Using a Cognitive Network Model of Moral and Social Beliefs to Explain Belief Change
CChanging Beliefs about Scientific Issues: The Role ofMoral and Social Belief Networks
Jonas Dalege and Tamara van der Does
Equal authorship, order determined by universe splitter. Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501.
Abstract
The skepticism towards childhood vaccines and genetically modified (GM) foodhas grown against scientific evidence of their safety. Distrust in scientific researchhas important societal consequences, from the spread of diseases to hunger in poorerregions. However, these scientific beliefs are hard to change because they are en-trenched within many related moral beliefs and perceived beliefs of one’s socialnetwork. To understand when belief change is possible, we propose a cognitive net-work model which integrates both moral and social beliefs and provides testableempirical predictions. Using a probabilistic nationally representative longitudinalstudy, we find that individuals who changed their beliefs, either towards more pos-itive or negative beliefs about childhood vaccines or GM food, had a reduction inthe estimated dissonance of their cognitive belief network. These results are in linewith model predictions, shed light on the mechanisms leading to belief change, andhave implications for science communication.
Introduction
The World Health Organization (WHO) lists vaccination hesitancy as one of the tengreatest threats to global health [44]. Erroneous beliefs regarding vaccines, somewhatcommon in the US [21], can accelerate or even re-ignite the spread of diseases globally.In another recent report, the WHO also points out that around 45% of deaths amongchildren under 5 years of age are linked to undernutrition [45]. Even though the scientificcommunity has confirmed that currently approved GM crops are safe and could providehigher yields [8], many US Americans are skeptical about this technology [20, 22]. Otherbeliefs inconsistent with scientific knowledge, such as climate change denial, can havesimilar detrimental consequences for society. In order to develop successful public sciencecommunication, we need to understand how skeptical beliefs about scientific issues canbe changed.In this paper, we propose a cognitive network model inspired by statistical physicsto explain belief change about GM food and childhood vaccines. We consider this modelto be a useful analogy to represent cognitive processes related to belief change. We1 a r X i v : . [ c s . S I] F e b stimate and test this model using data from a longitudinal nationally representativestudy with an educational intervention. We investigate 1) whether beliefs become moreinterdependent (formalized as temperature) over time, 2) whether estimated potentialdissonance (formalized as energy) relate in expected ways to self-reported feelings ofdissonance, and 3) whether estimated potential dissonance can be used to predict beliefchange in response to the intervention. By combining a unifying predictive model with anexperimental longitudinal dataset, we expand upon the strengths of earlier investigationsinto science communication and belief change dynamics.Previous empirical research on beliefs about GM food and childhood vaccines hasfound that skepticism about their safety is shaped by both related moral beliefs (e.g.,care for others, concerns about the environment, importance of naturalness, and purity)and perceived beliefs of trusted social groups, such as doctors or family members [2, 7,30, 31, 34, 40, 42]. Studies focusing on changing these beliefs have therefore tried tovary the framing of the factual information and the source of information, with mixedsuccess [4, 29, 36, 39]. This literature sheds light on important related beliefs (both moraland social) as determinants of beliefs about GM food and childhood vaccines. However,these empirical studies tend to focus on specific interventions and populations [12] andrarely develop a unifying model to understand the processes underlying belief changemore generally.Processes of belief change have received a lot of attention across disciplinary fields,but understanding and predicting belief change remains difficult due to the variety offactors shaping this process (for a review, see [23]). Mirroring findings from empiricalresearch on GM food and childhood vaccines, two important sets of factors have emergedas consistently important for belief change. First, individuals hold many related personalbeliefs, such as moral beliefs. In social psychology, the concept of dissonance was devel-oped to understand when and why individuals might change their beliefs when they areincoherent with each other [13, 19]. Within this approach, incoherent beliefs translateinto feelings of dissonance and belief change if enough attention is paid to these beliefs.Building on this concept of dissonance, more recent research has modeled the relation-ship between personal beliefs using cognitive network models to predict belief dynamics[9, 11, 32, 35, 43]. Second, individuals’ beliefs are shaped by their social networks. Instatistical physics, models of opinion dynamics can predict change over time within asocial network [5, 37]. These models, however, generally do not take into account thatthe beliefs held by one’s social network do not directly influence one’s own beliefs. In-stead, their influence is mediated by how one perceives beliefs in one’s social network[1, 6, 18, 28]. These two strands of research tend to focus on either related personalbeliefs or social networks, without incorporating the two within a testable model.In recent years, a few belief change models were developed to focus specifically onthe interaction between related personal beliefs (e.g., moral beliefs) and beliefs aboutone’s social network (social beliefs). These classes of models considerably improvedour understanding of belief change. In general, these models have either focused ondissonance between all moral and social beliefs using the statistical physics concept ofenergy [25], or on network imbalance between personal and social beliefs (e.g., belief A2s positively connected to beliefs B and C, but belief B and C are negatively connected)[3, 16, 33, 38, 41]. Models based on dissonance were able to predict belief change usingestimated energies from reported moral and social beliefs [25]. However, these modelsdid not take the network structure of related moral beliefs into account. Models basedon network imbalance were able to predict distributions of beliefs [41] and provide anexplanation of how minorities can convince majorities [38]. Empirical tests of whetherthese model can predict belief change are yet lacking in the literature.Our cognitive network model integrates both moral and social beliefs and can explainempirical dynamics over time to predict belief change. We extend the recent AttitudinalEntropy (AE) framework [10], a statistical physics model which conceptualizes individualattitudes as networks. Within this framework, individuals change their beliefs towardsmore consistency in order to reduce their attitudinal entropy (a measure of randomnessand unpredictability). The fundamental units are spins representing beliefs. We build onthis model to include both moral and social beliefs. While the AE framework treats beliefsas binary, here we generalize to beliefs that can take any value between -1 (completedisagreement) and 1 (complete agreement). The main concepts and their measures onthe individual level are listed in Table 1.In our model, couplings between beliefs (both moral and social) represent the strengthand sign (positive or negative) of the relationships between beliefs. These couplings areestimated using partial correlations between nodes in the network. The strength of thecouplings in the network determines the probability that beliefs are in consistent states.A network with strong couplings is more likely to have consistent beliefs, while a networkwith weak couplings is more likely to have inconsistent beliefs. The sign of the couplingsin the network determines which belief states (spins) can be regarded as consistent. Let’sassume, for example, that the belief that vaccines are safe and the belief that they areeffective are positively connected, and that the belief that vaccines are safe is negativelyconnected to the belief that pharmaceutical companies are only interested in makingmoney regardless of patients’ health. The belief network would be highly consistent ifthe individual agrees with the former two beliefs and disagrees with the later belief (or,conversely, disagrees with the former two beliefs and agrees with the later belief).Energy can be understood as a formalization of the psychological concept of potentialdissonance. Potential dissonance refers to the actual inconsistency between beliefs andis translated into felt dissonance if enough attention is given to these beliefs. Accordingto classic psychological theories and the AE framework, felt dissonance leads to beliefchange because individuals want their beliefs to be in a consistent state [10, 19]. Energyis measured as the product of each pair of beliefs (spins) and their relationship (coupling)multiplied by -1. A consistent network has low energy and an inconsistent network hashigh energy.Temperature can be interpreted using several psychological processes that reducedisorder and randomness, such as attention and thought directed at beliefs, with lowertemperature corresponding to higher attention and thought. Temperature is estimatedusing the average of scaling values transforming individual couplings (estimated partialcorrelations) into measured correlations. Therefore, temperature relates to the inter-3able 1: Overview of model parameters within the statistical physics framework, andtheir corresponding psychological constructs and methods of estimation. Statisticalphysics term Psychological construct Estimation
Coupling ω ij Relationship between two be-liefs. Partial correlation between b i and b j controlled for all other beliefs.Energy H Potential dissonance. Product of self-reported belief scores b i b j and ω ij multiplied by -1. Measuresmisalignment of beliefs with estimatedconsistent network structure.Temperature /β Subsumes several processesthat decrease disorder andrandomness of belief networkssuch as attention and thoughtdirected at the beliefs. Average of belief-specific scaling values.Scaling values of b i and b j are estimatedin order to transform ω ij into measuredcorrelations. Measures inverse of inter-dependence between beliefs.dependence between beliefs: High measured correlations between beliefs result in lowestimated temperature, while low measured correlations between beliefs result in highestimated temperature. Temperature thus influences belief change through its scaling ofthe couplings. Lower temperatures increase the impact of couplings on the belief states,while higher temperatures reduce the impact of the couplings.Relationships between different concepts in our model can be expressed by Equations1 and 2: H ( b i ) = − (cid:88) ω ij b i b j (1)where H ( b i ) is the energy (potential dissonance) of a spin representing a belief, b i isthe value of this particular belief in the belief network (moral or social), and ω ij is thecoupling (relationship between beliefs) between b i and another belief in the network, b j .We omit an external field (external information) originally included in the AE framework,because our focus lies on the couplings between beliefs. The probability that a belief willchange is described as: P ( b i → b (cid:48) i ) = 1 / (1 + e β ∆ H ( b i b (cid:48) i ) ) (2)where P ( b i → b (cid:48) i ) is the probability that the belief changes its state , ∆ H ( b i b (cid:48) i ) is thedifference in energy between the two belief states, and β is the inverse temperature ofthe system. The probability of belief change thus increases when the energy of the newstate is lower than the current state and when temperature is sufficiently low.When temperature is low (paying attention to the belief), individuals are motivatedto change their beliefs so that the energy of their belief network becomes lower. As seenin Figure 1a-b, consistent consistent belief states (low energy states) are much more likelythan inconsistent belief states (high energy states) when temperature is low enough. Tonote, our model does not differentiate between the direction of belief change, but insteadproposes that beliefs are more likely to move to a consistent state if the network estimated4igure 1: Expected probability given energy and temperature of the system with ex-amples of network systems. Network nodes represent the direction of the belief andedges represent the direction of the relationship between beliefs (blue=positive andred=negative). Network systems in low temperature (a) tend to move towards lowerenergy state or higher consistency states (b). Network systems in high temperature (c)have similar probabilities of going both to high or low energy states.temperature is low and the energy is high. On the other hand, when temperature is high(attention is scattered), different configurations of beliefs are equally likely even if theirenergies are different (see Figure 1c).This model has several empirical predictions. First, the model predicts that thetemperature of the belief network should decrease, or interdependence between beliefsshould increase, when individuals pay attention to their beliefs. Second, belief networkenergies are expected to be negatively related to self-reported feelings of dissonance.Third and most crucially, belief change is predicted to be more likely when individuals’belief network energies are high and temperature is sufficiently low. In order to test thesepredictions, we need longitudinal data on beliefs over time from which we can estimatean statistical model that reflects our theoretical model. Results
We used a nationally representative longitudinal study of beliefs about GM food andchildhood vaccines to test implications of our model (see Methods for details on thestudy design and questionnaire). This study included both moral beliefs related to the5afety of each technology (e.g., GM food [Childhood vaccines] are beneficial to children,GM food [Childhood vaccines] are part of our tradition) and social beliefs about theirsafety (e.g., % of medical doctors belief GM food [Childhood vaccines] is [are] safe, %of my family and close friends belief GM food/Childhood vaccines is/are safe). Weassessed these beliefs four times across three waves of data collection (over an averageof 30 days): once in the first and third wave and twice in the second wave (before andafter the intervention). In the second wave, we presented individuals with an educationalintervention about the safety of GM food and vaccines.Using these data, we estimated belief networks and variation in temperature at thegroup level. We fitted different specifications of our general theoretical model on thefour time points. These specifications focused on constraining partial correlations to beequal, intercepts (mean values) to be equal, and temperature to be equal (see Methodsfor details on network estimation). Additionally, we tested whether the data can becaptured best by a dense network (all beliefs are directly connected to all other beliefs)or a sparse network (some beliefs are not directly connected). The results indicatedthat a sparse network with equal partial correlations and equal intercepts between timepoints and varying temperature across time points fitted the data best. This implies thatthe network structure remained constant throughout time, but that the interdependencebetween beliefs varied.The estimated group-level networks for beliefs regarding GM food and childhoodvaccines are shown in Figure 2a and 2b. In both networks the moral and social beliefs wereconnected to each other but formed two distinct clusters. Most beliefs were positivelyconnected but there were some negative connections as well. The GM food networkwas more densely connected than the childhood vaccines network, indicating that beliefstoward childhood vaccines were more specific than the beliefs toward GM food (i.e., thehigher density of the GM food network indicates that beliefs toward GM food are morehighly correlated than beliefs toward childhood vaccines). Using this empirical networkmodel derived from our theoretical model, we tested our three empirical predictionsdescribed above.
Temperature over Time
A low estimated network temperature, or high interdependence between beliefs, is nec-essary for the relationship between energy and belief change to hold. Systems in lowtemperature are more likely to move from inconsistent states to consistent states, whilesystems in high temperature have similar probabilities of changing to any state. As hy-pothesized above, attention to beliefs should lead to lower temperature. We thereforeexpected that temperature of the network would decrease as individuals took part in thelongitudinal survey about their beliefs surrounding the safety of GM food and childhoodvaccination.As can be seen in Figure 3a and 3b, the temperatures of both belief networks de-creased with time, implying that all beliefs became more interdependent during our GMfood and childhood vaccines studies. The sharpest decrease in the temperature was ob-served between the first and second time point, implying that the sharpest increase in6
M food Childhood vaccines
Agc Com ChiCouEnv FamFrC GodAll Inf NatTraOnE FaF GovJou MedOnC GeP Sci (a)
Agc ComChiCou EnvFamFrC GodAllInf NatTraOnE FaFGovJou MedOnCGeP Sci (b)
Moral beliefsAgc: Appropriate agencies approveCom: Companies and individuals benefitChi: Beneficial to childrenCou: Positive for countryEnv: Beneficial to environmentFam: Positive for family FrC: Free to chooseGod: God approvesAll: All individuals benefitInf: Information is sharedNat: NaturalTra: Part of traditionSocial beliefsOnE: Online expertsFam: Family and friendsGov: Governmenal agenciesJou: Journalists at favorite media Med: Medical doctorsOnC: Online communityGeP: General publicSci: US scientists
Figure 2: Belief networks for GM food (a) and childhood vaccines (b). Beliefs includemoral (orange nodes) and social beliefs (green nodes). Edges represent partial correlations(couplings) between two beliefs controlled for all other beliefs. Blue (red) edges representpositive (negative) partial correlations and the widths of the edges correspond to thestrength of the partial correlations. 7
M food
Time points T e m pe r a t u r e W1 W2a W2b W3 . . . (a) Childhood vaccines
Time points T e m pe r a t u r e W1 W2a W2b W3 . . . (b) Figure 3: Changes in estimated temperature of belief networks through time for GMfood (a) and childhood vaccines (b).the interdependence between beliefs was observed between the first and second measure-ment. The decreasing temperature over time is in line with our model’s postulate asthe questionnaire and educational intervention probably increased attention directed atthe issues. It is noteworthy that simply administering a questionnaire has the strongestimpact on temperature. A relatively low temperature between wave 2a (beliefs measuredbefore the intervention) and wave 2b (beliefs measured after the intervention) meansnetworks should be more likely to move from high energy states to low energy states.In psychological terms, more attention during the administration of the educational in-tervention should enable potential dissonance to be translated to felt dissonance andbelief change. Granted our estimated energies relate to measured psychological factorsas specified in our model.
Energy and Self-reported Dissonance
We tested whether individual belief network energies (see Methods for their calculation)relate to felt dissonance as specified in our model. To do so, we measured self-reported feltdissonance in each of the three waves. In the second wave dissonance was measured afterthe intervention. We therefore correlated dissonance in this wave with the energies basedon the beliefs measured after the intervention. We expected a positive relation betweenenergy and self-reported dissonance, given sufficiently low temperature. Indeed, withenough attention directed to the subject at hand, individuals should be more sensitiveto beliefs that might be contradictory from one another and report feelings of beinguncomfortable, uneasy, and bothered [13, 18]. Therefore, there should be a positivecorrelation between energies and felt dissonance which increase over time, as temperature8 F e l t d i ss onan c e (a) Wave 1 r = −0.20*** (N.B.: r = −0.24***, P.B.: r = 0.19***) −0.04 −0.03 −0.02 −0.01 0.00r = −0.14*** (N.B.: r = −0.24***, P.B.: r = 0.37***) (b) Wave 2GM food −0.04 −0.03 −0.02 −0.01 0.00r = −0.06 (N.B.: r = −0.10, P.B.: r = 0.27***) (c) Wave 3 −0.04 −0.03 −0.02 −0.01 0.00 F e l t d i ss onan c e (d) r = 0.28*** (N.B.: r = −0.08, P.B.: r = 0.33***) −0.04 −0.03 −0.02 −0.01 0.00r = 0.34*** (N.B.: r = −0.03, P.B.: r = 0.37***) (e) Childhood vaccinesEnergy −0.04 −0.03 −0.02 −0.01 0.00r = 0.31*** (N.B.: r = −0.18, P.B.: r = 0.33***) (f) Figure 4: Relationship between belief network energies and self-reported felt dissonance.Black dots represent individuals who had belief sum scores lower than 0, indicatingnegative beliefs. Red triangles represent individuals who had belief sum scores equalor higher to 0, indicating neutral or positive beliefs. N.B.: Correlation estimates forindividuals holding negative beliefs. P.B.: Correlation estimates for individuals holdingneutral or positive beliefs. 9ecreases.The prediction that belief network energies and self-reported dissonance correlatepositively received support among some groups of participants. The relationship betweenenergies and self-reported dissonance in each wave, separating participants who first heldpositive or negative beliefs about GM food or childhood vaccines, is shown in Figure4a-f. When considering all participants together, the correlations between belief networkenergies and dissonance for GM food did not follow a clear pattern and were mostly ofweak magnitude. However, when considering participants with negative beliefs and thosewith positive beliefs separately, we found some interesting trends. There was a positiverelationship between belief network energies and self-reported dissonance for participantsholding somewhat positive beliefs about either topic. The relationship did not hold forparticipants with negative beliefs.Felt dissonance was also influenced by one’s original beliefs. Across studies andwaves (Figure 4a-f), holding negative views towards vaccines was associated with higherfelt dissonance. Because there were more participants holding negative beliefs aboutGM food than about childhood vaccines, we only observed a positive correlation betweendissonance and energies for all participants in the childhood vaccines group. Participantsholding negative beliefs toward GM food and childhood vaccines probably felt dissonancedue to their impression that they were taking part in a study run by individuals withdifferent beliefs. Participants were aware that the study was run by scientists, who arelikely to hold positive beliefs toward GM food and childhood vaccines. Therefore, theseparticipants probably experienced dissonance due to their beliefs being inconsistent withtheir impression of who created the questionnaire, and not due to the inconsistency oftheir own beliefs.Given that temperature of the belief network decreased with time, correlations be-tween energies and felt dissonance should be expected to increase with time. This ex-pectation received some support: For GM food, the correlation between dissonance andenergies somewhat increased for individuals holding positive beliefs between the firstand second wave (where the sharpest drop in temperature took place). For childhoodvaccines the correlation increased somewhat between the first and second wave for allparticipants. It is noteworthy that the variations in temperature where rather minor(the average correlation between beliefs toward GM food varied between .29 and .40 andfor beliefs toward childhood vaccines varied between .34 and .37, indicating that therewere significant but rather minor variations in temperature), so we did not expect highvariations in the correlations between energies and dissonance.
Energies Predicting Belief Change
Most of our participants changed their beliefs over time, but not always in the expecteddirection. We measured belief change in moral beliefs by comparing the mean of moralbeliefs pre- and post-experimental intervention. We focused on moral beliefs becausethey reflect participants’ own opinions to a larger extent than their social beliefs (whichwould be harder to change). In our sample of N=974 participants, 46% on averagehad changes in their networks towards more accepting (positive) beliefs regarding GM10 . . . . . . GM foods
Energies A bo l u t e be li e f c hange −0.045 −0.035 −0.025 −0.015 −0.005 0.005 (a) . . . . . . Childhood vaccines
Energies A bo l u t e be li e f c hange −0.045 −0.035 −0.025 −0.015 −0.005 0.005 (b) Information Farmers Scientists Tradition Simple Big corporations
Information Farmers Scientists Tradition Simple E ne r g i e s (c) GM foods − . − . Information Scientists Simple Big corporations E ne r g i e s (d) Childhood vaccines − . − . Figure 5: Relationships between belief network energies before interventions and ab-solute change of beliefs during interventions (a), (b) and differences in belief networkenergies before (lighter saturation of bar colors) and after (darker saturation of bar col-ors) the interventions (c), (d). (a) and (b) show that belief network energies correlatewith whether individuals will change their beliefs during interventions. (c) and (d) showthat these changes in beliefs are driven towards lower energy states. Colors of points andbars correspond to interventions. Error bars in (c) and (d) indicate means ± Discussion
In this paper, we showed that dissonance – formalized as belief network energies – pre-dicted belief change. We did so by proposing a model which combines both social andmoral beliefs and testing it using a longitudinal survey. Expanding on the AE framework[10], we estimated cognitive networks combining social and moral beliefs. We found that12hile the network structure of the belief networks remained constant over time, inter-dependence (formalized as temperature) of beliefs increased over waves. As expected,estimated energies generally reflected self-reported feelings of dissonance. Finally, wefound that individual-level energies were related to belief change after an educationalintervention on the safety of GM food and vaccines. While our formal network modelis only an analogy for actual cognitive processes, these findings show its usefulness indisentangling the many psychological factors influencing belief change.We have two main contributions. Our first main contribution is our unifying modelcombining social and moral beliefs into a single cognitive network build through a sta-tistical physics framework. This model extends our recent framework for unifying moraland social beliefs [23] by also taking the network structure of all beliefs into account.Additionally, this model draws on previous research combining moral and social beliefs[25] and theoretical network models on relationships between beliefs [38, 41]. Previousresearch on belief formation and change have stressed the importance of both these setsof factors as individuals make decisions. Due in part to lack of cross-disciplinary re-search, however, the combination of both sets in one framework remains rare. In thispaper, we draw on social psychology and statistical physics to not only incorporate beliefsacross these two domains, but include them as part of an interacting network. We hopethis research encourages more studies of the interactions between social and moral beliefnetworks as important processes for belief change.Our second main contribution is that our model is able to empirically predict beliefchange. Many belief dynamic models have remained untested on empirical data. Inaddition to a formal model, we provide empirical predictions about belief change usingdata collected specifically to answer these questions. Using a model based in socialpsychology, we bridge the gap between belief dynamics models in statistical physics andempirical work on science communication. The statistical physics parameters in ourmodel have clear psychological meaning: Belief network energies provide a formalizationof potential dissonance and temperature provides a formalization of attention directed atan issue. Additionally, our model also illuminates some of the mechanisms behind beliefchange: Individuals are motivated to reduce dissonance between beliefs and reconfiguretheir beliefs to allow lower dissonance. Such reconfiguration can be, but is not necessarily,in line with the aim of the intervention. The direction in which individuals change theirbeliefs does not only depend on the intervention but also on the easiest way for individualsto reduce their dissonance.There are some limitations to the study. First, we estimated temperature per timepoint for the whole group of participants because current network estimation methods arenot able to estimate temperature separately for each individual. The group-level networktemperature thus likely represents the average temperature of the group with individualvariation possibly captured by variations in energy. A longer longitudinal study and moreadvanced methods would enable individual-level estimates for temperature, or attentionto the survey. Second, we did not have an empirical measure of attention and so couldonly infer that our estimated measure of temperature was related to attention throughother proxies. However, temperature could reflect many psychological processes leading13o the likelihood of belief networks moving to more consistent states or not. Third, ourmodel was not able to explain the direction of belief change towards either acceptanceor rejection of the safety of GM food and vaccines and only focused on absolute beliefchange. Future research should expand on this model to provide ways to explain whysome individuals accept or reject an experimental intervention. Finally, we focused oncognitive beliefs of one individual at a time, however, individuals are connected withinlarger social networks which influence the dynamics of belief change over a large popu-lation. We hope that subsequent research will continue to bridge social psychology andstatistical physics to model and test belief change at the individual and societal level.This research has implications for science communication regarding issues critical tothe health of many. We expect that scientific educational interventions that focus onreducing the belief network’s dissonance will be more effective in changing the mindsof science skeptics. This applies specifically to the case of beliefs about GM food andvaccines but can be expanded to many other scientific issues, such as climate change. Thisstudy shows that given enough attention to the issue, individuals do change their mindif this enables less dissonance between all their beliefs within their cognitive network.Science communication should take into account how different moral and social beliefs areconnected to each other to draft educational interventions that could lower the dissonanceof the belief network in a way that leads to more acceptance of scientific facts. Furtherinvestigations to translate our findings to science communication might help combatingerroneous and socially-detrimental beliefs.
Methods
Study Design
We conducted a longitudinal study with an experimental component over three waveson a probabilistic national sample in the United States. To select participants for thestudy, we screened N=2,482 participants for their beliefs about the safety of GM foodand childhood vaccines. We selected N=1,832 individuals who were somewhat hesitantabout the safety of GM food or vaccine for the main experimental study. In other words,we only included individuals who selected a number between 1 and 6 (included) forthe screener question “Do you think it is unsafe or safe to eat GM food?” or “Do youthink childhood vaccines are unsafe or safe for healthy children?” with the options from1-completely unsafe to 7-completely safe.Of the 1,832 selected participants, 974 completed the three waves with no missingvalues on any relevant questions. In each analysis, we included all participants, who hadno missing values on the questions relevant for the analysis. The first wave, on average90 days after the screener, questioned participants about their beliefs about the safety ofGM food and childhood vaccines as well as about related moral concerns and perceivedbeliefs of social contacts and sources. These questions were then administered again inwave 2, on average 20 days later, both before and after an experimental manipulation,and again in wave 3, on average 10 days later.14 uestionnaire and Intervention
To measure individuals’ moral and social beliefs about GM food and childhood vaccines,we included questions about related moral beliefs [26], and participants’ perception of thebeliefs of relevant social groups [24]. Haidt [27] identifies six moral foundations relevantfor different groups of U.S. Americans: Care, Fairness, Loyalty, Authority, Purity, andLiberty. We developed two questions for each of the moral foundations. For the socialnetwork, we focused on perceived beliefs about the safety of GM food or vaccines fromdirect social contacts (family and close friends, online community) and relevant sourcesof information (medical doctors, scientists, governmental agencies, online influencers,journalists, and the US general public). Full list of questions focused on moral and socialbeliefs are in Supplementary Table 1.We included other questions relevant for the model in each wave of the questionnaire.First, we developed three questions focused on felt dissonance. These questions asked ifthe participant felt at ease, unbothered, and comfortable (all also on a scale from 1 to 7and recoded so that higher values indicate higher dissonance). We averaged these threeitems into an index of felt dissonance. Cronbach’s alphas in the different waves were highfor both GM foods and childhood vaccines (GM foods wave 1: .93, wave 2: .93, wave 3:.94; Childhood vaccines wave 1: .92, wave 2: .93, wave 3: .95), indicating high reliability.In the second survey wave, participants were randomized into different experimentalgroups that received scientific facts about GM food and vaccines combined with messagestargeting different social and moral considerations. The Supplementary Materials includethe experimental conditions for participants selected for the GM food study (N=443) andthe childhood vaccines study (N=338) (see Supplementary Table 2). Each message withinthe GM and vaccines surveys had similar levels of readability and word count.
Network Estimation
We estimated belief networks including moral and social beliefs for GM food and child-hood vaccines, respectively. We implemented our theoretical model using the GaussianGraphical Model (GGM), which is the most common approach to estimate networks fromcontinuous data. Edges in a network represent partial correlations between two nodeswhile controlling for all other nodes. Modelling the variance-covariance matrix Σ can bedone in the following way [15]: Σ = ∆( I − Ω) − ∆ (3)where Ω represents the partial correlations between nodes and measures the couplings ω of our theoretical model. ∆ represents a diagonal scaling matrix with values scalingthe partial correlations on the diagonal and 0s on the off-diagonal. These scaling valuesmeasure the temperature β of our theoretical model. The difference between these scalingvalues and temperature is that there is one scaling value for each belief, while there isa single value for temperature in our theoretical model. The reason to have a separatescaling value for each belief is that scaling a GGM by a single value often results in avariance-covariance matrix that is not positive definite. As is the case for temperature,15ower scaling values result in higher correlations between beliefs, because the model-implied correlations result from dividing the partial correlation between two given beliefsby the product of their scaling values. The average of these scaling values can thereforebe regarded as a measure of temperature.We fitted networks separately for GM foods and childhood vaccines across the differ-ent time points and increasingly constrained the parameters of the specifications of ourmodel in several steps and assessed the fit of these different specifications based on theBayesian Information Criterion (BIC). These specifications were estimated using the R-package psychonetrics [14]. We compared the fit of eight specifications of our model withincreasing constraints of the estimated networks. We first let all parameters vary freelyacross time points and subsequently constrained the following parameters to be equalacross time points: partial correlations between nodes ( Ω ), intercepts (mean values) ofthe nodes, and scaling values ( ∆ , as a proxy of temperature). We include constraints inthe intercepts, because this allows us to use an approach similar to testing measurementinvariance and makes variations in the scaling values identifiable. We tested each con-straint using either a dense (all nodes being connected) or sparse network (some couplingsset to 0). We determined which couplings were set to 0 using a prune-step-up procedure,which sets a given coupling to 0 and tests whether this results in better or worse modelfit. We then selected the best fitting specification of the model.For both the GM food and the childhood vaccines networks, the best fitting specifica-tion of our theoretical model was a sparse model (i.e., some partial correlations betweenbeliefs were set to be 0) with equal partial correlations across time points (i.e., partialcorrelations between all beliefs were set to the exact same values at every time point) andintercepts (mean values) but unconstrained temperature across time points (see Supple-mentary Table 3 for fit measures of the different specifications of the model), implyingthat the network structure remained constant over time, while temperature varied overtime. Calculation of belief network energies
To calculate belief network energies per person at each time point, we used estimatedpartial correlations of the belief network. We multiplied the partial correlation betweenany given two beliefs with the scores the given individual had on these beliefs. The beliefnetwork energy is then the sum of these pairwise energy scores multiplied by -1.
Validation
In order to test the validity of the model, we first compared estimated and self-reportedcentrality of beliefs and then analyzed the relationship between individual and groupvariances. Investigating the relationship between estimated and self-reported centralityallowed us to test whether the estimated network structure is in line with the subjectiveperception of the participants. For this analysis, we made use of additional questionsin our data. Participants rated how important their different beliefs are for their beliefabout the safety of GM food or childhood vaccines. Participants also rated to what16xtent they believed that GM food or childhood vaccines are safe. For this analysis, were-estimated the belief network including the safety beliefs. Results of this analysis areshown in Supplementary Figure 1. We found that estimated measures of centrality inrelation to the safety of GM food and childhood vaccines correlated with self-reportedimportance of moral and social beliefs.Investigating the relationship between individual and group variances allowed us totest whether the group-level network is likely to be representative of individual-levelnetworks. The results of this analysis are shown in Supplementary Figure 2. We foundthat questions with high individual-level variance over time tended to also have highergroup-variation at one time point. No covariates predicted differences between individualand population estimates. Therefore, we do not see evidence of bias from estimating thesenetworks at the group-level instead of at the individual-level.
Meta-Analyses on Energies and Belief Change
Correlation between energies and absolute belief change
To test whether belief network energies predict belief change, we first correlated beliefnetwork energies and absolute belief change separately for each intervention and foreach topic (these correlations and their associated significance levels can be found inSupplementary Table 4). We then transformed these Pearson’s correlation into Fisher’sz-scores and entered the scores into a random-effects meta-analyses separately for GMfood and childhood vaccines. Finally, we re-transformed the Fisher’s z-scores back tocorrelation coefficients for ease of interpretation.
Differences between energies before and after the interventions
To test whether belief network energies decrease after the interventions, we first calculatedthe mean differences between energies before and after each intervention separately foreach topic (these mean differences and their associated significance levels can be foundin Supplementary Table 5). We then transformed these scores into standardized meanchange scores and entered the scores into a random-effects meta-analyses separately forGM food and childhood vaccines. Finally, we re-transformed the standardized meanchange scores back to raw differences for ease of interpretation.
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The authors thank Mirta Galesic and Henrik Olsson for comments and discussion. JonasDalege was in part supported by a grant from the National Science Foundation (BCS-1918490) and by an EU Horizon 2020 Marie Curie Global Fellowship (No. 889682).Tamara van der Does was supported in part by a grant from the National Science Foun-dation (DRMS-1757211) and a grant from the National Institute of Food and Agriculture(NIFA-2018-67023-27677).
Supplementary Materials
Supplementary Table 1: Questions about moral and social beliefs related to scientificissues (GM food or childhood vaccines).
Moral Social