REPORT
Social Prevalence Is Rationally Integrated in
Belief Updating
Evan Orticio
, Louis Martí, and Celeste Kidd
Département de psychologie, Université de Californie, Berkeley
Mots clés: belief change, belief prevalence, misinformation, cue integration
un accès ouvert
journal
ABSTRAIT
People rely on social information to inform their beliefs. We ask whether and to what degree
the perceived prevalence of a belief influences belief adoption. We present the results of two
experiments that show how increases in a person’s estimated prevalence of a belief led to
increased endorsement of said belief. Belief endorsement rose when impressions of the belief’s
prevalence were increased and when initial beliefs were uncertain, as predicted by a Bayesian
cue integration framework. Ainsi, people weigh social information rationally. An implication of
these results is that social engagement metrics that prompt inflated prevalence estimates in
users risk increasing the believability and adoption of viral misinformation posts.
INTRODUCTION
The amount of data required to construct all of our beliefs “from scratch” is intractable given
the limitations of our attention and the complexity of the world. En plus, most truths can-
not be determined by direct reference to the physical world anyway (Festinger, 1954). Plutôt,
relevant evidence remains inaccessible to the individual for most real-world beliefs and must
be mediated through other agents (Perfors & Navarro, 2019). Belief formation thus depends on
information sampled from the social world. This process is distinct from normative social influ-
ence, in which conformity to a group norm takes precedence over conflicting private informa-
tion about the ground truth (Deutsch & Gerard, 1955). Plutôt, this social sampling is necessary
for acquiring information that is complex or otherwise unavailable to the learner.
Empirical evidence makes clear that social information affects beliefs, even while it leaves
open how and why specific social information is integrated. This work dates back to Asch
(1951), who demonstrated that people can report erroneous perceptual judgments when influ-
enced by inaccurate information from confederates. De même, appeals to expert consensus
effectively promote belief change, Par exemple, for anthropogenic climate change (Goldberg
et coll., 2020; van der Linden et al., 2019; van der Linden, Leiserowitz, et coll., 2015), nuclear
pouvoir (Kobayashi, 2018), GMOs (Kerr & Wilson, 2018), and vaccination (van der Linden,
Clarke, & Maibach, 2015). These social influences could be the result of social pressures to
conform to others, especially those of higher status. Van der Linden et al.’s Gateway Belief
Model (2019) argues instead that social information simply licenses belief revision. Alterna-
tivement, a rational account would predict social information should be integrated with the per-
son’s a priori beliefs in ways that are sensitive to the reliability of both information sources.
Citation: Orticio, E., Martí, L., & Kidd, C.
(2022). Social Prevalence Is Rationally
Integrated in Belief Updating. Open
Esprit: Discoveries in Cognitive Science,
6, 77–87. https://doi.org/10.1162/opmi
_a_00056
EST CE QUE JE:
https://doi.org/10.1162/opmi_a_00056
Supplemental Materials:
https://doi.org/10.1162/opmi_a_00056
Reçu: 11 Mars 2021
Accepté: 6 Avril 2022
Intérêts concurrents: The authors
declare no conflict of interest.
Auteur correspondant:
Evan Orticio
eorticio@gmail.com
droits d'auteur: © 2022
Massachusetts Institute of Technology
Publié sous Creative Commons
Attribution 4.0 International
(CC PAR 4.0) Licence
La presse du MIT
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
Evidence in support of rational accounts of social information integration includes that indi-
viduals find a larger number of people more convincing than a smaller number (par exemple., Bond,
2005). Relatedly, the number of endorsers of a belief is known to be a key influencer of belief
adoption. Par exemple, Ransom et al. (2021) found that the raw number of people endorsing a
view was a more important predictor of belief adoption than the diversity of arguments made.
Some evolutionary models of social learning also have a rational flavor, suggesting intelligent
organisms sometimes learn socially by adopting a copy-when-uncertain strategy. Learners
copy the behavior of others when they have no relevant private information (Kendal et al.,
2009; Rendell et al., 2010; Toelch et al., 2014). This evidence is consistent with the rational
uptake of social information into one’s behaviors, but examines cases of discrete choice rather
than graded integration of new social information with held beliefs.
Informational Social Influence as Cue Integration
The role of social information in belief formation may be better understood within a cue integra-
tion framework, borrowed from the perception literature (par exemple., Ernst & Banks, 2002; Knill &
Richards, 1996). Observers combine signals from different perceptual senses to arrive at a uni-
fied percept. In forming a new belief, a learner similarly integrates private information, like
domain-relevant knowledge, with social information, like the prevalence of a belief in a sampled
population. Surtout, each cue is flexibly weighted according to its estimated reliability.
Strong reliance on social information can be rational, especially under conditions of un-
certainty. Within this framework, even the conformity to the majority in Asch’s (1951)
line-matching experiments could reflect optimal information integration rather than—or in
addition to—normative pressure to conform. If the participant assumes that others are unbi-
ased and have low error rates, as would reasonably be expected in simple perceptual tasks,
then the probability of the participant being correct given the confederates’ convergence on a
different answer is low (Toelch & Dolan, 2015). Ainsi, an optimal Bayesian learner would give
high weight to the social information.
The Role of Social Information in Misinformed Belief
These principles may also explain viral cases of online misinformation. Much of the existing
literature on conspiracy and pseudoscientific beliefs has sought to explain them away by
appealing to ancillary influences on belief formation, like emotionality ( Vlasceanu et al.,
2020), political extremism ( Van Prooijen et al., 2015), inattentiveness (Pennycook & Rand,
2019), and bullshit receptivity (Pennycook & Rand, 2020). Cependant, these arguments fail to
acknowledge that many online platforms have created an environment that makes rational belief
formation processes highly susceptible to misinformation. False news has been found to spread
“farther, faster, deeper, and more broadly” than true news online ( Vosoughi et al., 2018,
p. 1150), due in part to the formation of echo chambers. Given the high-virality potential of
online misinformation, it is likely that people encounter high social engagement metrics, like
the number of likes and shares, accompanying false claims. These metrics may serve as a cue
to a belief’s prevalence in the population, which may in turn impact the user’s own impression
of the belief’s legitimacy. This information may be particularly problematic when it is encoun-
tered while a person is “doing their own research” and thus in a state of high uncertainty.
Overview of Present Research
We conduct two experiments to test whether increasing the perceived social prevalence of a
belief increases its believability in the absence of direct evidence. Experiment 1 tests this
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
hypothesis using a set of current, real-world conspiratorial and pseudoscientific beliefs. Nous
further test whether prevalence information is integrated rationally as predicted by a cue inte-
gration framework. If so, the social prevalence cue should be weighted against existing evi-
dence such that it elicits the strongest belief change (un) when new data is most convincing, que
est, estimates of the belief’s prevalence change the most in response to the data, et (b) quand
the initial belief is most uncertain. Experiment 2 replicates Experiment 1 but implements a
cover task to reduce possible demand characteristics. Dans la section suivante, we present the
methods for each experiment and then discuss the results of both together.
Understanding how social prevalence estimates impact belief adoption is important for
understanding how to develop interventions against echo chambers online. The ubiquity
and prominence of inflated cues to the social prevalence of beliefs (par exemple., via visible metrics
of likes, shares, or views) may increase engagement while at the substantial cost of leading
people to be more likely to adopt beliefs they would not under less artificial circumstances.
EXPERIMENT 1
Participants read a series of statements relating to real-world conspiratorial, pseudoscientific,
or misinformed beliefs (par exemple., “The earth is flat,” “Wearing masks is harmful to the health of the
mask wearer,” “The U.S. government planned the 9/11 attack on the World Trade Center”; voir
the Supplemental Materials for the full list). We chose beliefs that are recently attested but
thinly and weakly held (Martí et al., 2021). These low-probability beliefs serve as a stringent
test of the strength of social influence. On each trial, participants provided (1) a likelihood
estimate of the belief (“How likely do you think it is that the statement is true?” on a 0–100
slider scale), et (2) a prevalence estimate (“How many people out of 100 do you think
believe the statement is true?»). The experiment began with three simple practice trials involv-
ing statements of fact (par exemple., “Plants need water to grow”) with feedback. We included four
more trials of the same type in the main task without feedback as attention checks, for a total
de 37 trials.
Participants repeated the same trials in a shuffled order in a second block. Cependant, before
evaluating the likelihood and prevalence of each statement, participants viewed a sample of
data indicating how many of 10 survey respondents believed the shown sentence (voir
Chiffre 1). The sample for the 10 people approximately matched the participant’s own estimate
for the prevalence of the belief in block 1 (Control condition) on half of the trials. On the other
half of trials, the number of people in the sample endorsing the pseudoscientific or conspira-
torial belief was 40% higher than the participant’s initial prevalence estimate (Higher Preva-
lence condition). Par exemple, if a participant estimated in block 1 que 19 de 100 people
believe the given statement is true, then in block 2 they would be shown that 2 of the 10
survey respondents believe the statement (Control condition) ou 6 of the 10 believe it (Higher
Prevalence condition). Note that, for variation, some statements were related to an attested
conspiracy or pseudoscientific belief but worded in their inverse (true) forms, Par exemple,
“Humans have landed on the moon.” In this case, the prevalence of the sample was 40%
lower, c'est, in the direction of the empirically unsupported belief, in the Higher Prevalence
condition. These items are reverse coded in our analyses, so we retain the Higher Prevalence
label for simplicity. The participants then gave estimates for the prevalence and likelihood of
the belief.
We debriefed participants at the end of the experiment. We provided a representative prev-
alence estimate of all of the beliefs based on a large sample of over 900 Americans (Martí
et coll., 2021) and reminded participants that prevalent beliefs are not necessarily true.
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
Chiffre 1. Example trial from block 2.
Experiment 1 guarded against the risk of participants feeling pragmatic pressure to change
their prevalence and belief estimates by nature of being asked twice (par exemple., demand charac-
teristics) in two ways. D'abord, we collected ratings for a large number of statements (30) dans
shuffled orders to make remembering what had been asked previously difficult. Deuxième,
we asked participants after the experiment what they believed the experiment to be about
in order to determine whether participants guessed the purpose and may have altered their
responses accordingly. Experiment 2 adds the additional guard of a cover task.
EXPERIMENT 2
Experiment 2 replicates Experiment 1 with one change: before block 2, participants were
told that the prevalence data was part of a memory task. This cover task was intended to
provide an additional guard against demand characteristics. We instructed participants to
memorize how many of the 10 survey respondents believed each statement in preparation
for a memory quiz.
Similar levels of belief change across the two experiments would suggest that any
observed belief change is not driven by demand effects. Participants’ responses in a debrief-
ing survey provide further evidence against the role of demand effects (see the Supplemental
Materials).
Participants
We recruited 608 (N = 403 in Experiment 1; 205 in Experiment 2) American adults fluent
to participate in an 18-min online experi-
in English through Prolific (www.prolific.co)
ment. Only American adults participated because some experimental
items referenced
U.S.-specific cultural beliefs. We compensated participants at a rate of $10/hour, avec
an opportunity to receive a bonus for good performance. We obtained informed consent
from all participants and used methods approved by the University of California, Berkeley
Comité d'examen institutionnel. We preregistered both experiments prior to data collection at
https://aspredicted.org/sy9wv.pdf
(Experiment 1) and https://aspredicted.org/vc8jr.pdf
(Experiment 2).
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RÉSULTATS
Exclusions
Experiment 1. Eighteen participants were excluded for failing more than one of four attention
checks, et un supplémentaire 19 participants were excluded for giving blank or unreasonable
responses to one or more of six bot-catch questions (par exemple., “What’s your favorite frozen treat?»)
intermixed between experimental trials. These subject-level exclusions resulted in a final
sample of 366.
In addition to these preregistered exclusions, we also excluded trials in which participants
initially endorsed the empirically unsupported belief with a likelihood rating of over 60%,
because the 40% exaggeration in the Higher Prevalence condition could not be applied to
ces. These trials constituted 13.1% of our data, and their removal did not significantly affect
the interpretation of any analyses (see the Supplemental Materials).
Experiment 2. Three participants were excluded for failing more than one of four attention
checks. No additional participants were excluded, yielding a final sample of 202 participants.
Trial-level exclusions (14.6% of all trials) were made using the same criteria as Experiment 1,
as preregistered.
Participants Revise Their Estimates of Prevalence in Light of Prevalence Data
If our manipulation worked as intended, participants’ estimates of the preva-
Experiment 1.
lence of these beliefs should have increased after seeing the Higher Prevalence data, mais
remained the same in the Control condition. En moyenne, participants’ prevalence estimates
increased by 21.0% in the Higher Prevalence condition and remained relatively stable in the
Control condition (decreased by 1.7%). A t test indicates that this difference is statistically
significant (95% CI = [22.1, 23.4]; t(6904.9) = 65.75, p < .001, d = 1.35), confirming the effec-
tiveness of the manipulation.
Experiment 2. Participants’ prevalence estimates increased by 25.6% in the Higher Prevalence
condition and marginally decreased by 1.0% in the Control condition. A t test indicates that
this difference is statistically significant (95% CI = [25.8, 27.5]; t(3991.8) = 61.59, p < .001,
d = 1.71).
Participants Revise Their Beliefs in Line With New Prevalence Information
Experiment 1. Our main prediction was that participants would increase their endorsement of
a belief when given data indicating that the belief is more prevalent than they expect. Figure 2
shows the mean amount of belief change per item in each condition for both experiments (for
a breakdown by item, see the Supplemental Materials). As predicted, participants’ ratings of
the likelihood of these beliefs increased by a mean of 5.44% in the Higher Prevalence con-
dition and remained relatively stable (0.46% increase) in the Control condition (95% CI =
[4.43, 5.52]; t(9046.5) = 17.82, p < .001, d = 0.365), indicating that exposure to samples with
higher belief prevalence influences the plausibility of the belief.
Experiment 2. The main effect of condition was replicated. Participants’ likelihood ratings
increased by a mean of 6.59% in the Higher Prevalence condition, compared to an increase
of 1.22% in the Control condition (95% CI = [4.59, 6.15]; t(5049.1) = 13.50, p < .001, d =
0.375).
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
Figure 2. Boxplot of belief change after seeing a sample of data that either matched participants’
expectations (Control) or indicated a higher prevalence of belief (Higher Prevalence) for Experi-
ments 1 and 2. Points represent the mean belief change per item, with lines showing the effect of
condition for each item.
Belief Change Is Commensurate With Change in Prevalence Estimate
If social prevalence is treated as an independent source of information that is
Experiment 1.
integrated rationally with prior beliefs, then greater changes in one’s estimation of the preva-
lence of a belief should result in stronger belief updating. That is, a stronger prevalence cue
should carry more weight and have a stronger effect on the ultimate belief. Figure 3 shows the
relationship between change in prevalence estimate and resulting belief change within the
Higher Prevalence condition of both experiments. We ran a linear mixed-effects model pre-
dicting belief change with condition and change in prevalence estimate as fixed effects and
random intercepts per participant and item. This model revealed significant main effects of
condition (β = 1.29, t = 3.91, p < .001) and change in prevalence estimate (β = 0.16, t =
9.01, p < .001), suggesting that larger increases in prevalence estimates of a belief led to larger
increases in personal belief endorsement. There was no significant interaction (p = .81). The
model accounted for 19.0% of the variance in belief change (conditional R2).
Experiment 2. A linear mixed-effects model with an identical structure revealed only a signif-
icant main effect of change in prevalence estimate (β = 0.16, t = 6.05, p < .001). Unlike in
Experiment 1, the main effect of condition was not significant after controlling for change in
prevalence estimate (p = .16). The model accounted for 16.4% of the variance in belief
change.
Belief Change Is Dependent on Initial Certainty
Experiment 1. We predicted that rational belief updating should also depend directly on the
initial certainty of the belief. While novel evidence about social prevalence should bear sig-
nificant weight under conditions of uncertainty, high-certainty beliefs should be relatively
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Figure 3. Mean belief change vs. mean change in prevalence estimate for each item in the
Higher Prevalence conditions of Experiments 1 and 2. Lines represent the fit from linear regression
for each dataset with 95% confidence intervals.
resistant to change regardless of social prevalence. Figure 4 illustrates the relationship between
initial belief (directly related to certainty) and belief change across prevalence conditions. We
operationalize certainty as the absolute distance from 50% on the likelihood scale. We fit a
linear mixed-effects model with standardized certainty and prevalence condition as fixed
effects and random intercepts per participant and item. The model revealed main effects of
both scaled certainty (β = 2.42, t = 11.91, p < .001) and prevalence condition (β = 4.93,
t = 18.91, p < .001), as well as a significant interaction (β = −2.84, t = −10.76, p < .001).
The model accounted for 18.1% of the variance in belief change. Only in the Higher Prev-
alence condition, where belief change was motivated by data, lower levels of certainty
predicted higher belief change as hypothesized.
We replicated our predicted effect of certainty with an additional linear mixed-effects
model using change in prevalence estimate as a continuous predictor instead of the dichoto-
mous condition variable. This model had an otherwise identical structure to the first. Again,
main effects of standardized certainty (β = 1.33, t = 8.69, p < .001) and change in prevalence
estimate (β = 0.17, t = 25.59, p < .001) were significant. Crucially, the same significant inter-
action was observed (β = −1.92, t = −14.99, p < .001), such that with higher changes in prev-
alence estimates, initial certainty of a belief negatively predicted belief change. This model
accounted for 23.7% of the variance in belief change.
The positive relationship between certainty and belief change in the Control condition is
not predicted by rational accounts of belief change and likely stems from an inherent property
of our experimental design. Participants’ estimates of prevalence were more likely to differ
more from their own initial beliefs when their own initial beliefs were more certain. This pat-
tern is consistent with weak priors resulting in a person reverting to their knowledge of social
prevalence when making up their mind. Therefore, the difference between the data shown and
the participant’s own initial belief was higher under conditions of high certainty. To control for
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Figure 4. Mean belief change vs. mean initial belief for each item, by condition. Lines represent
the fit from linear regression for each condition, with 95% confidence intervals. As initial belief
increases toward 50% likelihood, certainty decreases. Belief change is plotted directly against
certainty in the Supplemental Materials.
this confound, we added the raw difference between the participant’s initial prevalence esti-
mate and their own initial belief as a fixed effect to the previous model, and used it to predict
belief change in the Control condition. This model revealed that, after controlling for the con-
found, the unpredicted positive effect of certainty in the Control condition disappeared (p =
.28). The predicted effects remained: prevalence change (β = 0.21, t = 13.15, p < .001), the
difference between initial prevalence estimate and initial belief (β = 3.85, t = 19.22, p < .001),
and the negative interaction between certainty and prevalence change (β = −1.92, t = −12.18,
p < .001) all stayed significant. The model accounted for 25.7% of the variance in belief
change. The negative interaction suggests that certainty also drove belief change in a rational
manner in the Control condition when changes in prevalence estimates were sufficiently high.
Identical linear mixed-effects models replicated all of the effects from Exper-
Experiment 2.
iment 1. The first model using prevalence condition as a predictor revealed a significant
main effect of scaled certainty (β = 2.48, t = 8.59, p < .001), a significant main effect of
prevalence condition (β = 5.45, t = 14.58, p < .001), and a significant negative interaction
(β = −3.75, t = −9.90, p < .001). The model accounted for 16.5% of the variance in belief
change. The second model using prevalence change as a predictor revealed a significant
main effect of scaled certainty (β = 0.87, t = 4.09, p < .001), a significant main effect of
prevalence change (β = 0.19, t = 19.37, p < .001), and a significant negative interaction
(β = −1.96, t = −10.33, p < .001). This model accounted for 18.9% of belief change. As
before, after controlling for the confound, the unpredicted positive effect of scaled certainty
became nonsignificant (p = .25). Also as before, predicted effects in the model still
OPEN MIND: Discoveries in Cognitive Science
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
replicated: we observed a main effect of prevalence change (β = 0.22, t = 9.03, p < .001), a
main effect of the difference between initial prevalence estimate and initial belief (β = 3.65,
t = 11.89, p < .001), and a negative certainty by prevalence change interaction (β = −1.02,
t = −4.21, p < .001). This model accounted for 18.6% of belief change.
GENERAL DISCUSSION
In two experiments, we demonstrated that increasing people’s perceptions of the general prev-
alence of a belief can cause them to endorse that belief more strongly, devoid of any direct
evidence. Participants were presented with new prevalence data from an anonymous 10-
person sample that conflicted with their prior about a belief’s prevalence by a uniform amount.
This social prevalence clue alone was enough to inspire belief change, despite the fact that all
items pertained to uncommon, empirically unsupported beliefs from a variety of real-world
domains. Additionally, belief change conformed to two key predictions of a Bayesian cue inte-
gration framework. First, belief change was sensitive to the reliability of the new prevalence
cue. When the new prevalence data was deemed more reliable, as indexed by larger changes
in prevalence estimates, belief change increased. Second, belief change was governed by the
initial certainty of the participant’s belief, with more weakly held beliefs changing more dra-
matically. These results were replicated in Experiment 2, thus ruling out the role of demand
characteristics. Taken together, these findings suggest that decontextualized, nonauthority
social prevalence information serves as a cue that people rationally integrate with existing pri-
vate evidence according to the relative reliability of both information sources.
It is important to note that participants in our experiment were not simply blindly updating
their beliefs to match the prevalence information that they were shown. Recall that the prev-
alence data shown in the Control condition matched participants’ initial estimates of the
broader prevalence of a belief, and not their personal ratings of its likelihood. Participants were
aware of this distinction; their initial prevalence estimates differed from their own initial like-
lihood estimates by a mean of 16.5% across experiments. Thus, before encountering the prev-
alence manipulation, participants demonstrated an implicit understanding that their belief may
not be representative of that of the broader population. Further, prevalence data in the Higher
Prevalence condition was 40% higher than the participant expected, yet participants’ final
prevalence estimates changed by a mean of only 22.6%. Thus, participants did not uncritically
trust the prevalence data, but rather integrated it with their existing belief about the prevalence
of each claim.
Further evidence of this rational integration is that changes in prevalence estimates did not
always lead to changes in private endorsement of the belief. For example, in Figure 4, we see
that people do not update their beliefs when they are held with high certainty. A cue integra-
tion framework also predicts cases in which consensus information does not motivate belief
change. Instead, the prevalence cue is evaluated against the strength of one’s prior belief. The
possibility of bias or error in social evidence may be particularly salient in domains with wide-
spread ignorance or strong political polarization (Lees & Cikara, 2021). There is evidence that
people are able to correct for such bias. Learners rationally discount the weight of a group’s
testimony when their source is shared and thus statistically dependent ( Whalen et al., 2018;
but cf. Yousif et al., 2019). Sensitivity to possible selection bias also can lead people to para-
doxically draw weaker conclusions from stronger evidence when the evidence is presented by
a social agent (Perfors et al., 2018). Future work should investigate cues people use to judge
the reliability of prevalence data in paradigms like ours.
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Beliefs Rationally Integrate Social Prevalence Orticio et al.
Implications for Countering False Beliefs Online
Our findings have direct implications for interventions against the spread of misinformation
online. We found that inferring a belief is more prevalent increases the likelihood of belief
adoption; thus, high-engagement metrics attached to viral misinformation posts may promote
stronger adoption of misinformed beliefs online. This could explain why people rate news
from low-credibility sources as higher quality when engagement metrics are present (Chung,
2017). Further, high-engagement metrics elicit more sharing and less fact-checking from users
in a simulated social media feed (Avram et al., 2020). This is of particular concern for viral
misinformation posts, which can bear engagement numbers in the hundreds or thousands,
as opposed to our experimental manipulation with data on 10 people. Hiding social engage-
ment metrics entirely for posts relaying false or misleading information may therefore help
reduce false belief. Future work should test interventions along these lines in an effort to coun-
ter the online misinformation crisis.
ACKNOWLEDGMENTS
We thank Steve Piantadosi, Holly Palmeri, Carolyn Baer, members of the Kidd Lab, and anon-
ymous reviewers for constructive feedback on this work.
FUNDING INFORMATION
CK, Hellman Fellows Fund. CK, Defense Advanced Research Projects Agency (US), Award ID:
HR001119S0005. CK, Berkeley Center for New Media.
AUTHOR CONTRIBUTIONS
EO: Conceptualization: Equal; Formal analysis: Lead; Methodology: Lead; Visualization:
Lead; Writing – original draft: Lead; Writing – review & editing: Lead. LM: Methodology:
Supporting; Resources: Lead. CK: Conceptualization: Equal; Formal analysis: Supporting;
Funding acquisition: Lead; Methodology: Supporting; Supervision: Lead; Visualization: Sup-
porting; Writing – original draft: Supporting; Writing – review & editing: Supporting.
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