729

at work simultaneously. While this weakness does not fundamentally challenge the 730

reported findings, implementing an intermixed design such as the ones proposed 731

in [27], [18] or [19] could yield more powerful predictions and interpretations. A second 732

constraint of our experiment design is that in some conditions we could not reach the 733

pre-determined sample size necessary to achieve the power 1 − β = .95. We note however 734

that our findings seem robust, even when applying design changes such as different ways 735

to account for the influence of compliance (S1 Table) or changing the dependent 736

variable (S6 Analyses), suggesting that this problem might be not too concerning. 737

Another limitation of the design is that, given that the attitude of the observed 738

agent was fixed, social distance from the agent and attitude change are correlated. This 739

means that we may be missing a connection between how close one’s initial attitude is 740

to the observed agent’s and how much she will conform after learning. Indeed, recent 741

research suggests that similarity with the observed agent influences the effect of 742

conformity [21]. To solve this problem, in future experiments we propose to dynamically 743

adjust the attitude of the agent depending on participants’ own attitude. This design 744

can also help to understand what happens when prosocial participants observe an 745

antisocial agent and vice versa. We have deliberately excluded this question from 746

consideration in our experiment because we were not sure ex ante if we would manage 747

to separate the effect of learning about a very socially distant agent from the drift of 748

attitudes towards selfishness (though, ex post we know that such time-dependence is not 749

a likely explanation of the findings, which should make it straightforward to test 750

hypotheses about observing others with very different attitudes). Previous results 751

suggest however that, at least concerning antisocial participants, cross-type conformity 752

should be less pronounced than same-type conformity [26]. 753

We would like to note that, contrary to the predictions of the norm learning 754

hypothesis, attitude change in the Individual condition was not significantly smaller 755

than attitude change in the Group condition. This unexpected result could be linked to 756

the fact that participants were not informed about the size of the group, which in turn 757

could have influenced their representation of the agent. A key direction for the future 758

research will be to explore the relationship between group size and attitude change 759

(e.g., [93]). Another possible explanation for the lack of the difference between the 760

Individual and Group conditions could be that participants in the Group condition were 761

not connected in any way with the group of people whose behaviour they observed, and 762

that they would have conformed more on average had they identified more with the 763

group. This scenario could be compatible with recent findings suggesting that norms 764

are stronger when there is a stronger group identification [27, 94]. Testing this idea 765

would require more rigorous control of the perception of the group by participants. 766

Finally, we would like to comment on the implicit assumption that we make when 767

analysing responses in the norm elicitation task. Specifically, we assume that the norms 768

elicited in the Computer condition were not influenced by the predicting of computer’s 769

behaviour in the second task, and thus these norms are those that participants had in 770

September 7, 2021 22/36 mind while choosing in the first part of the resource-allocation game. It can be argued 771

that learning about the computer’s “attitude” can change the perception of norms and 772

that our assumption is therefore incorrect. We disagree with this opinion on the 773

following grounds. The computer is not a social agent, so whatever it is doing should 774

not, by definition, change the perception of the social environment that participants are 775

in. This is evident from the fact that attitude conformity is not significant in the 776

Computer condition after regressing compliance to authority against attitude 777

convergence. Moreover, in a post-experimental questionnaire, 66 of the 74 participants 778

in the Computer condition reported that, in their opinion, the computer was acting 779

either according to a mathematical rule (e.g., addition or subtraction between the 780

players’ payoffs; N = 62), or randomly (N=4). It is thus unlikely that these participants 781

’humanised’ the choices made by the computer agent. The fact that we do not find any 782

differences in the elicited norms across the three conditions is much more likely to 783

reflect the stability of normative beliefs across conditions rather than beliefs that change 784

in all three conditions in exactly the same way. It can nonetheless still be argued that 785

the mere experience of the task influences norm perception. This idea has been directly 786

tested by [95] who found no evidence to support it. Overall, we believe therefore that 787

our treatment of norms in the Computer condition is legitimate. 788

Conclusion 789

In conclusion, we find that compliance to authority and learning how consistently others 790

follow social norms are the most likely explanations behind prosocial and antisocial 791

conformity. We hope that these findings will shed some light on the polarisation and 792

viral diffusion of information online, that it will push towards a similar systematic 793

exploration of preferences across other domains, and to a renewed interest in the 794

cognitive and brain processes underlying these changes. 795

Data and Code Availability 796

Behavioural and computational data, as well as a live version of the code used for the 797

analyses are available via the Open Science Framework (osf.io/p5xq3). 798

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September 7, 2021 29/36 Supporting information 799

S1 Fig. 800

A B

Group | | | || | ||| | | || | ||||| | || |||||||||||| |||||||||||||||||||||| ||| | | |||||||||||||||||||||||| |||||| | | |||||| | | |

Individual | || | || | || | | | || | ||| || ||| || || |||| ||||||| |||| | ||||| | |||||||||||||||||||||| || ||| | | ||| | | | | |

Computer | | || || || | | | | |||||| ||||||||||||||||||||||| | ||| ||||| || ||| | |||||||||||||||||||||||||| | | || | | |

Baseline | | || ||||| | | |||||| || ||||||||||||||||||||||||||||||||||||||||||| |||||||||||||||| | ||| | |||||||||||||||||||||||||||||||||||||||| |||||||| | | | | | |

-45° -30° -15° 0° 15° 30° 45° 0° 15° 30° 45° 60° 75° 90° 105° 120° 135°

abefore sbefore C D

Group | | ||||||||||||||||||||||||||| | | || | | | | | | |||||||||||||||||||||||||||||||||||||||||||||||| || | || | || | | | | ||

Individual | |||| |||||||||||||||| | |||||| | ||| | | | | | ||||||||||||||||||||||||||| | ||||||||| || ||| | | | || | | |

Computer | | |||||||||||||||||| ||||| |||| ||| | ||| | | | | |||||||||||||||||||||||||| ||||| || | || | ||| | | | |

Baseline | ||||||||||||||||||||||| ||||||| ||||||||| || | | | | | | | | ||||||||||||||||||||||||||||||||||||||||||||||||||||| ||| |||| | || |||| | | | | | | |

-10 0 10 20 30 40 0% 10% 20% 30%

kbefore e before Fig 8. Starting Parameters’ Values. Individual parameters’ distribution before manipulation, by condition. Each vertical line represents a participant, jittered for illustration purposes. Parameter α represents participants’ estimated social attitude; σ estimates participants consistency across choices, κ indicates the penalty points of the default allocation with respect to the alternative allocations; ε indicates the percentage of trials in which there was likely a response mistake by the participant.

S1 File. List of allocations. An .xlsx file containing all the allocations used in the 801

task: osf.io/y8v63. 802

September 7, 2021 30/36 S1 Methods. Preregistration amendments. This study was originally 803

preregistered at the Open Science Framework osf.io/th6wp. Although we tried to be as 804

faithful as possible to the original project, we made some changes which we report here: 805

• Design: the original plan to recruit 100 participants was not reached due to a 806 limited subject pool. 807

• Hypotheses: 808

1. We added the time-dependence hypothesis (participants change attitude even 809

in the absence of another agent). 810

2. The norm learning hypothesis does not strictly exclude attitude change in 811

the Individual condition. 812

3. New prediction for Preference Learning: increase in consistency. 813

• Modelling: 814

1. Results presented are based on the original 100,000 MCMC iterations, with 815

all parameters well below Rˆ < 1.10. To achieve the more conservative 816

threshold of Rˆ < 1.05 for all parameters, we ran 222,500 iterations with 817

thinning = 4, while also excluding one participant from the Baseline 818

condition. Results are statistically equivalent to those presented in the 819

article. 820

2. We introduced the bias parameter κ to account for any additional preference 821

for the alternative or the default allocation, ceteris paribus. When 822

considering for instance a logistic regression model with choice as the 823

predicted variable, κ can be thought as the intercept of the regression. 824

Previous findings suggest that participants might choose the alternative 825

allocation more often than predicted by the original choice models, given 826

that introducing a fixed option in the choice might bias the expectations of 827

participants on how to respond, regardless of the payoffs (see [53]). 828

3. We introduced the error parameter ε, transforming the model into a mixture 829

between the original preference model and an unbiased coin. This parameter 830

accounts for the possibility that, in some trials, participants answer randomly 831

due to attention gaps or motor mistakes (implementation errors [78] that 832

otherwise would be unaccounted for. 833

4. We changed the operationalisation of the dependent variable (Section 834

Manipulation Phase). 835

• Analyses: 836

1. We could not test for participants’ numeracy as originally planned due to a 837

problem with the software that inflated the number of mistakes by 838

participants. The mistake was due to the program recognising input from the 839

numeric pad as different symbols than digits, thus counting correct inputs as 840

mistakes. We decided to drop this measure since our recruitment schedule 841

prevented us to fix this problem in time for the data collection. 842

• Names: 843

1. Epistemic Uncertainty → Preference Learning 844

2. Preference Temperature → Stable Attitude 845

3. Preference Uncertainty → Variable Attitude 846

September 7, 2021 31/36 S1 Analyses. Model identification. Here we test whether Stable Attitude and 847

Variable attitude models can be identified. Since we were unable to compute a 848

confusion matrix given the high computational resources required to simulate such 849

complex hierarchical models multiple times, we relied on our DIC metric for a single set 850

of simulated data. We first generated data based on both the Stable Attitude and 851

Variable Attitude models, using the same design structure of the experiment and with 852

the same number of participants in each condition. We then fitted the resulting 853

simulated data to both models. As expected, data generated from the Variable Attitude 854

model was fitted best by the Variable Attitude model (DIC = 34128.15) than by the 855

Stable Attitude model (DIC = 37441.68), and data generated from the Stable Attitude 856

model was fitted best by the Stable Attitude model (DIC = 36015.08) than the Variable 857

Attitude model (DIC = 37758.68). 858

S2 Analyses. Attitude Convergence δdiff Parameter Recovery. We test 859 whether the winning model Variable Attitude is able to correctly recover simulated data 860

about our main variable of interest, attitude convergence. To this end, we simulate data 861

based on the estimated hierarchical population parameters and generate data for the 862

same number of participants in each experimental condition. We repeat model fitting 863

using the same procedure for real data, and compute the differences between original 864

simulated data and the values recovered by the model. Results reveal a decent recovery 865 of δdiff, with a correlation between simulated and recovered values of r = .85 ([.82,.88], 866 Pearson’s product-moment correlation, p < .001; Fig 9), a root mean squared error of 867 ◦ ◦ 5.5 and a root median squared error of 2.4 . 868

S3 Analyses. Balance Between Conditions. We test whether experimental 869

conditions are balanced in terms of gender, age, and starting social attitude. Whereas 870

we do not find any differences in terms of gender (Chi squared test, χ(3) = 1.37, 871

p = .713), we do find that participants in the Individual condition are younger than 872

participants in Baseline (Dunn’s post-hoc pairwise comparisons: W = 2.91, p = .015, 873 BF10 =) and Group (W = 2.80, p = .015, BF10 =) conditions. Whereas this differences 874 are statistically significant, in practice the age gap is of around 5 months (Individual: 875

M = 21 years, 9 months; Baseline: M = 22 years, 3 months; Group: M = 22 years, 4 876 months). We also compare average starting attitude αbefore for prosocial and antisocial 877 participants by means of a linear regression model with α1 ranks as predicted variable 878 and condition and interaction between categorisation and condition. We defined 879

pairwise contrasts within each category (i.e., control prosocial participants versus group 880

prosocial participants). All contrasts are not statistically significant (all p > .163). 881

S4 Analyses. Attitude Distance From the Agent Before Prediction. Given 882 that attitude convergence δdiff depends on the initial attitude distance from the agent, 883 we test whether there are any differences in distance across conditions by means of a 884 2 Kruskall-Wallis rank-sum test (Figure 10). The test is significant (χ (3) = 11.52, 885 2 p = .009, ε = .03[.01,.08]), and post-hoc Dunn’s tests reveal that participants in the 886

Group and Individual conditions are on average significantly closer to their agents than 887 participants in the Baseline condition (Group: p = .015, r = .19[.08,.32], BF10 = 4.34; 888 Individual: p = .015, r = .20[.05,.33], BF10 = 4.27), whereas there is no difference 889 across other comparisons (p > .05). If participants in the Group and in the Individual 890

conditions had an average initial attitude closer to the agent than participants in the 891

Baseline condition, then their maximum possible attitude convergence must have been 892

smaller than that of Baseline participants. Since participants’ attitudes in the 893

Individual and Group conditions converge more than those in the Baseline condition, 894

September 7, 2021 32/36 22.5° diff 0°

-22.5° recovered d

-45°

-45° -22.5° 0° 22.5° simulated d diff

Fig 9. Parameter recovery for simulated δdiff values. On the x axis are the generated data, on the y axes, the values recovered by the model.

this evidence–if anything–supports the idea that differences in attitude convergence 895

across conditions cannot be explained by differing initial distances. 896

S5 Analyses. Time Dependence Analyses. Here we provide quantitative tests 897

for the measures capturing change in the proportion of alternative choices and changes 898

in α. For the former, we consider prosocial trials for participants categorised as 899

prosocial, and antisocial trials for participants categorised as antisocial. We run a 900

mixed-effects logistic regression on these trials, with participant as a random effect, 901

alternative choice (dummy: 1 = alternative chosen) as the predicted variable and, as a 902

predictor variable, a dummy indicating whether the trial was before the manipulation, 903

or if after the manipulation in what given condition (e.g., after the manipulation in the 904

Group condition). According to this model, compared to trials before the manipulation, 905

the proportion of alternatives chosen decreased in the Baseline condition (β = −.242, 906

Standard Error S.E. = .040, p < .001), did not significantly change in the Computer 907

condition (β = .073, S.E. = .054, p = .178), and increased in the Individual (β = .301, 908

S.E. = .056, p < .001) and in the Group (β = .363, S.E. = .046, p < .001) conditions. 909

We additionally test whether participants become more or less polarised after 910 manipulation (H1 : δα 6= 0) Due to model misspecification (i.e., non-normality of data, 911

September 7, 2021 33/36 Baseline

* Computer * Individual

Group

-60° -30° 0° distance from agent -|a 1 - aobs| Fig 10. Distance from observed agent, by condition. Crossbar plot of participants’ attitude distance from the agent’s before the manipulation phase. The graph includes all participants. Error bars indicate t-adjusted, 95% Gaussian confidence intervals.

Shapiro-Wilk test, all p < 0.039), we apply non-parametric tests for the analyses. 912

Participants’ social attitude became more polarised in all conditions except Baseline 913

(two-tailed Wilcoxon signed-rank test; Baseline: log(V ) = 8.39, p = .990, 914 ◦ ◦ ◦ δα = 0 [−1 , 1 ], r = .00[−.16,.17], BF01 = 10.19; Computer: log(V ) = 7.60, p = .001, 915 ◦ ◦ ◦ δα = 4 [2 , 6 ], r = .38[.18,.59], BF10 = 104.59; Individual: log(V ) = 7.46, p < .001, 916 ◦ ◦ ◦ δα = 7 [3 , 10 ], r = .50[.31,.68], BF10 = 826.95; Group: log(V ) = 8.24, p < .001, 917 ◦ ◦ ◦ δα = 5 [3 , 7 ], r = .52[.37,.68], BF10 > 10000). 918

S6 Analyses. Attitude Polarisation. Here we report the main results of the 919 experiment using attitude polarisation δα in place of attitude convergence δdiff. These 920 tests show that the results are robust to the specification of the dependent variable. 921 Full sample, H1 : δα > 0. Due to model misspecification (i.e., non-normality of 922 data, Shapiro-Wilk test, all p < 0.039; inequality of variances, Fligner-Killeen test, 923

p < 0.001), we apply non-parametric tests for the analyses. Participants’ social attitude 924

became more polarised in all conditions except Baseline (one-tailed Wilcoxon 925 ◦ ◦ ◦ signed-rank test; Baseline: log(V ) = 8.39, p = .495, δα = 0 [−1 , 1 ], r = .00[−.16,.17], 926 ◦ ◦ ◦ BF0+ = 12.40; Computer: log(V ) = 7.60, p < .001, δα = 4 [2 , 6 ], r = .38[.18,.59], 927 ◦ ◦ ◦ BF+0 = 209.14; Individual: log(V ) = 7.46, p < .001, δα = 7 [3 , 10 ], r = .50[.31,.68], 928 ◦ ◦ ◦ BF+0 = 1653.85; Group: log(V ) = 8.24, p < .001, δα = 5 [3 , 7 ], r = .52[.37,.68], 929 BF+0 > 10000). 930 Attitude polarisation also differs by condition (Kruskal-Wallis rank-sum test, 931 2 2 χ (3) = 45.52, p < .001, ε = .10[.06,.17]). Baseline differs from all other conditions 932 (Computer: W = 3.19, p = .003, r = −.23[−.37, −.09], BF10 = 8.97; Individual: 933 W = 4.22, p < .001, r = −.29[−.43, −.13], BF10 = 107.69; Group: W = 5.57, p < .001, 934 r = −.37[−.49, −.23], BF10 = 4882.74). Whereas no other difference is significant, there 935 is substantial evidence (BF01 = 5.78) for no difference between Group and Individual 936 condition. 937 Participants with compliance index < 25%, H1 : δα > 0. Due to model 938 misspecification (i.e., non-normality of data, inequality of variances), we apply 939

non-parametric tests for the analyses. For participants below threshold, average 940

attitude polarisation is significantly different from zero in the Individual and Group 941

September 7, 2021 34/36 conditions but not in the Baseline condition, whereas there is not enough evidence for 942

either hypothesis in the Computer condition (one-tailed Wilcoxon signed-rank test; 943 ◦ ◦ ◦ Baseline: log(V ) = 8.01, p = .493, δα = 0 [−1 , 1 ], r = .00[−.19,.20], BF01 = 9.21; 944 ◦ ◦ ◦ Computer: log(V ) = 7.05, p = .056, δα = 2 [0 , 4 ], r = .22[−.02,.47], BF10 = 1.59; 945 ◦ ◦ ◦ Individual: log(V ) = 6.93, p < .001, δα = 5 [2 , 8 ], r = .52[.31,.74], BF10 = 591.57; 946 ◦ ◦ ◦ Group: log(V ) = 7.97, p < .001, δα = 5 [3 , 7 ], r = .48[.30,.65], BF10 = 2302.02). 947 Attitude polarisation also differs by condition (Kruskal-Wallis rank-sum test, 948 2 2 χ (3) = 28.87, p < .001, ε = .09[.05,.18]). Baseline differs from Group and Individual 949 conditions (Individual: W = 3.75, p < .001, r = −.17[−.36, −.02], BF10 = 29.10; Group: 950 W = 4.92, p < .001, r = −.34[−.47, −.19], BF10 = 248.05). Group condition is also 951 statistically different from the Computer condition, although Bayes Factor suggests 952 evidence is anecdotal (W = 2.53, p = .023, r = .21[.06,.37], BF10 = 1.16). Whereas no 953 other difference is significant, there is substantial evidence for no difference between 954 Group and Individual condition (BF01 = 5.17). 955 Robust regression. In support of the compliance hypothesis, we find that the 956

weights for the main effect of Group and Individual conditions are significant, whereas 957

that of the Computer condition is not (Baseline: β = .14[−1.18, 1.46], t = .211, p = .833; 958

Computer: β = −.41[−2.27, 1.44], t = −.438, p = .662; Individual: β = 3.73[1.70, 5.75], 959

t = 3.60, p < .001; Group: β = 4.47[2.95, 5.99], t = 5.75, p < .001). Furthermore, the 960

interaction term with compliance is only significant in the Computer condition 961

(β = 27.17[15.57, 38.77], t = 4.59, p < .001) and not in the other experimental 962

conditions (all p > .05). 963

S1 Table. Varying the Compliance Index. The main results presented in the 964

paper account for authority compliance by using a preregistered index. Table 2 below 965

shows that these results are largely consistent using different thresholds for compliance. 966

In accordance with the results of the robust regression in the main test, as the threshold 967

becomes more stringent, the less significant is attitude convergence in the Computer 968

condition, and the more different is attitude convergence between the Computer and 969

Group conditions. 970

S7 Analyses. Attitude Convergence and Consistency Increase. As an 971

exploratory question, we asked whether participants would become more consistent the 972

more they conform. We tested whether attitude convergence and consistency increase 973

were positively correlated by means of a directional Spearman’s rank correlation. 974

Correlation was not significant in any condition after correcting for multiple 975

comparisons (all p > .998). 976

Acknowledgments 977

We would like to thank Dimitris Katsimpokis, Stephan Nebe, and the members of the 978

Learning and Decision Making group at University of Trento for invaluable comments. 979

GC acknowledges the financial support of the European Research Council (ERC 980

Consolidator Grant 617629). All mistakes are our own. 981

September 7, 2021 35/36 Statistical test Number of observations 36/36

Wilcoxon signed-rank Kruskal-Wallis Dunn's 2 Group Individual Computer Baseline Total W/nobs χ post-hoc z ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ 100% 18.01 22.08 32.46 41.98 5.86 4.68 1.76 97 66 73 132 368

⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ Left: attitude 40% 17.86 19.54 30.57 38.85 5.66 4.40 1.66 93 56 71 123 343

⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ 35% 15.49 18.91 30.35 35.79 5.52 4.18 1.94 92 55 67 117 331

⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎ 30% 12.63 18.28 29.78 34.5 5.46 4.05 2.31 91 54 63 116 324 for Wilcoxon rank-sum and signed-rank 001.

⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎ ⁎ | r

25% 10.37 16.58 27.52 31.72 5.20 3.90 2.48 86 50 60 109 305 | Threshold p < . ⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎ 20% 9.25 16.58 29.04 38.54 5.81 4.11 3.02 82 50 57 104 293

⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎ ⁎⁎ 01; ***: 15% 8.54 15.59 27.04 33.42 5.37 3.88 2.92 78 46 54 93 271

⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎⁎ ⁎⁎ ⁎⁎ p < . 10% 6.85 14.61 25.83 34.76 5.39 3.99 3.15 72 41 47 85 245 05; **:

p < .

Group > 0

Computer ≠

for the Kruskal-Wallis test), from green (low) to red (high). Asterisks code

Individual > 0 Computer Computer > 0 2

ε

Group ≠ Baseline Group

√ Individual ≠ Baseline Right: sample size. Colourstests, code effect size ( convergence greater than zero, attitude convergence comparison across conditions; significance: *: Table 2. Results of main tests using different thresholds. September 7, 2021