Consistently refusing to go along both helps and hinders minorities to induce social tipping

Abstract

To create a more sustainable society, changing unsustainable social conventions is crucial. But when are small groups of people most effective at triggering social tipping necessary for convention change? Literature suggests non-conformist minorities exert more influence over individual attitudes of majority members when they oppose the majority convention consistently. However, social change requires not just individual attitude change among some majority members but that the entire society, over time, tips from one convention to a new one. Using a multi-round group experimental paradigm, we empirically examine whether minorities trigger social tipping more successfully when being consistent in their choices. In line with past theorising, we find that consistent minorities are perceived as more confident, which promotes tipping. We also find that consistent minorities are perceived as uncompromising, which surprisingly impedes rather than promotes tipping. Future research building on our work may ultimately provide practical guidance for activists: projecting as much confidence as possible through consistency while occasionally conceding to avoid appearing uncompromising may turn out to be an ideal cocktail when it comes to promoting tipping.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-39481-9.

Introduction

From obtaining protein primarily from plants rather than animals to adopting more sanitary ways of greeting one another: many existing social conventions need to change to address global crises like climate change and pandemics. Such change is typically initiated by minorities that start abandoning the current convention¹ and occurs via social tipping: a process where once a critical mass of people has stopped following a convention, the rest of the group rapidly follows in doing so as well^2,3. Such social change can occur relatively quickly. During the pandemic, it only took a few weeks for people to stop shaking hands, and past social transitions towards sustainability took as much as four decades less than technological transitions⁴. But when are minorities most effective in triggering tipping? Minority influence literature demonstrates that minorities who adhere to their principles consistently, as compared to being more unstable in countering the status quo, tend to be more influential in changing others’ attitudes⁵. However, social change requires not just individual attitude change but that the entire society, over time, tips from one convention to a new one—i.e., from one stable state to another stable state². Such research examining whether factors like minority consistency also facilitate societal-level change is surprisingly scarce⁶, likely partly because of the lack of experimental paradigms capable of demonstrating convention change. Thus, while it is clear that consistency breeds attitude change, it is unclear whether appearing consistent will actually help minorities to reach social tipping points. To address this question, we employ a recently developed experimental paradigm⁷ to empirically examine the causal role of minority consistency in group-level convention change.

The employed experimental paradigm was structured as a coordination game, which allowed us to replicate the fact that social conventions are characterised by the underlying motive to match one’s own action with that of others. Social conventions instruct people how to behave when there are multiple, equally attractive behaviours, and it is in everyone’s self-interest that everyone behaves the same^8–10. A prototypical example of how coordination is at the core of conventions is choosing whether to use cash or debit cards as the default payment method—it matters little which of them a given society chooses as long as we all assume the same default. Additionally, wherein a change of convention from cash to card payments has occurred in many countries (e.g., the Netherlands), others persist in using cash as the default payment method (e.g., Germany), further showcasing how conventions are often arbitrary and primarily driven by localised social influence forces.

Deviating from a convention results in a failure to coordinate with others and is consequently socially costly for the deviant—i.e., others might refuse to associate themselves with an individual with whom they cannot coordinate. Examples of these social costs are the inability to pay for services in the cash vs. card example above and the ridicule people who refuse to eat meat receive from meat-eaters¹¹. Because of the convenience of following conventions and the social costs of deviating from them, conventions typically remain stable across long periods and only change when a shock to the social system occurs. While a range of factors can provide this shock (see earlier examples¹²), it is often triggered by minority groups of non-conformist people who decide that change is necessary and start deviating from the current convention despite the costliness of doing so¹.

If a minority manages to initiate a convention change process successfully, the remainder of this process occurs in the form of social tipping^2,3,13. Social tipping begins with people slowly becoming convinced by the minority and converting away from the status quo convention to the minority alternative. As soon as enough people within the group adopt the alternative—i.e., a tipping point is reached—a self-perpetuating feedback loop sets in that causes a quick change among the rest of the society (resulting in a prototypical s-shaped change curve – see Fig. 1)^7,14,15. This self-perpetuating mechanism is triggered by the fact that when enough people switch, it becomes increasingly desirable for others to abandon the old convention as well since it will no longer facilitate social coordination, while the new one increasingly will^16,17.

Fig. 1.

An example of an s-curve emerging from social tipping.

Regarding the role of minority consistency in this social tipping process, past research has already empirically established that individual majority members are more likely to change their attitudes when facing a consistent minority¹⁸. Specifically, a large meta-analysis proposed two possible arguments for why consistent minorities are more influential in provoking this attitude change than inconsistent minorities (and might also be better at provoking social tipping): perceptions of confidence and uncompromisingness⁵. On the one hand, the willingness to stand by its position regardless of the inconvenience and other (social) costs signals that the minority is confident about its position and believes in its validity. Such confidence, in turn, encourages majority members to seriously question the status quo, consider the minority position as a viable alternative to the status quo, and potentially adopt it ¹⁹. On the other hand, a consistent minority also displays that it is unlikely to budge to or negotiate with the majority (i.e., that it is uncompromising), which places the responsibility for resolving the group conflict in the hands of the majority members. Thus, this reasoning suggests that, regardless of whether they believe in the minority position or not, majority members may start adopting the minority alternative as the only way out to deal with this uncompromisingness and so re-establish the ability to cooperate in the group⁵. Note that the majority may also react by excluding the minority from the group⁶, but in our study we exclude this possibility, allowing us to examine when the minority is more likely to convert the majority.

While past studies have demonstrated that consistent minorities are better at changing individual attitudes of majority members, researchers have thus far only hypothesised that this increased influence might, on the group-level, lead to minorities triggering social tipping more successfully when being consistent⁶. The proposed effects of minority consistency on social change have not actually been empirically tested. Testing such societal-level outcomes is essential as, while individuals doubting their attitudes and considering changing their behaviour might result in widespread social change^2,19,20, that is all but guaranteed. Research suggests that people’s behaviour does not necessarily match up to their attitudes/beliefs, so it is even less of a certainty that, as a result of attitude changes, the entire group will tip from one convention to another⁶. Similarly, past literature has only hypothesised that confidence and uncompromisingness might underly the effect of minority consistency on social tipping. However, their mediating role in the process thus far has gone untested.

To fill both gaps, we employ a recently developed group experimental paradigm⁷, which allows us to examine the effectiveness of a minority in triggering social tipping under different conditions. Based on the assumption that the effects of minority consistency on attitude change discovered in past literature translate into eventual social tipping, we preregistered a hypothesis proposing a positive effect of minority consistency on social tipping, which might be further mediated by confidence and uncompromisingness. However, due to the lack of available group-level over-time evidence in the literature, there is high uncertainty surrounding the direction of these mediating effects. Accordingly, we analyse data using methods (i.e., Bayesian statistics) that allow us to weigh the strength of evidence for all directions of the different effects. And indeed, we find only a small overall positive effect of consistency on tipping: consistency promotes social tipping via boosting confidence perceptions. We however also find that appearing uncompromising does not facilitate tipping as initially hypothesised, but rather, reversely, impedes it.

The employed social tipping game is structured as a repeated group coordination game played in groups of 12, which condenses the convention change processes that normally take days up to decades into a single 30-minute experimental session⁷. In each round of the game, players individually chose either Tao or Eta (Fig. 2, top panel) and then received feedback on what percentage of other players in the group chose either Tao or Eta and on which other players chose either of the options (Fig. 2, bottom panel). Afterwards, they moved on to the next round, allowing them to update their decision. The game concluded when all members of the group chose the same option in a given round (or up to a maximum of 24 rounds).

Fig. 2.

Individual choice page (above) and feedback page (below) in the experimental game.

Within this setting, the game mirrors real-world convention change by letting participants first create a natural status quo convention (i.e., a choice everyone in the group is choosing) and then introducing a minority that aims to overthrow it, thus inducing participants with a decision conflict between following the status quo convention or establishing a new convention around the minority-backed alternative. The decision conflict was induced via a particular combination of monetary incentives, while the minority countering the status quo is enacted by 3–4 participants in the group actually being confederate bots (see Methods - Experimental game for details). These confederate bots also allow us to vary consistency on the group level by countering the status quo consistently or inconsistently across conditions (see Methods - Minority Consistency Manipulation for details). In sum, our game created the needed conditions for answering our research question: after a social convention is established, do minorities overthrow it more effectively when they consistently oppose the majority preference?

Across the experimental groups, multiple social tipping patterns emerged. The three observed patterns were (a) all participants eventually switching to the minority alternative (Fig. 3, left panel), (b) a majority of participants sticking to the status quo despite minority pressure (Fig. 3, right panel), and (c) a majority but not all participants switching to the minority alternative (Fig. 3, middle panel). While (a) and (b) unequivocally represent a group having tipped or not having tipped, respectively, (c) cannot be classified as easily. Since our analysis required a binary dependent variable representing whether a given group experienced social tipping or not, we use multiple raters to classify the (c) sessions as either tipping or not tipping (see Methods - DV Classification Task for details).

Fig. 3.

Prototypical sessions representing the three change patterns observed across the experimental sessions.

In sum, in the dependent variable of our main analysis, experimental groups are scored either as having tipped (1) or not (0), whereby tipping implies either unanimous conversion to the minority side, or having been classified as having tipped by our coders (see Supplement 1 for a plot of tipping patterns within all experimental groups marking which are treated as having experienced social tipping in our dependent variable). To measure the two mediators (i.e., confidence and uncompromisingness), we used single-item self-report measures that participants filled in after the game concluded (see Methods - Mediator Measures for details). The main analysis employs a Bayesian parallel mediation model with thoughtful priors (see Methods - Statistical Approach for details), but we additionally conduct a range of robustness checks with alternative model specifications and dependent variable operationalisations (see Methods - DV Classification Task and Methods – Statistical Approach for details).

Results

The Bayesian parallel mediation model with thoughtful priors we employ entails defining prior distributions of all the model parameters and then observing what posterior distributions emerge when combining the prior distributions with the data. There are two main reasons why a Bayesian approach is particularly fitting for our data. First, we can make inferences on the strength of evidence for the proposed directional vs. the null hypothesis in a natural way using the posterior distributions. Given the level of uncertainty about the direction of minority consistency effects on social tipping, weighing the evidence for and against the hypothesis is an important first step towards understanding the role of minority consistency in social tipping. Second, analysing the data on a group level leads to a smaller sample size and, in such cases, a Bayesian approach with thoughtful priors provides less biased estimates than a frequentist approach²¹.

The results of our Bayesian parallel mediation analysis are reported in Table 1. The consistent sessions (37/56; 66%) tipped more frequently than the inconsistent sessions (28/56; 50%), providing small to moderate evidence for the hypothesis that minority consistency has a small positive total effect on tipping (β = 0.17, Lower Credibility Interval (hereafter LCI) = − 0.01, Higher Credibility Interval (hereafter HCI) = 0.36). When looking at the mediated paths in the model, it becomes clear why the total effect of consistency is rather small.

Table 1.

Bayesian parallel mediation analysis of the effect of consistency on social tipping likelihood via confidence and uncompromisingness Perceptions.

	DV: Tipping likelihood	DV: Confidence	DV: Uncompromising
Consistency (c’/a1/a2)	0.15 [− 0.03, 0.33]	0.22 [0.07, 0.38]	0.17 [− 0.02, 0.34]
Confidence (b1)	0.33 [0.11, 0.53]
Uncompromising (b2)	− 0.33 [− 0.52, − 0.16]
Indirect effect via confidence (a1 x b1)	0.07 [0.01, 0.15]
Indirect effect via uncompromising (a2 x b2)	− 0.06 [− 0.13, 0.01]
Total effect (c)	0.17 [− 0.01, 0.36]
Intercept (α1/α2/α3)	0.68 [0.21, 1.00)	3.27 [3.16, 3.38]	3.79 [3.66, 3.91]
Variance (σ21/σ22/σ23)	0.22 [0.17, 0.29]	0.17 [0.13, 0.22]	0.24 [0.18, 0.30]

The numbers outside brackets display the parameter estimate, while the numbers in brackets are the lower and upper bounds of the 95% credibility intervals of the estimate.

In line with classical minority influence literature and our pre-registration (Moscovici et al., 1969, Wood et al., 1994), we observe strong evidence that participants perceive the confederates as being more confident (β = 0.22, LCI = 0.07, HCI = 0.38) when they are consistent instead of inconsistent, and that this confidence in turn increases the likelihood of a group tipping to a new convention (β = 0.33, LCI = 0.11, HCI = 0.53). Also in line with our initial hypotheses, we observe small to moderate evidence that group members perceive the consistent confederates as being more uncompromising (β = 0.17, LCI = − 0.02, HCI = 0.34). However, importantly and in direct opposition to our pre-registration, strong evidence emerges suggesting appearing uncompromising does not increase but actually decreases the likelihood of social tipping to a new convention (β = − 0.33, LCI = − 0.52, HCI = − 0.16).

In other words, our data imply that being consistent can help minorities trigger tipping via emanating confidence (β = 0.07, LCI = 0.01, HCI = 0.15), but also impede it via appearing uncompromising (β = − 0.06, LCI = − 0.13, HCI = 0.01). The two indirect effects work in opposing directions and are similar in size. Yet, the latter, but not the former, includes zero in the CI and this helps to explain why the direct effect of consistency on tipping is still positive, but modest (β = 0.15, LCI = − 0.03, HCI = 0.33).

In sum, we find partial support for the assumptions made in past individual-level minority influence studies: minority consistency boosts confidence perceptions, which in turn promotes tipping. Consistency also makes our confederates seem more uncompromising, but rather than promoting tipping, appearing uncompromising impedes tipping.

We conduct several robustness and sensitivity analyses (see Methods - DV Classification Task and Methods – Statistical Approach for details). Specifically, we first re-estimate our model with the originally preregistered DV (only full conversion representing tipping) and additionally with a DV including the 2 plots for which there was an equal split in the classification task on whether they represent social tipping as representing tipping instead of not representing social tipping. Second, to examine the sensitivity of our model estimates on the chosen thoughtful priors, we also re-do our main analysis for all three DVs employing uninformative and highly informative priors. All different combinations of alternative DV operationalisations and uninformative/highly informative priors replicate the patterns of the main analysis above (see Supplement 3), thus suggesting the findings are robust.

Discussion

The largest meta-analysis of minority influence effects found that consistent minorities are better at changing individual attitudes than consistent ones and suggested two mechanisms that might drive this increased success: confidence and uncompromisingness⁵. However, whether consistent minorities are more effective at triggering group-level tipping has not been tested. Although the literature suggests that consistent minorities are more likely to change majority members’ attitudes, our findings suggest that consistency only has a rather small positive effect on the likelihood of majority members tipping to a new convention. Instead, the role of minority consistency is more nuanced and conflicting: in line with early minority influence studies²², we observed that a consistent minority is perceived as more confident about its stance, which in turn led to a higher likelihood of social tipping. Consistent minorities are also perceived as uncompromising, but appearing uncompromising led to the opposite effect: it decreased the likelihood of the group tipping to the minority side.

So why does being seen as uncompromising reduce the likelihood of others following? This unexpected finding could be accounted for by a theoretical account of minority influence proposed by Mugny²³. They propose a distinction between a style of behaviour and a style of negotiation with the majority group, wherein the most influential minorities are expected to be those who adopt a consistent style of behaviour but are more flexible in their negotiation with the majority group. Conventions exist to ease coordination between people on issues on which they hold a strong motive to coordinate⁹. Therefore, style of behaviour and style of negotiation are inextricably the same when it comes to convention change: a minority consistently deviating from the current convention (style of behaviour) will inevitably break group coordination and thus come off as inflexible in how it negotiates with the majority (style of negotiation). The two mechanisms we measured are then likely each capturing one side of this coin: uncompromisingness focuses more strongly on the interpersonal negotiation dynamics (i.e., minority members ‘were unlikely to change their New Product choice and side with the rest of the group’) whereas the confidence refers more to the behaviour itself by referring to the actual choice behaviour (i.e., minority members ‘were confident in the New Product they were choosing during the game’). Heightened uncompromisingness perceptions of the consistent minority resulting in lower tipping likelihood that we observe thus aligns with Mugny²³ who proposes that too much consistency in the negotiation style will make a minority come off as inflexible and uncompromising, which in turn evokes negative emotions and reactance in majority members (i.e., if you refuse to budge, I will not listen to you either! ), thereby discouraging them from considering and adopting the minority’s alternative to the status quo^23–25.

The outcomes of the present study may also serve as a guideline for researchers hypothesising about and examining social change. Specifically, the surprising findings nicely showcase that when extrapolating past individual-level theorising to group-level outcomes, one should pay close attention to the specifics of the social change setting. As mentioned above, in our convention change setting, the paradoxical role of minority consistency was likely more pronounced due to the coordination motives underlying conventions: when it comes to conventions, style of behaviour and style of negotiation cannot be separated. In other social change settings (e.g., norm change, diffusion of a new behaviour), this may be the case to a lesser extent and thus, the effects discovered in our study might be less pronounced or even flip entirely. For example, one can be consistently vegan (consistent behaviour style) yet be forgiving to others still eating meat and not demand them to also eat vegan when they go out to a restaurant together (flexible negotiation style). Therefore, future studies should align their theorising to the incentives and motivations driving individual behaviour in the specific social change setting they study.

Furthermore, the described discrepancy between past mainstream theorising and our findings also highlights the importance of using multi-round group-level methods for examining social change phenomena rather than testing them via individual-level proxies (see earlier work⁶ for an extended account of this argument). Past literature has proposed a range of factors that might determine how influential a minority is (e.g., in-group/out-group identities, minority size, social pressure—see earlier reviews¹⁸) and illustrated the effects of such factors on varying individual-level outcomes. However, to truly examine the role of these factors in minorities provoking actual social change and thus maximise the relevance of practical implications that can be drawn from social change studies, future research should employ group-level methods like the experimental game used in the present paper, to truly tap into the effects of hypothesised factors on group-level/society-level outcomes.

In this work, we tried to emulate the process of convention change with a controlled laboratory experiment. While our experimental game reliably replicates some hallmark features of real-life convention change (i.e. sudden convention change after a long delay), our results may not automatically generalize to all real-life instances of convention change, for two reasons. First, we restrict our experimental game to only allow majority members to stick to the status quo or switch to the minority alternative. However, in real life, the majority can also deal with dissidents by excluding minority members from the group⁶ and there is evidence of people often doing so when minorities refuse to budge²⁶. While this third route is unlikely when it comes to e.g. colleagues or family members, there are other situations where social exclusion is a viable option to deal with dissidents (e.g., online spaces). Therefore, future research should examine what reactions minority consistency produces when majority members have the additional option to expel the minority from the group, which provides them with the option of re-establishing group coordination without bowing to the minority and experiencing the hard decision conflict recreated in our study. Second, the inconsistent condition is implemented in our game via a minority group in which two members consistently counter the majority and two randomly shift back and forth between the status quo and minority alternative. While this makes it highly comparable to the consistent condition (i.e., it has the same average size as the consistent one and minimally differs from it in how inconsistent it is), this specific operationalisation can also be interpreted as a sign of divisions or fragmentation within the minority group rather than a sign of individual inconsistency of minority members. To examine whether the discovered effects are primarily driven by individual inconsistency of minority members or the perceived fragmentation of the group itself, future research should aim to disentangle the two.

On a more general note, it is important to realize here that we used a relatively artificial setting to capture the process of convention change. This allowed us to isolate the causal influence of minority consistency, with participants choosing between two novel products that they had not considered before the experiment. While this method maximizes internal validity, in real life, people may already have pre-existing attitudes, which could alter tipping dynamics. Thus, while our method led to insights that ultimately could help activists to develop strategies to expedite tipping points, more work is needed before a one-to-one translation to practical advice can be made.

Methods

Participants

Our sample consisted of 952 participants collected on Prolific. While we collected data across all countries available on the platform, we restricted the sample to only contain people who speak English as a first language since the experimental game instructions are quite complex and might cause issues to non-native speakers. To ensure sufficient quality of the sample, further restrictions were placed in terms of the maximum number of studies a participant was allowed to have participated on the platform previously (max = 200) and the approval rate of the participant in the studies they have participated in previously (only participants with 100% approval rate). Last, since each session of the study contained confederate bots that participants were not aware of, we also restricted the sample to only participants who have indicated they would be comfortable partaking in a study that involves deception.

Within the collected sample, 126 participants terminated their participation before the experimental game began, which left us with a final analysable sample of 826 participants. Of this final sample, 62% were women, 35% were men, 2% indicated another gender, and 1% preferred not to declare their gender. The mean age within our sample was 31 years old (SD = 12.06).

Participants were randomly distributed across 112 experimental groups, 56 of which were confronted with a consistent minority and 56 with an inconsistent one. Each of these groups consisted of 9 real participants and 3 confederates/bots (consistent condition) or 8 real participants and 4 confederates/bots (inconsistent condition) and represented a separate experimental group that played the game and within which social tipping was observed. Each session lasted for up to 30 min, and every participant who completed their participation in the experimental game was compensated with a fixed payoff of £3.20. In addition to that, participants could also earn a monetary bonus depending on the decisions they made in the game (min = £0, max = £1.58). The experimental sessions were carried out between April 25th and May 13th 2022. We obtained active informed consent from all participants before they began their participation. The experimental protocols in the study were carried out in line with relevant guidelines and regulations. The ethical approval for the given study and its data management plan was provided by the University of Groningen Faculty of Economics and Business Institutional Review Board (approval number FEB-20220404-13495). The study preregistration is available on https://aspredicted.org/9V3_M9Q.

Experimental game

In our experiment, we employ a social tipping game previously used in earlier work²⁷ and extensively described in Mlakar et al. ⁷. In the following paragraphs, we stick close to the description of this game to retain as much clarity in the explanation as possible. In our experiment, participants joined an experimental session and began playing the game as soon as they clicked the link on the Prolific website, where each of the experimental sessions was posted as a separate study that only the number of participants required for a given session could join. After opening the study, each participant could immediately read game instructions and answer a few questions regarding the game with immediate accuracy feedback to strengthen their understanding of the game rules. These instructions were then succeeded by a page on which participants had to wait for enough participants to join the game and finish reading the instructions before the game began. The waiting page included a range of elements to ensure participants did not leave the study due to boredom, including a counter showing how many more participants they are still waiting for before the game began and a short recap of the instructions. After this introductory process, they were able to begin playing the social tipping game. The game was employed as a task in which participants’ goal was to, within a maximum of 24 rounds, reach a group consensus on a binary choice.

This task was introduced to participants via a cover story: they were asked to imagine that they are a part of a board of directors. Then, as a board, their duty was to reach a unanimous agreement on which of the two imaginary new products, called Tao and Eta, they would like to launch. They tried to reach unanimous agreement by, in each round, first independently choosing one of the two products (Fig. 2, top panel) and, second, observing the proportion and nicknames of other participants that chose each of the two products in the given round (Fig. 2, bottom panel). After inspecting everyone’s choices, they were able to proceed to the next round, where the whole process repeated again. The process kept repeating itself until the round in which participants unanimously chose the same product (i.e., coordinated) or up to a maximum of 24 rounds whenever no consensus was reached (the limit of maximum number of rounds was set for practical considerations to ensure the experiment finished within a reasonable time).

Participants were unaware that some of the “players” in the game were actually computer-generated bots. These confederates/bots helped mirror how convention change occurs in the real world within the experimental game by first helping participants create a natural status quo social convention, and afterwards behaving as a committed minority advocating for an alternative to the established status quo convention. Accordingly, their behaviour was programmed to unfold in two distinct stages throughout the course of the game. In the initial stage, the majority of bots aligned their choices with the product supported by most participants, thereby facilitating the establishment of a group-wide status quo convention. The second stage began in the round when, for the first time, all participants except one selected the same product, signifying the formal establishment of the status quo convention (Tao). At this point, the bots transitioned into their role as a committed minority, consistently selecting the alternative product (Eta) for the remainder of the game. Each round, participants were thus presented with the choice of either adhering to the status quo convention or diverging from it by choosing the minority alternative.

The experimental framework further incorporated two monetary incentives for participants designed to model the dynamics of social tipping and convention change. The first incentive aimed to encourage coordination within the group by rewarding participants with a bonus payment if they successfully reached consensus. However, this bonus progressively decreased with each passing round, ultimately reaching zero if the group failed to achieve unanimous agreement by the end of the 24 rounds of the game. The second incentive was structured to reinforce inertia, capturing the tendency of individuals to rely on habitual behaviours or exhibit status quo bias. This inertia mechanism was implemented by distributing a portion of the group bonus to each participant, with the amount proportional to the frequency with which they chose the product that ultimately became the consensus. Both aspects—being consistent with past choices but wanting to coordinate with others—are crucial to modelling social conventions: they are characterised by the coordination motive, social costs associated with deviating from the status quo, and the decision conflict associated with these conflicting motives^9,15.

Dropout treatment

Since the game was carried out online, all the game pages enforced a time limit so as to make sure the game concluded for all participants in a timely fashion. However, that also meant that a certain number of participants dropped out either before the game or missed a few rounds of the game itself. Whenever a participant missed making a choice in a given round or dropped out of the study completely, their choice(s) was/were replaced by a bot that aligned with what the majority of other participants chose in the given round so as to minimise the effect replacing the choices of those participants has on the progression of the game.

Minority consistency manipulation

We randomly assigned participants to groups featuring either consistent or inconsistent minority confederates. Groups in the consistent condition featured 9 participants and 3 confederates who, after the initial convention was established, consistently voted for the alternative to the status quo. Groups assigned to the inconsistent minority condition consisted of 8 participants and 4 confederates. Here, 2 confederates consistently chose the alternative, while the other 2 kept randomly switching between choosing the alternative and the status quo. This approach allowed us to vary minority consistency while keeping the average fraction of minority support for the alternative to the status quo at a constant 25% ¹.

DV classification task

Following our preregistration, we initially planned to operationalise social tipping likelihood (dependent variable, hereafter DV) as the proportion of sessions in which all actual participants unanimously switched to the confederates’ position—i.e., full conversion to the minority side (Fig. 3, left panel). This full conversion occurred in 52 of the 112 (46%) experimental sessions, with 30 of the 56 (54%) sessions in the consistent condition and 22 of the 56 (39%) sessions in the inconsistent condition converting fully. However, the data also included 41 sessions where no full conversion to the minority side occurred, while the plots seem to indicate a change process reminiscent of social tipping (Fig. 3, middle panel).

To ensure ecological validity of the social tipping definition in our paradigm, we created a more fine-grained definition of the DV using a classification task. In this task, we recruited 5 independent raters that were blind to the hypotheses of this study and not co-authors of the paper, but were researchers in the field of social psychology generally knowledgeable about tipping points. Each of them received a Qualtrics survey that described social tipping based on the definition provided in Milkoreit² and with an example of a tipping plot provided (see Supplement 2 for the exact text and image displayed to raters). After that, the survey provided them, in random order, 45 plots for which they had to assess whether the plots represent social tipping under the provided definition or not. Of those 45 plots, 41 were plots that we were interested in classifying as they contained a majority of participants at some point of the game following the bots in adopting the alternative to status quo, but never reaching full conversion to the alternative. The other 4 plots served as an understanding check of whether the raters understood the definition of social tipping, with two of them representing sessions where a full explosive conversion to the alternative occurred (i.e., clear examples of social tipping) and two of the sessions where the fewest participants ever transitioned away from status quo (i.e., clear examples of no social tipping). For each presented plot, the raters had to simply choose whether it represents social tipping under the provided definition or not. While making their choices, they could open a pop-up message containing a short recap of the social tipping definition to refresh their memory if they so desired.

Of the 5 raters, one failed to classify all four understanding check plots correctly, so we removed them from our analysis, which left us with data from the other 4 raters that we used in the analyses. The interrater reliability of the 4 valid raters was 0.80, which represents a substantial level of agreement between the raters. Of the 41 relevant plots, the 4 raters unanimously classified 11 plots as representing social tipping and 14 plots as not representing social tipping, a majority of 3 raters classified 2 further plots as representing social tipping and 12 further plots as not representing social tipping, and for 2 plots there was a 50–50 split among the raters in terms of whether they represent social tipping or not. In our main DV, the 13 sessions at least a majority of raters classified as social tipping are considered social tipping, while the other 26 sessions where at least a majority classified them as not social tipping and the 2 sessions with a 50–50 split are considered not social tipping (see Fig. 4).

Fig. 4.

Overview of the number of different types of sessions in our study and their tipping classification: tipping (green) or no tipping (red).

To make sure that the inclusion of those 2 sessions as not representing tipping does not impact our results, we conduct a robustness check of our main analysis with a DV that is changed insofar as it also considers those 2 sessions as representing tipping (Supplement 3, Table 3.2). Last, to also align our analyses with our preregistration, we conduct a further robustness check where only the sessions with full conversion are considered as tipping, but the sessions included in this classification study and other sessions with no full conversion are considered as not social tipping (Supplement 3, Table 3.1).

Mediator measures

To operationalise the mediators, participants evaluated the perceived confidence and uncompromisingness of the minority confederates on a scale from ‘1 - Strongly disagree’ to ‘5 - Strongly agree’. We measured confidence with an item stating ‘I think Players *numbers of minority confederates* were confident in the New Product they were choosing during the game’ (M_overall = 3.39, SD_overall = 1.02; M_incon = 3.26, SD_incon = 1.02; M_con = 3.49, SD_con = 1.00) and uncompromisingness with an item stating ‘I think Players *numbers of minority confederates* were unlikely to change their New Product choice and side with the rest of the group’ (M_overall = 3.86, SD_overall = 1.05; M_incon = 3.77, SD_incon = 1.09; M_con = 3.93, SD_con = 1.01). The items referred to all three minority members in the consistent condition and all four minority members in the inconsistent one. Because we conduct our main analyses on a group level, we employ unweighted group means of the participants’ confidence and uncompromisingness ratings in a given session.

Statistical approach

Our main analysis is carried out as a Bayesian structural equation (parallel mediation) model. Following the recommendations²¹ for obtaining unbiased structural equation estimates in small samples set forth by Smid et al. (2020), we implement thoughtful priors in our model: informative priors wherein the parameter space for the estimated parameters is limited by excluding the values that are impossible or improbable given the type of data at hand but making no assumptions about the direction or the size of a given parameter. According to the meta-analysis of prior distribution usage in Bayesian analysis of small sample studies²¹, this Bayesian approach with thoughtful priors leads to more unbiased parameter estimates than naively employing uninformative priors or using frequentist approaches.

Specifically, we define a uniform prior distribution of intercepts in our regressions spanning across the values which the dependent variable in a given regression covers (i.e., 1–5 for regressions where uncompromisingness and confidence are DVs and 0–1 for the regression where social tipping likelihood is the DV). Similarly, we assume a normal distribution for our beta coefficients with a mean of 0 and a standard deviation chosen in a manner that ensures 99.7% of estimates possible on the distribution fall within the values covered by the scale of a given dependent variable (SD = 1.77 for regressions where uncompromisingness and confidence are DVs and SD = 0.11 for the regression where social tipping likelihood is the DV). Since we do not have any concrete assumptions about the variance and covariance parameters, we leave the prior distributions of those parameters uninformative. The Gelman-Rubin statistic as well as trace plots both indicate a good convergence of our model (see Methods and Supplement 4).

While employing thoughtful priors should lead to the most unbiased estimates, we also want to ensure that our findings are not overly sensitive to the chosen priors. Therefore, we further conduct a sensitivity analysis using two extreme cases, uninformative (Supplement 3, Table 3.4.1, 3.4.2, and 3.4.3) and highly informative priors (Supplement 3, Table 3.3.1, 3.3.2, and 3.3.3). Each of these prior specifications is carried out in combination with all three DV specifications discussed in the section above. Unlike thoughtful priors, uninformative priors do not make any highly restrictive assumptions about the parameters and thus lead to estimates closely resembling those of frequentist statistical approaches. On the other hand, highly informative priors make even more restrictive assumptions than the thoughtful priors employed in our main analysis: not only do they delimit the impossible and improbable parameter space, but they also make assumptions on the direction and size of the effect. In our case, this means that in the model with highly informative priors we kept most prior distributions the same as in the model with thoughtful priors, with the only difference being that we defined the mean of the prior normal distribution of beta coefficients in our regressions to be a small effect in the direction of our proposed hypotheses (M = 0.2 for all the betas in regressions where uncompromisingness and confidence are DVs and M = 0.1 for all the betas in the regression where social tipping likelihood is the DV).

We implemented three Markov chains for estimating each parameter and set a different starting value for each of them. The simulation included an initial adapt/burn-in phase consisting of 6,000 iterations, while the sample simulation consisted of 10,000 iterations succeeding those. The Gelman-Rubin statistic displays a value smaller than 1.1 for all parameters, thus indicating good convergence of the model. We also inspect the trace plots of the given model as well of a model where the sample simulation iterations are doubled to 20,000, and both of those further confirm that the model achieved good convergence (see Supplement 4 for the Gelman-Rubin statistic and trace plots).

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Z.M. wrote the paper and SI, with input from all authors. Z.M., J.W.B, H.R., and B.M.F. contributed equally in designing and interpreting the research; Z.M. performed the research and analysed the data.

Funding

The work of Z.M. was partially supported by the European Union under the Horizon programme (CAPABLE project—grant number 101056891). Views and opinions expressed are however those of the authors only.

Data availability

The data analysed in this paper and the R code for the analyses conducted are available in an OSF repository on the link https://osf.io/cp7de/?view_only=c75d92e880a84864bbe7934a92a46a55.

Declarations

Competing interests

The authors declare no competing interests.