Experimental evidence for tipping points in social convention

Abstract

Tipping points in social convention
Once a population has converged on a consensus, how can a group with a minority viewpoint overturn it? Theoretical models have emphasized tipping points, whereby a sufficiently large minority can change the societal norm. Centola et al. devised a system to study this in controlled experiments. Groups of people who had achieved a consensus about the name of a person shown in a picture were individually exposed to a confederate who promoted a different name. The only incentive was to coordinate. When the number of confederates was roughly 25% of the group, the opinion of the majority could be tipped to that of the minority.
Science , this issue p. 1116

Full text

SOCIAL SCIENCE
Experimental evidence for tipping
points in social convention
Damon Centola
1,2
*, Joshua Becker
1
, Devon Brackbill
1
, Andrea Baronchelli
3
Theoretical models of critical mass have shown how minority groups can initiate
social change dynamics in the emergence of new social conventions. Here, we study
an artificial system of social conventions in which human subjects interact to establish
a new coordination equilibrium. The findings provide direct empirical demonstration
of the existence of a tipping point in the dynamics of changing social conventions.
When minority groups reached the critical mass—that is, the critical group size for
initiating social change—they were consistently able to overturn the established
behavior. The size of the required critical mass is expected to vary based on
theoretically identifiable features of a social setting. Our results show that the
theoretically predicted dynamics of critical mass do in fact emerge as expected
within an empirical system of social coordination.
Observational accounts of rapid changes in
social conventions have suggested that ap-
parently stable societal norms can be ef-
fectively overturned by the efforts of small
but committed minorities (1–3). From social
expectations about gender roles in the workplace
(4) to the popular acceptance of (or intolerance
toward) tobacco use and marijuana use (5), ac-
counts of changing social conventions have hy-
pothesized that minority groups can trigger a
shift in the conventions held by the majority of
the population (1–3,5,6). Although this hypoth-
esis presents a striking contrast to the expecta-
tions of classical equilibrium stability analysis
from economic theory (7,8), it can nevertheless
be well explained by the theory of critical mass
as posited by evolutionary game theory (9–11).
This theory argues that when a committed mi-
nority reaches a critical group size—commonly
referred to as a “critical mass”—the social system
crosses a tipping point. Once the tipping point is
reached, the actions of a minority group trigger a
cascade of behavior change that rapidly increases
the acceptance of a minority view (12–14).
The simplest formulation of critical mass
theory maintains that small groups of regular
individuals—that is, with the same amount of
social power and resources as everyone else—
can successfully initiate a change in social con-
ventions. According to this view, the power of
small groups comes not from their authority or
wealth but from their commitment to the cause
(14,15).
Thus far, evidence for critical mass dynamics
in changing social conventions has been limited
to formal theoretical models and observations
from qualitative studies. These studies have pro-
posed a wide range of possible thresholds for
the size of an effective critical mass, rangingfrom
10% of the population up to 40%. For instance,
theoretical simulations of linguistic conventions
have argued that a critical mass composed of 10%
of the population is sufficient to overturn an
established social equilibrium (14). By contrast,
qualitative studies of gender conventions in
corporate leadership roles have hypothesized
that tipping points are only likely to emerge
when a critical mass of 30% of the population
is reached (3,16). Related observational work
on gender conventions (17)hasbuiltonthisline
of research, speculating that effective critical
mass sizes are likely to be even higher, ap-
proaching 40% of the population. Despite the
broad practical (18,19) and scientific (1,12)
importance of understanding the dynamics of
critical mass in collective behavior, it has not
been possible to identify whether there are in
fact tipping points in empirical systems because
such a test requires the ability to independently
vary the size of minority groups within an evolv-
ing system of social coordination.
We addressed this problem by adopting an
experimental approach to studying tipping-
point dynamics within an artificially created
system of evolving social conventions. Following
the literature on social conventions (9,20,21),
we study a system of coordination in which a
minority group of actors attempt to disrupt an
established equilibrium behavior. In both our
theoretical framework and the empirical setting,
we adopt the canonical approach of using co-
ordination on a naming convention as a general
model for conventional behavior (21–24). Our
experimental approach is designed to test a
broad range of theoretical predictions derived
from the existing literature on critical mass
dynamics in social conventions.
We first synthesized these diverse theoret-
ical and observational accounts of tipping-point
dynamics to derive theoretical predictions for
the size of an effective critical mass (25). Based on
earlier theoretical (9,26) and qualitative studies
of social convention (20,23), we propose a simple
model of strategic choice in which actors decide
which social conventions to follow by choosing
the option that yields the greatest expected in-
dividual reward given their history of social in-
teractions (9). In this individual learning model,
people coordinate with their peers so long as
they benefit individually from coordinating. The
RESEARCH
Centola et al., Science 360, 1116–1119 (2018) 8 June 2018 1of4
1
Annenberg School for Communication, University of
Pennsylvania, Philadelphia, PA, USA.
2
School of Engineering,
University of Pennsylvania, Philadelphia, PA, USA.
3
Department of Mathematics, City, University of London,
London, UK.
*Corresponding author. Email: dcentola@asc.upenn.edu
Fig. 1. Predicted tipping points in social stability. (A) Theoretical modeling of the proportion
of outcomes in which the alternative behavior is adopted by 100% of the population. In this
system, the number of agents (N) = 1000, the number of interactions (T) = 1000, the number of past
interactions used in agent decisions (M) = 12. (B) The size of the predicted critical mass point is
shown as a function of individuals’average memory length, M,where(N= 1000, T= 1000).
The dashed lines indicate the range enclosed by our experimental trials, showing the largest
unsuccessful minority (21%) and the smallest successful minority (25%). Although the expected size
of the critical mass point increases with M, this relationship is concave, allowing the predicted
tipping point to remain well below 50% as Mgets large (>100). (Inset) Effect of increasing population size
on the precision of the size of the committed minority (C)prediction(M=12,T= 1000). For N<1000,
small variations in the predicted tipping point emerge due to stochastic variations in individual
behavior. Shaded region indicates Csizes where success was observed frequently but without
certainty. Above this region, for larger Csizes, the probability of success reaches 1; for Csizes below
this region, the likelihood of success goes to 0.
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model predicts a sharp transition in the collec-
tive dynamics of social convention as the size of
the committed minority reaches a critical frac-
tion of the population (Fig. 1). When the size of
the committed minority is below this predicted
tipping point, the dominant social convention is
expected to remain stable, whereas above this
size it is expected to change (25).
Our theoretical predictions for the size of the
critical mass were determined by two parame-
ters: individual memory length (M) and popu-
lation size (N). Explorations of these parameters
(Fig. 1) show that the predicted size of the tipping
point changes with individuals’expected memory
length (M). When participants have shorter
memories (M< 5 interactions), the size of the
critical mass is smaller. Even under the assump-
tion that people have very long memories (M>
100 interactions), the predicted critical mass size
remains well below 50% of the population (25),
indicating that critical mass dynamics may be
possible even in systems with long histories.
Variations in population size were explored com-
putationally in the range 20 < N< 100,000 and
were not found to significantly affect the pre-
dicted criticalmass size (25). Figure 1 shows that
for populations in the range 20 < N< 1000,
stochastic fluctuations introduce a small uncer-
tainty into the estimate of the critical mass size.
However, for population sizes N> 1000, the
predicted tipping point for social change is con-
stant and independent of N[complete details
in (25)].
We recruited 194 subjects from the World
Wide Web and placed them into online com-
munities where they participated in a social
coordination process (27,28). Upon arrival to
the study, participants were randomly assigned
to participate in one of 10 independent online
groups, which varied in size from 20 to 30
people. In a given round of the study, the mem-
bers of each group were matched at random
into pairs to interact with one another. Within
each pair, both subjects simultaneously assigned
names to a pictured object (i.e., a face), attempt-
ing to coordinate in the real-time exchange of
linguistic alternatives (20,25). If the players
entered the same name (i.e., coordinated), they
were rewarded with a successful payment; if
they entered different names (i.e., failed to co-
ordinate), they were penalized. In each commu-
nity, individuals interacted with each other
over repeated rounds of randomly assigned pair-
ings, with the goal of coordinating with one
another (25). Participants were not incentiv-
ized to reach a “global”consensus but only to
coordinate in a pairwise manner with their part-
ner on each round. Participants were financially
rewarded for coordinating and financially pun-
ished each time they failed to coordinate with
each other (25). Once a convention was estab-
lished for the entire population, the incentives
strongly favored coordinating on the equilib-
rium behavior.
After each round, the participants could see
only the choices that they and their partner had
made, and their cumulative pay was updated
accordingly. They were then randomly assigned
to interact with a new member of their group,
and a new round would begin. These dynamics
reflect common types of online exchanges, in
which community members directly interact with
the other members of a large, often anonymous
population—using, for instance, chat interfaces
or messaging technologies—leading them to
adopt linguistic and behavioral conventions that
allow them to effectively coordinate their actions
with other participants’expectations (20,29 30).
Consistent with these types of settings, partic-
ipants in the study did not have any informa-
tion about the size of the population that was
attempting to coordinate nor about the number
ofindividualstowhomtheywereconnected
Centola et al., Science 360, 1116–1119 (2018) 8 June 2018 2of4
Fig. 2. T ime s eries showing adoption of the al ternative convent ion by noncom mitted
subjects (i.e., experimental subjects). Gray lines indicate the popularity of the established
convention; black lines show the adoption of the alternative convention. Success was
achieved when more than 50% of the noncommitted population adopted the new social
convention. Trials in the left column show failed mobilization, whereas trials in the right
column show successful mobilization. A transition in the collective dynamics happens when
Creaches ~25% of the population. Each round is measured as N/2 pairwise interactions,
such that each player has one interaction per round on average.
RESEARCH |REPORT
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(9,20,23). In every group, this interaction pro-
cess quickly led to the establishment of a group-
wide social convention, in which all players in
the network consistently coordinated on the
same naming behavior (20,25). Once a con-
vention was established among all experimental
participants, we introduced a small number of
confederates (that is, a “committed minority”)
into each group, who attempted to overturn
the established convention by advancing a novel
alternative (25).
Trials varied according to the size of the com-
mitted minority (C) that attempted to overturn
the established convention. In total, we studied
the dynamics of critical mass in 10 independent
groups, each with a committed minority of a
fixed size. Across all 10 groups, the sizes of the
committed minorities were in the range (15% <
C< 35%).
Figures 2 and 3 report tipping-point dynamics
in the collective process of overturning an
established equilibrium. Consistent with the
expectations of our theoretical model (using
empirically parameterized values of Nand M),
when the size of the committed minority reached
~25% of the population, a tipping point was
triggered, and the minority group succeeded in
changing the established social convention.
Five trials were conducted. Each trial was
composed of two communities—one with the
committed minority below the expected critical
size (C< 25%) and one with it equal to or above
(C≥25%). In every trial, the community with C<
25% had only small numbers of converts to the
minority view. Over the course of these trials,
each of these converts eventually reverted to the
dominant norm. Continuous interactions led to
occasional switching by subjects throughout the
study. However, over all the trials, in the condi-
tion where the minority group was smaller than
25% of the population, on average only 6% of th e
noncommitted population adopted the alternative
behavior by the final round of the study.
For each of these unsuccessful trials, we
conducted a corresponding trial using another
population of the same size but with a larger
committed minority (25% ≤C≤31%). In all
these groups, the alternative norm reached
the majority of the population within the ex-
perimental window of observation (Figs. 2
and 3). Over all trials, populations with C≥25%
were significantly more likely to overturn the
dominant convention than populations with
acommittedminoritybelow25%(P=.01,
Wilcoxon rank sum). We found that in one case
(Trial 1) this transition from failure to success
was the result of increasing the size of the com-
mitted minority by only one person.
Figure 3 shows a summary of final adoption
levels across all trials, along with expectations
from our empirically parameterized theoretical
model, with 95% confidence intervals. Popula-
tions with committed minorities ranging from
25% ≤C≤27% achieved uptake levels between
72 and 100% within the empirical observation
window. At C= 31%, the committed minority
achieved consensus within the window of em-
pirical observation. Figure 3 compares these
observations to numerical simulations of the
theoretical model using population sizes and ob-
servation windows (Trounds of interaction) com-
parable to the experimental study (N= 24, T=
100, M= 12). Memory length for these simulations
was calibrated using subjects’empirical memory
lengths in this study based on their observed
behavior over all 10 groups. A memory length
in the range 9 ≤M≤13 provides a good ap-
proximation of subjects’observed behavior, cor-
rectly predicting 80% of subjects’choices across
all trials (25). The theoretically predicted critical
mass size from this model fit the experimental
findings well (Fig 3). Numerical analyses indicate
that with larger population sizes, the critical mass
point becomes more exact (See Figs. 1 and 3),
approaching 24.3% of the population.
Our experimental results do not show agree-
ment with theoretical predictions from models
of social convention that predict low critical
mass thresholds, at 10% of the population. How-
ever, our findings show good agreement with
qualitative studies of gender conventions within
organizational settings (3), which hypothesized
that a critical mass of ~30% could be sufficient to
overturn established norms (16). Our results may
suggest that in organizational contexts—where
population boundaries are relatively well defined
and there are clear expectations and rewards for
social coordination among peers—the process of
normative changes in social conventions may be
well described by the dynamics of critical mass.
The design choices that aided our control of
the study also put constraints on the behaviors
that we could test. Our experimental design pro-
vided subjects with social and financial incen-
tives that strongly favored coordinating on an
established social convention (25). However, in
the real world, individuals’emotional and psy-
chological commitments to established behav-
iors can create additional resistance to behavior
change (31). To further explore these expecta-
tions, supplementary analyses of our theoretical
model (fig. S7) (25) extend our basic predictions
to consider how the critical mass size may differ
under conditions of greater social entrenchment.
When actors are more conservative—exhibiting an
explicit bias in favor of the established convention
(based on a skewed best-response calculation
favoring the equilibrium behavior)—tipping-point
dynamics were still predicted to be achievable by
committed minorities with only marginally larger
group sizes.
In delimiting the scope of our findings, we
emphasize that the critical mass value of 25%
is not expected to be a universal value for chang-
ing social conventions. Our results demonstrate
that within an endogenous system of social co-
ordination, tipping-point dynamics emerged con-
sistent with theoretical expectations. Further
work is required to determine the applicabil-
ity of our findings to specific social settings. In
particular, alternative empi rical parameter-
izations of our model can result in alternative
predictions for the expected size of the critical
mass. We expect that the findings from our
study can be considerably expanded by future
empirical work studying the dynamics of tipping
points within other empirical systems of so-
cial convention.
For instance, an important setting in which
these results might be usefully applied concerns
the growing ability of organizations and govern-
ments to use confederate actors within online
spaces to influence conventional behaviors and
beliefs. Recent work on the 50 Cent Party in
China (32,33) has argued that the Chinese
government has incentivized small groups of
motivated individuals to anonymously infiltrate
social media communities such as Weibo with
the intention of subtly shifting the tone of the
collective dialogue to focus on topics that cel-
ebrate national pride and distract from collec-
tive grievances (32). We anticipate that social
media spaces of this kind will be an increasingly
important setting for extending the findings of
our study to understand the role of committed
minorities in shifting social conventions. Sim-
ilarly, the results from our study may also be
usefully applied to the dynamics of critical mass
in other online settings, such as changing social
expectations regarding (i) the standards of ci-
vility on Facebook and other online discussion
forums (19,34), (ii) the acceptability of bullying
behavior in adolescent chat groups (35), and
Centola et al., Science 360, 1116–1119 (2018) 8 June 2018 3of4
Fig. 3. Final success levels from
all trials (gray points indicate trials
with C< 25%; black points indicate
trials with C≥25%. Also shown
is the theoretically predicted critical
mass point (solid line) with 95%
confidence intervals (N=24,T= 45,
M=12; gray area indicates 95% con-
fidence intervals from 1000 replications).
The dotted line indicates C=25%.
The theoretical model of critical mass
provides a good approximation of the
empirical findings. For short time periods
(T< 100 interactions), the critical mass
prediction is not exact (ranging from 20%
<C< 30% of the population); however,
over longer time periods (T> 1000) the transition dynamics become more precise (solid line, 25).
RESEARCH |REPORT
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(iii) the appropriate kinds of content to share
with strangers over social media (36), all of
which have been suggested to exhibit suscep-
tibility to shifts in conventional behavior as a
result of the activity of a small fraction of the
population (19,34,36).
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ACKNO WLED GME NTS
We gratefully acknowledge research assistance from S. Kim
and N. Herbert, helpful suggestions from P. S tarr and
A. van de Rijt, and programming assistance from A. Wagner
and R. Overbey. This research was approved by the Institutional
Review Board at the University of Pennsylvania, where the
study was conducted, and it included informed consent by all
participants in the study. Funding: The authors received
no external funding in support of this research. Author
contributions: D.C. and A.B. designe d the study. J.B. and
D.B. collected the data. D.C., J.B., D.B., and A.B. analyzed
the data. D.C. wrote the manuscript. All authors commented
on and approved the final manuscript. Competing interests:
The authors declare that they have no competing interests.
Data and materials availability: The datasets are available
upon request and upo n publication wil l be publicly availa ble
for download from the university Web site: http://ndg.asc.upenn.
edu/exp eriment s/crea ting-c ritical -mass. Upon publication,
the data will be available at Dataverse, doi:10.7910/DVN/11HUAG.
The code in R is available on GitHub at https://github.com/
NetworkDynamicsGroup/BestResponseNameGame.
SUPPLEMENTARY MATERIALS
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Supplementary Text
Figs. S1 to S7
References (37)
3 January 2018; accepted 20 April 2018
10.1126/science.aas8827
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Experimental evidence for tipping points in social convention
Damon Centola, Joshua Becker, Devon Brackbill and Andrea Baronchelli
DOI: 10.1126/science.aas8827
(6393), 1116-1119.360Science
, this issue p. 1116Science
opinion of the majority could be tipped to that of the minority.
name. The only incentive was to coordinate. When the number of confederates was roughly 25% of the group, the
about the name of a person shown in a picture were individually exposed to a confederate who promoted a different
devised a system to study this in controlled experiments. Groups of people who had achieved a consensuset al.Centola
Theoretical models have emphasized tipping points, whereby a sufficiently large minority can change the societal norm.
Once a population has converged on a consensus, how can a group with a minority viewpoint overturn it?
Tipping points in social convention
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MATERIALS
SUPPLEMENTARY http://science.sciencemag.org/content/suppl/2018/06/06/360.6393.1116.DC1
REFERENCES http://science.sciencemag.org/content/360/6393/1116#BIBL
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