BRIEF REPORT
Paradoxical Effects of Persuasive Messages
Rahul Bhui and Samuel J. GershmanHarvard University
BAThe same persuasive message can be interpreted in a positive or negative way, challenging ourability to predict its effectiveness. Here, we analyze theoretically and experimentally how causalreasoning contributes to this process of interpretation and can produce attitude reversals due tothe network structure of beliefs. We conduct two vignette experiments, one based on the famousslogan of the car rental agency Avis (“We’re No. 2—that means we try harder”), and the otherbased on online product reviews. When participants’ contextual beliefs about the economicenvironment are manipulated, message effectiveness changes as predicted by a Bayesianmechanism in which seemingly negative information is “explained away” in a more positivelight, or vice versa. Thus, causal reasoning may help account for certain counterintuitive kindsof high-level attitude change.
Keywords: causal reasoning, Bayesian inference, judgment, attitude change
Supplemental materials: http://dx.doi.org/10.1037/dec0000123.supp
Many public health or advertising campaignsare based on persuasive messages that attemptto shift the audience’s preferences. However,these campaigns may have counterintuitive ef-fects because people can interpret the samemessage in different ways. Clever senders canharness the power of reinterpretation to turnsuperficially negative information to their ben-efit. For example, in 1962 the car rental agencyAvis fought back against their more popular
competitor Hertz using the now-famous slogan“We’re No. 2—that means we try harder” (Er-iksson & Holmgren, 1995). This reconceptionof second place as “underdog” rather than“loser” was considered tremendously success-ful, and the Avis campaign has been regarded asone of the most iconic ad campaigns of the 20thcentury. What makes messages like this con-vincing? When can seemingly unfavorable in-formation be viewed in a more flattering light?We show that such phenomena can be naturallyaccounted for in a Bayesian framework. Due tothe structure of causal representations, informa-tion which is overtly negative can have indirectpositive implications, or vice versa.
Abundant work in social and consumer psy-chology has studied how content and contextinfluence persuasion (e.g., Petty & Cacioppo,1996). A long-standing line of research ana-lyzes attitude change using theories of probabi-listic and causal reasoning (e.g., Hahn & Oaks-ford, 2007; McGuire, 1960a, 1960b; Wyer &Goldberg, 1970). Models of Bayesian argumen-tation provide a computational framework that
X Rahul Bhui, Department of Psychology and Center forBrain Science, and Department of Economics, Harvard Uni-versity; Samuel J. Gershman, Department of Psychologyand Center for Brain Science, Harvard University.
We thank Andrei Shleifer for many helpful discussions.This work was sponsored in part by the Harvard Mind/Brain/Behavior Initiative.
The data and code used for analysis are available at https://github.com/r-bhui/persuasive-messages
Correspondence concerning this article should be ad-dressed to Rahul Bhui, Department of Psychology and Cen-ter for Brain Science, Harvard University, 52 Oxford Street,Cambridge, MA 02138. E-mail: [email protected]
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.Decision
© 2020 American Psychological Association 2020, Vol. 2, No. 999, 000ISSN: 2325-9965 http://dx.doi.org/10.1037/dec0000123
1
can make specific predictions about how mes-sage content and context interact nonadditively,complementing more qualitative approaches.This formalization enables greater theoreticalrigor, helping to clarify the cognitive mecha-nisms underlying persuasion and to sharpenpredictions about when messages will succeedor fail. The Bayesian approach has been shownto account for variation in judged argumentstrength (Hahn & Oaksford, 2006, 2007; Hahn& Hornikx, 2016; Zenker, 2013), and Bayesiannetworks capture more sophisticated levels ofreasoning that contribute to persuasiveness(Hahn, Oaksford, Harris, 2013; Harris, Hahn,Madsen, & Hsu, 2016).
Circumstances under which seemingly nega-tive messages can be interpreted positively (orvice versa) have been studied in various fields,such as the boomerang effect in social psychol-ogy (Hovland, Janis, & Kelley, 1953) and two-sided communication in marketing (Crowley &Hoyer, 1994). The boomerang effect refers tosituations in which weak positive messages pro-duce negative changes in beliefs, and two-sidedmessages are those which admit negative infor-mation to raise persuasive power. However,definitions of argument strength tend to bevague or even circular. For example, Petty andCacioppo (1986, emphasis removed) consider a“strong message” to be “one containing argu-ments . . . such that when subjects are instructedto think about the message, the thoughts thatthey generate are predominantly favorable” (p.133) which begs the question. The Bayesianframework provides a clearer characterizationof argument strength based on probabilistic rea-soning, and permits a more rigorous depictionof the cognitive computations involved.
Explanations of these phenomena based onBayesian argumentation have lagged behind,however. Analysis of reversals has been restrictedto the “faint praise effect” whereby weak positiveinformation has a negative effect on beliefs. Har-ris, Corner, and Hahn (2013) explain this by arational argument from ignorance: if the (in-formed) source had stronger positive evidence,they would have provided it, and thus the absenceof evidence implies evidence of absence. Whilethis mechanism is a possible source of reversals, itis distinct from our focus in this article.
Here, we consider how attitude reversals canoccur due to positive or negative information be-ing “explained away” (Pearl, 1988), a mechanism
which has not been previously identified in studiesof Bayesian argumentation. Messages can indicatevalue-irrelevant reasons for apparently good orbad observations. This could cause a reversal ifthe alternative explanation is convincing enoughto account for the information by Bayesian stan-dards. We investigate this mechanism more con-cretely in two different situations.
First, in the Avis scenario, we examine how theseemingly negative attribute of being the second-place competitor can be interpreted positively.Normally, being first place is good because it is asign of quality; however, this implication can beexplained away when popularity may be causedby quality-irrelevant factors like advertising orcustomer habit. According to our novel Bayesianaccount, the same slogan should be more convinc-ing in environments where the first-place com-pany does advertise more or where being firstplace is not a strong sign of quality.
Second, in the setting of online product re-views, we examine how the seemingly positiveattribute of a higher rating can be interpretednegatively. Higher ratings are typically a sign ofbetter product quality, but this is not the casewhen the reviews are fake or biased. This ac-count predicts that the most glowing reviewswill be most heavily discounted when fake re-views are sufficiently likely to exist (becausefraud will generally produce high ratings)—they become considered “too good to be true.”
We find some evidence supporting these pre-dictions in vignette experiments based on eachscenario. The impact of the message depends onthe sophisticated network of audience beliefs. Wethus provide novel demonstrations of how certainkinds of counterintuitive attitude change such as afamed real-world example can be understood interms of Bayesian argumentation. This helps us tomore precisely systematize our understanding ofpersuasion and preference reversals.
Theory
We first discuss our theoretical framework.To transparently illustrate the computationalcognitive principles involved, we construct asimple model of the mental representations ofmessage recipients. Our approach uses a Bayes-ian network as depicted in Figure 1, whichcomprises two types of components: nodes,which capture the relevant attributes in a sce-nario, and edges, which capture the causal rela-
2 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
tionships that connect attributes to each other.Individuals reason about what the magnitudesof different attributes collectively imply accord-ing to the structure of their beliefs. This rea-soning could be consciously accessible athigh levels, although it does not need to be.Note that these models are intended to capturethe representations that people hold in theirminds. The belief networks may not necessar-ily reflect the truth, only how message recip-ients view the world.
In our setup, people value one of the attri-butes v (of uncertain magnitude) which theyattempt to estimate based on other attributes, inparticular, the signal s. This signal can bethought of as a piece of information that istypically considered good due to its associationwith value. However, it can also be influencedby the alternative cause c, and hence is not anunambiguous sign of value. Messages can alterpeople’s preferences by changing their percep-tions of various elements in this network, di-rectly or indirectly (via inference). When thisleads people to attribute the signal more to thealternative cause, its connection to value isdampened. This mechanism attenuates the neg-ative impact of low signals and the positiveimpact of high signals. As a result, even whenthe signal is lower, the receiver’s estimate ofvalue may be higher if this is counteracted bythe attribution of the signal to the alternativecause.
There are multiple ways to mathematicallyspecify this mechanism, and, in what follows,we lay out two such cases (with the recognitionthat these are illustrative examples and not theonly specifications possible).1 In the Avis sce-nario, we suppose the network follows a linear
Gaussian structure, and also includes an extraedge between the valued attribute and the alter-native cause (which is further assumed to beobserved for simplicity). In the product reviewsetting, we suppose the signal comes from amixture model.
Avis Car Rental
We consider the relevant attributes in theAvis example to be the quality of a company’sproduct or service (q), its level of popularity (!),and its level of resources (r). Quality covers allaspects of dealing with a company, from thecondition of their cars to the excellence of theirservice. This is the valued attribute that poten-tial customers do not observe and are trying toinfer based on their belief network. Popularityrefers generally to the prevalence of the com-pany’s product or service among the market,measured along dimensions like market share ornumber of clients. Resources consist of moneyas well as equipment, experience, reputation,and other such forms of capital.
Figure 2 depicts a belief network that canaccount for the reversal in preferences causedby the Avis message. This network reflectsthree possible relationships. First, if a companyprovides high quality service, this will likelyattract clients and make the company more pop-ular; so there is a positive link from quality topopularity, with strength !. Second, popularitycan stem from sources that may not closelyreflect quality, like marketing or existing cus-tomer habits. Well-off established incumbentsare at an advantage here because, for instance,they have more capital to facilitate marketing;so there is a positive link from resources topopularity, with strength ". Third, resource-richcompanies can use their capital to deliver betterquality to their clients. They have more avail-able funds or accumulated experience withwhich to properly maintain their equipment; sothere is a positive link from resources to qualitywith strength #.
What might the Avis slogan of “We’re No.2—that means we try harder” entail? It clarifies
1 Due to the degrees of freedom that would be needed tofit the theoretical constructs from the data, we instead pres-ent simulations that mimic the qualitative features of par-ticipant judgments, and leave more direct model fits forfuture work.
Figure 1. A belief network that can lead to attitude rever-sals via “explaining away”. Nodes represent relevant attri-butes, and arrows represent the causal relationships betweenthem. Dashed nodes denote potentially unobserved attri-butes which may be inferred.
3PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
that they are indeed the smaller, second-placecompetitor. Customers may not have been sokeenly aware of or attentive to this informationbefore seeing the ad, and hence their percep-tions of ! and r are downgraded. By this ac-count, the key to Avis’s reversal lies in the linkbetween resources and popularity. If richercompanies are more able to buy popularity (i.e.,if " is large), then being worse off can actuallybecome an advantage. Second-place companiesdo not have as many resources with which tobuy popularity; therefore any popularity thatthey do have must be a result of their quality.The extent to which customers find this reason-ing convincing depends on the magnitudes ofthe relationships between variables.
Let us formalize this analysis. For transpar-ency, we assume the network follows a linearGaussian structure as follows:
q ! "r # $q, (1)
! ! %r # &q # $!, (2)
with the noise terms εq, ε! ~ N(0, 1). Customersreason about the attributes by estimating E(q | !,r). Rearranging Equations 1 and 2 gives us q $(!%"r % ε!)/! and ε! & !εq $ ! % (" & #!)r,and so we have that
E(q | !, r) ! (! ' %r ' E[$! | !, r]) ⁄ & (3)
!(! ' %r ' E[$!|$! # &$q ! ! ' (% # "&)r]) ⁄ &
(4)
!!! ' %r '! ' (% # "&)r
&2 # 1 " ⁄ & (5)
!&! # (" ' &%)r
&2 # 1. (6)
In the present account, the ad makes secondplace feel even less popular and poorer relativeto first place. Formally, suppose the ad de-creases perceptions of popularity and resourcesfor the second-place company by magnitudes'! ( 0 and 'r ( 0. This changes its inferredquality by
(E(q | !, r) !(&% ' ")(r ' &(!
&2 # 1. (7)
The ad benefits second place if
&%(r ) &(! # "(r. (8)
All else being equal, this model predicts thatthe ad will be most effective when " is high,because the greater popularity of the first-placecompany is then clearly due to their resourcesrather than their quality. This is the key pathwaythrough which “explaining away” operates. Italso predicts the ad will be most effective when# is low, because then the first-place company’sgreater resources do not translate into quality,which is what customers ultimately care about.This effect reflects a different Bayesian mech-anism, known as cue combination. The ! termhas an ambiguous effect that depends on thelink between resources and popularity, and thedegree to which perceptions of each are modi-fied.2 To test the simple predictions of thismodel, we conduct an experiment that varies the" and # parameters by changing the contextualinformation provided to participants.
Experiment
Participants. Two thousand participantsfrom the United States were recruited from Am-
2 Expression 8 also reveals a property of the ad’s bene-ficial effect that may not be obvious. It is modulated by therelationship between quality and popularity, and is equal tozero if this relationship is weak (i.e., if ! $ 0). This occursbecause resource level serves to explain away popularity—but this is pointless if low popularity does not carry negativeimplications needing to be explained away.
Figure 2. A belief network that can lead to the Avisphenomenon. Greek letters reflect the strengths of the causalrelationships. The link from quality (q) to popularity (!)reflects the direct negative implication of popularity levels.The link from resources (r) to popularity (!) enables pop-ularity to be explained away by quality-irrelevant sources.The link from resources (r) to quality (q) entails that re-sources can serve as a cue of value separate from popularity.
4 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
azon Mechanical Turk; each was paid $0.85 fortheir participation.3 The study was approved bythe Harvard Committee on the Use of HumanSubjects.
Procedure. Our experiment consisted of avignette synthesized from the Avis scenario,to tap the rich real-world thought processes ofparticipants while maintaining experimentalcontrol. Participants read the vignette de-picted in Figure 3, in which they were choos-ing a fictitious company to rent a car frombased on information provided about therental market. In order to focus on our mech-anism of interest, several aspects of thechoice problem like price, brand name, andphysical appearance were held constant. Par-ticipants were then presented a message basedon the “we try harder” slogan, and indicatedwhether the message made them “morelikely,” “equally likely,” or “less likely” topick the second-place company. Finally, par-ticipants were asked to write down any rea-sons for their answer as a free-text response.4
The focal context in all conditions consistedof two sentences that related to advertisinginequality and maintenance difficulty. Thesewere varied separately (with order counter-balanced) producing a control condition andtwo treatments. In the control condition, onesentence indicated that richer companiescould advertise more, and the other indicatedthat maintaining a fleet of cars was inexpen-sive. The former was modified to create the“advertising cap” treatment, in which bothcompanies were said to advertise about thesame amount. The latter was modified to cre-ate the “difficult maintenance” treatment, inwhich maintaining a fleet of cars was said tobe expensive.
Both of these treatments are predicted tomake participants respond less favorably tothe message. Intuitively, the advertising captreatment should weaken the link betweenresources and popularity, corresponding inour model to a decrease in the value of ". Thisshould reduce the audience’s ability to ex-plain away first place with quality-irrelevantfactors, and constitutes the most direct test ofour hypothesis. The difficult maintenancetreatment strengthens the link between re-sources and quality, corresponding to an in-crease in the value of #. This should enhancethe contribution of the resource cue, increas-
ing the audience’s direct inference of qualityfor the more well-off company.
Results
The observed preference changes due to themessage are displayed in Figure 4. Analysesexclude individuals who spent less than 30 sreading the vignette or who wrote less than 10characters in their free response, as a roughattention check, which is standard when usingthe Amazon Mechanical Turk pool, leaving1,711 participants in the sample.5 The propor-tion of participants more likely to pick No. 2dropped by 10 percentage points in the adver-tising cap treatment and by 4.5 percentagepoints in the difficult maintenance treatment.
We analyze the data using a Bayesian orderedlogistic regression, which assumes the discreteordered responses (less/equally/more likely topick No. 2) occur when the output of an under-lying linear model falls between various cut-points (the linear model and cutpoints are esti-mated). That is, for predictors X (experimentalcondition) and slope parameters B (interceptand effects of condition), less likely is reportedwhen BX & ε is less than some threshold, morelikely when it is greater than a higher threshold,and equally likely when it is between the lowerand higher thresholds. Bayesian analyses depictuncertainty in a nuanced way without the use ofarbitrary statistical cutoffs, helping to ensurethat the information contained in the data isneither overstated nor understated (Amrhein,Trafimow, & Greenland, 2019; Gelman et al.,2013; Hurlbert, Levine, & Utts, 2019; Mc-Shane, Gal, Gelman, Robert, & Tackett, 2019;Wasserstein, Schirm, & Lazar, 2019).6
3 This sample was based on a power calculation (fordetecting a difference in proportions of roughly 5 pp at 80%power) combined with budgetary constraints.
4 This was done on a separate page only after they se-lected one of the three options, and without prior warning,to avoid biasing the choice process.
5 The conditions had 586 (control), 563 (advertising cap),and 562 (difficult maintenance) participants. The exclusioncriterion was informed by pilot data.
6 This regression and those below were computed withthe brms package in R, and used the weakly informativedefault priors for coefficients recommended by Gelman etal. (2008), a Cauchy distribution with center 0 and scale 2.5(though alternative assumptions do not appreciably changethe results).
5PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
The results are reported in Table 1, andindicate that the advertising cap treatment hada negative effect (odds ratio [OR] $ 0.677,posterior 95% CI [0.542, 0.845], P(OR )1) ( 99.9%). The same conclusion is ob-tained from model comparison of a regressionthat includes experimental condition as a pre-dictor (using data from only the control andadvertising cap conditions) against a null re-gression that ignores it, according to the one-standard-error rule (Hastie, Tibshirani, &Friedman, 2009; 'WAIC [widely applicableinformation criterion] $ %9.31, SE $ 6.68).The Bayesian analysis suggests that the diffi-
cult maintenance treatment may have also hada negative effect (OR $ 0.841, posterior 95%CI [0.674, 1.060], P(OR ) 1) $ 92.8%),although the analogous model comparisondoes not yield evidence of this ('WAIC $%0.13, SE $ 2.86).7
To see whether the treatments influenced par-ticipants’ reasoning as anticipated, we hand-coded the free response data according to theexplicit reasoning provided. In particular, we
7 We note for completeness that if all participants areincluded, the values of P(OR ) 1) are 99.6% (advertisingcap) and 72.1% (difficult maintenance).
Figure 3. Text used in the experimental vignette. The bolded and bracketed text variedacross conditions (this text was formatted the same as surrounding text when shown toparticipants). An image of a vehicle on the beach (not displayed) was also shown in allconditions to split up the first block of text from the second block and to increase participantengagement with the task.
6 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
counted the frequency of responses which per-tained to No. 2 having less advertising (and thushaving a quality-irrelevant disadvantage) orfewer resources (and thus being less able toafford high quality). Most responses were vagueabout the precise thought process involved—and, as noted earlier, the reasoning need not beconsciously accessible. However, in a numberof cases participants were quite transparent. Ex-amples of the types of reasoning provided aredepicted in Figure 5. The former reasoning(which speaks in favor of No. 2) should be leastfrequent in the advertising cap treatment inwhich the advertising difference is negated. Thelatter reasoning (which speaks against No. 2)should be most frequent in the difficult mainte-nance treatment in which the cost of mainte-nance is raised.
Empirical stated reasoning patterns areshown in Figure 6, and corresponding Bayesianlogistic regressions are reported in Table 2. Theposterior probability that “less advertising” ismentioned less in the advertising cap conditionis 96.9% compared to the control condition and99.8% compared to the difficult maintenancecondition. This is recapitulated in the modelcomparisons of regressions that include experi-mental condition as a predictor against null re-gressions that ignore it (considering the pair-wise contrasts separately: 'WAICAC-Control $
%4.74, SE $ 2.46; 'WAICAC-DM $ %8.82,SE $ 3.29). The posterior probability that“fewer resources” is mentioned more in thedifficult maintenance condition compared to thecontrol condition is 88.5% and compared tothe advertising cap condition is 99.6%, but theanalogous model comparisons do not lead to thesame conclusion ('WAICDM-Control $ 0.23,SE $ 2.58; 'WAICDM-AC $ %4.53, SE $5.37). Thus, stated reasoning patterns appear toreflect variation according to the explainingaway mechanism, though not necessarily ac-cording to cue combination.
We note that explaining away could modu-late message strength in multiple ways. Forinstance, persuasiveness should be affected bythe perceived honesty of the source (Hahn et al.,2013), which may itself be influenced by themessage. Self-disclosure of negative informa-tion can make the source seem more credible(Crowley & Hoyer, 1994; Eisend, 2006; Pech-mann, 1990). While credibility from self-disclosure does not by itself explain the crucialconnection between being second place and try-ing harder, it may modulate message strengthhere. This might have occurred in our experi-ment; the proportion of participants who citedhonesty in their free response reasoning washighest in the difficult maintenance condition,8
where the message should be considered mostnegative, and this would have cut against thetreatment effect. To better explore phenomenalike this, in the following section we provide afuller examination of how perceived deceptioncan lead the audience to discount ostensiblybetter signals.
Online Product Reviews
We consider how higher ratings for a productcould make potential customers less inclined tobuy it. Generally speaking, good reviews withhigher star ratings are supposed to reflect betterunderlying quality of a product. However, theycould instead be fake reviews which are high
8 These responses were defined based on whether theycontained the text string “honest” (for example, in the word“honesty”), excluding by hand responses that did not indi-cate the participant felt the company to be honest. Theproportion in the difficult maintenance condition was 5.9%vs 3.8% in the control condition, greater with posteriorprobability 96.3% according to a Bayesian logistic regres-sion of response type on condition.
0.652
0.258
0.09
0.552
0.334
0.114
0.607
0.299
0.094
0.00
0.25
0.50
0.75
1.00
Control AdvertisingCap
DifficultMaintenance
condition
Pro
port
ion legend
Less likelyEqually likelyMore likely
Effect of advertisement on choosing No. 2
Figure 4. Preference changes due to message. Stackedbars depict proportions of participants in all response cate-gories. Bayesian 95% credible intervals shown based on aDirichlet-multinomial distribution with Jeffreys prior. Seethe online article for the color version of this figure.
7PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
regardless of quality. This issue seems to be ofgrowing concern, as retailers have increasinglycome under scrutiny for enabling fake reviewsto persist, and multiple websites have appearedto combat their spread (such as ReviewMetaand Fakespot). Excessively high ratings canthus make people suspicious that they are toogood to be true (Gunn et al., 2016). Conse-quently, a four-star rating may be more con-vincing than a five-star rating if the latter is astrong enough indicator of fraud.
To capture this formally, as depicted in Fig-ure 7, assume that the star rating (r) of a productdepends on its true quality (q) and whether ornot the reviews are fake (f), both of which areunobserved. We suppose both the ratings andquality take on integer values from 1 to 5, andthe status of the reviews is binary, with f $ 0when they are real and f $ 1 when they are fake.We further suppose that the ratings are gener-ated by a mixture model, such that they areequal to the true quality when reviews are real,
but are four to five stars (most likely 5) regard-less of quality when reviews are fake. For sim-plicity, we let the prior distribution of quality beuniform. We also leave aside the natural possi-bility that fake reviews tend to be generated bycompanies with low quality products (a nega-tive link from q to f), but this can be incorpo-rated into the model and would amplify poten-tial reversals.
Under the above assumptions, two useful quan-tities can be computed: the probability that thereviews are fake given the rating, P(f $ 1 | r), andthe expected quality given the rating, E(q | r). Thismodel makes key predictions regarding thesequantities, visualized by the simulations in Figure8. First, people will believe higher ratings aremore likely to be fake, and especially so when theprior probability of fake reviews is high.
P(f ! 1 | r) !P(r | f ! 1)P(f ! 1)
P(r)(9)
Table 1Posterior Estimates From Bayesian Ordered Logistic Regression of Message-Induced Preference Changeon Experimental Condition
Coefficient
Attitude change
Posterior mean Posterior 95% CI P(B ) 0)
Advertising cap %0.390 [%0.613, %0.169] (.999Difficult maintenance %0.174 [%0.394, %0.059] 0.928Cutpoint less | equally %2.406 [%2.612, %2.195]Cutpoint equally | more %0.612 [%0.772, %0.448]N 1711WAIC 3,056.41
Note. P(B ) 0) denotes the posterior probability that the coefficient is less than 0. WAIC $ widely applicable informationcriterion.
Figure 5. Examples of free-text responses providing reasons for the participant’s decision.
8 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
!P(r | f ! 1)P(f ! 1)
P(r | f ! 1)P(f ! 1) # P(r | f ! 0)P(f ! 0)
(10)
!P(r | f ! 1)P(f ! 1)
P(r | f ! 1)P(f ! 1) # #q P(r | f ! 0, q)P(q)P(f ! 0)
(11)
!P(r | f ! 1)P(f ! 1)
P(r | f ! 1)P(f ! 1) # #q 1$r ! q%P(q)P(f ! 0)
(12)
!P(r | f ! 1)P(f ! 1)
P(r | f ! 1)P(f ! 1) # P(q ! r)P(f ! 0)(13)
This expression is increasing in r since P(r |f $ 1) is increasing in r. For example, lettingP(r $ 5 | f $ 1) $ 0.8, P(r $ 4 | f $ 1) $ 0.2and P(f $ 1) $ 0.1, a five-star rating is fake with31% probability, a four-star rating is judged fakewith 10% probability, while a three-star rating isnever fake. This effect is moreover increasing inP(f $ 1). For example, if P(f $ 1) $ 0.25 instead,the respective ratings are judged fake with prob-abilities 57%, 25%, and 0%.
Table 2Posterior Estimates From Bayesian Logistic Regression of Free Response Reasoning onExperimental Condition
Reasoning (“less advertising”)
Coefficient Posterior mean Posterior 95% CI P(B ( 0)
Control 2.488 [%0.077, 7.713] 0.969Difficult maintenance 3.170 [0.615, 8.356] 0.998Intercept %7.661 [%12.749, %5.261]N 1711WAIC 129.08
Reasoning (“fewer resources”)
Posterior mean Posterior 95% CI P(B ) 0)
Control %0.610 [%1.687, 0.406] 0.885Advertising cap %1.680 [%3.434, %0.381] 0.996Intercept %3.999 [%4.670, %3.435]N 1711WAIC 208.00
Note. WAIC $ widely applicable information criterion; CI $ confidence interval.
0.0
1.0
2.0
3.0
Control AdvertisingCap
DifficultMaintenance
Control AdvertisingCap
DifficultMaintenance
Condition
Freq
uenc
y of
free
re
spon
se re
ason
ing
(%)
"No. 2 has less advertising"
"No. 2 has fewer resources"
Figure 6. Proportions of participants providing various types of free response reasoningacross experimental conditions. Bayesian 95% credible intervals shown based on a beta-binomial distribution with Jeffreys prior.
9PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Second, the positive effect of higher ratingson expected quality will be reduced when theprior probability of fake reviews is high. Intui-tively, a five-star rating could occur either be-cause the true quality is five or because thereviews are fake (in which case the true qualityis likely lower). Accounting for the latter pos-sibility dampens the impact of the signal.
P(q | r) !P(r | q)P(q)
P(r)(14)
![P(r | q, f ! 0)P(f ! 0) # P(r | q, f ! 1)P(f ! 1)]P(q)
#q
[P(r | q, f ! 0)P(f ! 0) # P(r | q, f ! 1)P(f ! 1)]P(q)
(15)
!1$r ! q%P(f ! 0) # P(r | f ! 1)P(f ! 1)
P(f ! 0) # 5P(r | f ! 1)P(f ! 1)(16)
E(q | r) ! #q
qP(q | r) (17)
!rP(f ! 0) # 15P(r | f ! 1)P(f ! 1)
P(f ! 0) # 5P(r | f ! 1)P(f ! 1)(18)
Expected quality is thus roughly a combina-tion of r (when P(f $ 0) $ 1) and the priormean of 3 (when P(f $ 1) $ 1). The fundamen-tal tension arises because when r increases, sodoes P(r | f $ 1), pulling the quality estimateback toward its prior mean. The balance be-tween these forces determines whether ratinghas a positive or negative effect on net, and ismodulated by P(f $ 1).
Third, these two effects should occur in tan-dem. In the present account, the attenuation ofvalue directly results from the increased attri-bution of ratings to fraud. Expressions 13 and18 reveal that both changes are modulated bythe term P(f $ 1), the prior probability thatreviews are fake. In the following experiment,we test the main predictions of the theory byvarying this probability.
Experiment
Participants. Nine hundred and six partic-ipants from the United States were recruitedfrom Amazon Mechanical Turk usingTurkPrime (Litman, Robinson, & Abberbock,2017); each was paid $0.25 for their participa-tion. This sample size was determined by a rulerecommended by Kruschke (2018), based onwhen the 95% highest density intervals (HDI)
Figure 7. A belief network that can lead to attitude rever-sals with product reviews.
Figure 8. Model simulation of inferences from review star ratings, with priors of fakereviews set as 0.1 (low), 0.25 (medium), and 0.5 (high), and P(r $ 5 | f $ 1) $ 1 % P(r $4 | f $ 1) $ 0.8. See the online article for the color version of this figure.
10 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
for parameters of interest (described below) areentirely contained inside or outside a region ofpractical equivalence (ROPE). Subjects wererecruited in batches of 100 until either theHDI & ROPE criterion was met, or 900 partic-ipants were reached (the latter occurred first,with minor discrepancies due to technical limi-tations). The study was approved by the Har-vard Committee on the Use of Human Subjects.
Procedure. In this experiment, participantsread the following text in which they wereasked to imagine buying a product (the examplereview was taken from an actual review ofearbuds on a retail website):
Suppose you are browsing a large online retailer, look-ing for a pair of earbuds. You know the average ratingfor earbuds sold on this website is 3 stars. You see 20reviews for an “Extra Bass Earbud Headset”, some ofwhich say things like “#/5 stars: Really good, I like itvery much.”
Participants were subsequently asked aboutwhether they would be more or less likely tobuy the product depending on whether thesereviews mostly gave the product three, four, orfive stars (every participant gave a response foreach star level). They described this attitudechange on a scale from %100 to &100, withpositive numbers meaning more likely and neg-ative numbers meaning less likely, and bignumbers reflecting how strongly they felt. Theywere also asked how likely they thought thereviews were fake or biased, depending on thestar ratings of the reviews, responding on ascale from 0 to 100 to reflect the likelihood.
We used a within-subjects design in which allparticipants were then told, “[s]uppose that the
manufacturer of these earbuds was the retailerrunning the website.” This information wasmeant to increase their prior belief of fake re-views, P(f $ 1), by conveying that the retailerwould be more willing and able to tolerate de-ceit. In light of the information, they were askedthe same questions regarding their likelihood ofbuying the product and their beliefs aboutwhether the reviews were fake, depending onstar rating. Thus, each participant provided sixattitude change responses and six fake beliefresponses in total.
Based on the theory, we hypothesized that:
1. The effect of star rating on attitude changewould be lowered when the retailer wasthe manufacturer.
2. The probability that the reviews were fakewould be increasing in star rating espe-cially when the retailer was the manufac-turer.
3. The magnitudes of these effects would bepositively correlated with each other (i.e.,their values would be negatively correlated).
Results
The effects of star rating and manufactureridentity on attitude change and fake review be-liefs are depicted in Figure 9. The results ex-clude people who provided any response thatwas not a number within the permissible bounds(%100 to &100 for attitude change, 0 to 100 forbeliefs), leaving 852 participants. We statisti-cally tested the three key predictions using aBayesian multilevel regression (including max-
Figure 9. Effect of star rating and manufacturer identity on attitude change and beliefs aboutfake reviews. Bayesian 95% credible intervals shown based on Cauchy (0, 10) prior. See theonline article for the color version of this figure.
11PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
imal random effects structure at the participantlevel). The two dependent variables of interestwere the degree to which participants weremore or less likely to buy the product, and theirbeliefs about whether the reviews were fake.The independent variables were the star ratingsof the reviews (with baseline set at 3 stars) andthe identity of the manufacturer, as well as theirinteraction.9
The results are shown in Table 3. In line withPrediction 1, higher star ratings do not boostone’s preference as strongly when the retailer isthe manufacturer, as revealed by the negativeinteraction term in the attitude change regres-sion. Consistent with Prediction 2, higher starratings particularly increase the perceivedchances of the reviews being fake in the samescenario, as revealed by the positive interactionterm in the belief regression. Moreover, as Pre-diction 3 implies, these effect magnitudes arepositively correlated across individuals, mean-ing the interaction coefficient values are nega-tively correlated (r $ %0.235, 95% Bayesian10
credible interval [%0.301, %0.170]). This lastobservation can be seen in Figure 10 whichdisplays the results among participant sub-groups defined based on the magnitude of thetreatment effect on attitude change (in the 5-starrating case); those who exhibit the steepest dropin attitude change when informed that the re-tailer is the manufacturer also exhibit the stron-gest increase in their beliefs that the reviews arefake.
In some cases higher star ratings even havenegative effects on attitude change, and thisoccurs for 142 participants (16.7% of the sam-ple). In the Appendix, we split participants upinto different subgroups based on the exact pat-tern of this effect, and show how such data canbe accommodated by the model or an extensionthat incorporates a distaste for fraudulent re-views.
Discussion
In this article, we analyze the effects of per-suasive messages using Bayesian networks tomodel the structure of mental representations, inorder to help understand how the same attributecan be considered good or bad. The Bayesianframework captures the ability of individuals toreason about the value implications of causalrelationships between attributes. As a result,
messages that alter perceptions of attributes canhave sophisticated indirect implications thatmay produce counterintuitive attitude changes.We focus on how apparently negative informa-tion could be explained away in a more flatter-ing light, and vice versa.
We conducted two vignette experiments totest the implications of this theorized mecha-nism. The first was styled after Avis Car Rentaland their famous advertisement proclaiming“We’re No. 2—that means we try harder.” Con-sistent with our focal mechanism, the positiveeffect of the Avis message was reduced whenhigh popularity was more difficult to explainaway by company resources (due to a cap onadvertising). Stated reasoning patterns followedsuit, as participants appeared least likely to citethe gap in advertising as an explanatory factorin this condition (where there was no gap).However, there was little support for anothermechanism, cue combination, which wouldhave weakened the message when resourcescontributed more strongly to quality (due tohigh vehicle maintenance costs), and this wasaccompanied by limited evidence that partici-pants were most likely to cite the resource dif-ference in that condition (where the importanceof the differential was enhanced).
The second experiment was styled after thesetting of online product reviews. In line withBayesian principles, the positive effect ofhigher ratings on attitude was diminished whenthe online retailer was also the product’s man-ufacturer (and hence more willing and able tofacilitate fake reviews). This attitude changewas linked to stated beliefs; discounting of par-ticularly high ratings was coupled (across par-ticipants) with an enhanced belief that the high-est reviews were fake or biased.
We do not claim that probabilistic reasoningexplains all possible elements of attitude change(or that our specific account is the only one at
9 The sampling rule was based on the HDIs in bothregressions for the coefficients on manufacturer identity andits interaction with star rating. We conservatively used aROPE spanning %1 to &1 and would have stopped onlywhen the HDIs for all of these coefficients fell into theROPE, absent the preset limit.
10 This was computed using the BayesFactor package inR, assuming noninformative priors for the means and vari-ances of the two populations and a shifted, scaled Beta(3,3)prior for the correlation magnitude, though alternative as-sumptions do not change the result.
12 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
play), merely that it helps to elucidate moreprecisely some of the key mechanisms in-volved. Petty and Cacioppo (1996) identifyseven theoretical approaches to understandingattitude change. These approaches either do notnaturally account for our results, or else overlap
with the Bayesian approach to the extent thatthey may apply.
1. According to theories of conditioning, at-titudes toward a cue are more favorablewhen the cue has been repeatedly paired
Table 3Posterior Estimates From Bayesian Multilevel Regressions of Attitude Change (Top) and Fake ReviewBelief (Bottom)
Attitude change
Coefficient Posterior mean Posterior 95% CI P(B ) 0)
Intercept 23.77 [20.93, 26.64] ).001Star rating 28.87 (0.79) [27.24, 30.44] ).001Retailer/Manufacturer %6.22 (%0.17) [%8.16, %4.34] (.999Star Rating * Retailer/Manufacturer %8.49 (%0.23) [%9.85, %7.12] (.999N 852
P(fake)
Posterior mean Posterior 95% CI P(B ) 0)
Intercept 25.55 [24.03, 27.15] ).001Star rating 9.79 (0.40) [8.86, 10.74] ).001Retailer/Manufacturer 0.20 (0.01) [%1.05, 1.49] 0.377Star Rating * Retailer/Manufacturer 3.71 (0.15) [2.80, 4.61] ).001N 852
Note. Standardized regression coefficients in parentheses describe effect size in units of the dependent variable’s standarddeviation. CI $ confidence interval.
Figure 10. Results based on splitting subjects into three groups based on the magnitude ofthe treatment effect in terms of attitude change (the gap between red and blue points in the toprow) when star rating is five. Left $ highest third, middle $ middle third, right $ lowestthird. Bayesian 95% credible intervals shown based on Cauchy (0, 10) prior. See the onlinearticle for the color version of this figure.
13PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
with something positive (e.g., Staats &Staats, 1958). However, the experimentalmessages are identical across treatments,and there is negligible crude contextualvariation to trigger different associations.
2. The message-learning approach assertsthat properties of the source, the message,the recipient, and the channel influencethe degree to which the message is com-prehended and retained (e.g., Hovland etal., 1953). Through this lens, the onlyvariation in our experiments is in thesource, and the notions of credibility andtrustworthiness that modulate its influenceare transparently represented in the Bayes-ian framework.
3. Judgmental theories entail that itemswhich fall below some reference point aregenerally evaluated less favorably (e.g.,Helson, 1964). In our first experiment, theadvertising cap treatment does not obvi-ously change expectations of quality,while the difficult maintenance treatmentmight decrease the expectation of qualitywhich would actually benefit secondplace. It is also not clear how referencedependence would produce the intricatepattern of results observed in our secondexperiment.
4. Motivational approaches argue that peo-ple attempt to maintain congruency intheir network of associated attitudes(e.g., Osgood & Tannenbaum, 1955).Bayesian models are not only able tonaturally encode this congruency via therational combination of cues (Gersh-man, 2019), but also account for theeffects of variation in prior beliefs as inour second experiment.
5. Attributional theories posit that attitudechanges are based on inferences thatpeople draw about the behavior of oth-ers and themselves (e.g., Kelley, 1973).Such inference is typically referred to ascausal, and its properties are readily castin Bayesian terms (Ajzen & Fishbein,1975).
6. Theories of self-persuasion focus on therole of internally generated information(e.g., Petty & Cacioppo, 1979). Yetthere is no obvious reason why any ofour treatments would influence the de-gree of self-involvement without ap-
pealing to variation in external informa-tion.
7. In combinatory approaches, evaluationis described as the integration (such asthe averaging) of different pieces of in-formation available about a stimulus(e.g., Anderson, 1971). Such theoriescan be formally derived from Bayesianfoundations, which also account for fac-tors that change the weighting of infor-mation, such as variation in prior beliefsas in our second experiment.
The Bayesian cognitive approach has provensuccessful in a variety of domains (e.g., Chater,Tenenbaum, & Yuille, 2006; Oaksford &Chater, 2007), and our work builds on this tra-dition as applied to persuasion (Hahn & Oaks-ford, 2007). To our knowledge, the only explicitanalysis of reversals in Bayesian argumentationrelates to the faint praise effect, in which weakpositive information impacts beliefs negatively.Harris et al. (2013) use the concept of epistemicclosure to account for this effect, arguing thatstronger positive information would have beenprovided were it available, and therefore itsabsence implies its nonexistence. However, thefaint praise effect does not suggest, for instance,why there is any connection between being sec-ond place and trying harder. Thus, we add to thecatalog of mechanisms that can produce rever-sals in Bayesian argumentation.
Our approach bears a connection to Bayes-ian models of belief polarization, in which thesame evidence can lead people with opposingpriors to strengthen their beliefs (Cook &Lewandowsky, 2016; Jern et al., 2009, 2014).While this literature focuses on the generalphenomenon of polarization, belief diver-gence necessarily implies the possibility ofreversals. Indeed, we do observe some partic-ipants in our experiments responding to infor-mation positively while others respond to theexact same information negatively, and eventhe same individuals can sometimes be in-duced to respond in both ways by shiftingtheir prior. Digging into the Bayesian mech-anisms that can give rise to polarization maythus shed light on the computational cognitiveprocesses that describe attitude reversalsmore broadly, and vice versa.
14 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Some research formally studies the interpreta-tion of messages using game theory to capturestrategic reasoning (Benz, Jäger, Van Rooij, &Van Rooij, 2005; Parikh, 2010).11 Interaction be-tween agents with various preferences generatesstatistical regularities that contribute to interpreta-tion. In this way, natural conversational inferencescan be derived as the result of equilibria in strate-gic games between senders and receivers. Whilevaluable, such analysis remains formally predi-cated on Bayesian reasoning of the sort we con-sider, since the receiver must interpret the mes-sage in light of the sender’s position and othercontext clues. Our work thus clarifies certainmechanisms for reversals that could illuminatecorresponding facets of strategic interaction.
We build on the Bayesian framework here toplainly clarify the mechanisms underlying judg-ment within a unified perspective. Althoughmany core implications of our work do not reston the assumption of exact Bayesian inference,it would be useful for further research to scru-tinize the precise quantitative match betweentheory and data. Participants in our experimentswere not provided with explicit probabilities,which reflects a more naturalistic decision set-ting but constrains the ability to conduct such aninvestigation. Other paradigms may be neededto explore a different region in this designspace.
Finally, although we describe messages asproviding tangible information, it is possiblethat they also draw attention to certain relation-ships between attributes. Even if no externalevidence is provided, drawing attention to ne-glected associations can induce a reinterpreta-tion of attributes. In our experiment, some par-ticipants stated that the Avis message madethem think about the situation in a new way(e.g., “I didn’t think at first about the idea thatRightway has to try harder to maintain business,but it makes sense since the other company hasalmost a monopoly on the market for rentalvehicles”). This suggests that the message maynot simply provide information, but could actu-ally increase the salience of previously unrec-ognized implications, causing people to inter-pret attributes in a different light. Such amechanism seems psychologically plausibleand is compatible with the formal analysis laidout in this article.
Constraints on Generality
We expect our results to generalize to the nat-uralistic domains described in the vignettes, pro-vided people hold the relevant causal schema andare engaged enough for it to be retrieved. Thoughthe experimental questions were hypothetical, wewould expect incentives to sharpen engagementand strengthen the effects. Indeed, customers cur-rently ordering products online seem quite sensi-tive to the possibility of fake reviews, as evi-denced by the development of ways to detectfraud (such as ReviewMeta and Fakespot) andsignal trustworthiness (such as Verified Purchaserlabels). However, the path from attitude to behav-ior is not so direct (the “attitude-behavior” gap).The influence of a persuasive slogan on car rentalsor of manufacturer identity on product purchaseswould be partially obscured by other factors suchas variation in prices, extra features, or recommen-dations from friends. Thus, when testing the be-havioral implications of attitudinal theories, caremust be taken to connect stated intentions to ulti-mate decisions (Morrison, 1979; Morwitz,Steckel, & Gupta, 2007).
Conclusion
Persuasion is challenging because the samemessage can be interpreted in different ways de-pending on one’s viewpoint. This variation maylead to counterintuitive preference changes, asseemingly negative information can be interpretedpositively, or vice versa. We analyze the multilay-ered impacts of messages with a Bayesian modelof the mental organization of attributes. We viewpeople as reasoning causally about attribute val-ues, and show that this structure can help explainhow convincing people find messages including arenowned real-world advertising slogan. In twovignette experiments, we predictably modulatemessage effectiveness by altering participants’ be-lief networks. Thus, our understanding of high-level attitude change may be enriched by formaldescriptions of Bayesian reasoning.
11 This includes Mullainathan, Schwartzstein, and Shle-ifer (2008) who also study the Avis phenomenon but as-sume that mental associations are naïve rather than causal.However, their model does not naturally connect persua-siveness with beliefs adjacent to a message’s main claim,and so does not obviously account for our treatment effects,in addition to having trouble systematically generatingbackfires.
15PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
References
Ajzen, I., & Fishbein, M. (1975). A Bayesian analy-sis of attribution processes. Psychological Bulletin,82, 261–277.
Amrhein, V., Trafimow, D., & Greenland, S. (2019).Inferential statistics as descriptive statistics: Thereis no replication crisis if we don’t expect replica-tion. The American Statistician, 73, 262–270.
Anderson, N. H. (1971). Integration theory and atti-tude change. Psychological Review, 78, 171–206.
Benz, A., Jäger, G., Van Rooij, R., & Van Rooij, R.(2005). Game theory and pragmatics. New York,NY: Springer.
Chater, N., Tenenbaum, J. B., & Yuille, A. (2006).Probabilistic models of cognition: Conceptualfoundations. Trends in Cognitive Sciences, 10,287–291.
Cook, J., & Lewandowsky, S. (2016). Rational irra-tionality: Modeling climate change belief polariza-tion using Bayesian networks. Topics in CognitiveScience, 8, 160–179.
Crowley, A. E., & Hoyer, W. D. (1994). An integra-tive framework for understanding two-sided per-suasion. Journal of Consumer Research, 20, 561–574.
Eisend, M. (2006). Two-sided advertising: A meta-analysis. International Journal of Research inMarketing, 23, 187–198.
Eriksson, P., & Holmgren, H. (1995). A book aboutthe classic Avis advertising campaign of the 60s.Dakini Books.
Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y.-S.(2008). A weakly informative default prior distri-bution for logistic and other regression models.Annals of Applied Statistics, 2, 1360–1383.
Gelman, A., Stern, H. S., Carlin, J. B., Dunson, D. B.,Vehtari, A., & Rubin, D. B. (2013). Bayesian dataanalysis. Boca Raton, FL: Chapman and Hall/CRC.
Gershman, S. (2019). How to never be wrong. Psy-chonomic Bulletin & Review, 26, 13–28.
Gunn, L. J., Chapeau-Blondeau, F., McDonnell,M. D., Davis, B. R., Allison, A., & Abbott, D.(2016). Too good to be true: When overwhelmingevidence fails to convince. Proceedings of theRoyal Society A: Mathematical, Physical and En-gineering Sciences, 472, 20150748.
Hahn, U., Oaksford, M., & Harris, A. J. L. (2013).Testimony and argument: A Bayesian perspective.In F. Zenker (Ed.), Bayesian argumentation (pp.15–38). New York, NY: Springer.
Hahn, U., & Hornikx, J. (2016). A normative frame-work for argument quality: Argumentationschemes with a Bayesian foundation. Synthese,193, 1833–1873.
Hahn, U., & Oaksford, M. (2006). A Bayesian ap-proach to informal argument fallacies. Synthese,152, 207–236.
Hahn, U., & Oaksford, M. (2007). The rationality ofinformal argumentation: A Bayesian approach toreasoning fallacies. Psychological Review, 114,704–732.
Harris, A. J. L., Corner, A., & Hahn, U. (2013).James is polite and punctual (and useless): ABayesian formalisation of faint praise. Thinking &Reasoning, 19, 414–429.
Harris, A. J. L., Hahn, U., Madsen, J. K., & Hsu,A. S. (2016). The appeal to expert opinion: Quan-titative support for a Bayesian network approach.Cognitive Science, 40, 1496–1533.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). Theelements of statistical learning: Data mining, in-ference, and prediction. New York, NY: SpringerScience & Business Media.
Helson, H. (1964). Adaptation-level theory: An ex-perimental and systematic approach to behavior:New York, NY: Harper and Row.
Hovland, C. I., Janis, I. L., & Kelley, H. H. (1953).Communication and persuasion; psychologicalstudies of opinion change. New Haven, CT: YaleUniversity Press.
Hurlbert, S. H., Levine, R. A., & Utts, J. (2019).Coup de grâce for a tough old bull: “Statisticallysignificant” expires. The American Statistician, 73,352–357.
Jern, A., Chang, K.-M., & Kemp, C. (2009). Bayes-ian belief polarization. In Advances in neural in-formation processing systems (pp. 853–861).
Jern, A., Chang, K.-M., & Kemp, C. (2014). Beliefpolarization is not always irrational. PsychologicalReview, 121, 206–224.
Kelley, H. H. (1973). The processes of causal attri-bution. American Psychologist, 28, 107–128.
Kruschke, J. K. (2018). Rejecting or accepting pa-rameter values in Bayesian estimation. Advancesin Methods and Practices in Psychological Sci-ence, 1, 270–280.
Litman, L., Robinson, J., & Abberbock, T. (2017).TurkPrime.com: A versatile crowdsourcing dataacquisition platform for the behavioral sciences.Behavior Research Methods, 49, 433–442.
McGuire, W. J. (1960a). Cognitive consistency andattitude change. Journal of Abnormal and SocialPsychology, 60, 345–353.
McGuire, W. J. (1960b). Direct and indirect persuasiveeffects of dissonance-producing messages. Journal ofAbnormal and Social Psychology, 60, 354–358.
McShane, B. B., Gal, D., Gelman, A., Robert, C., &Tackett, J. L. (2019). Abandon statistical signifi-cance. The American Statistician, 73, 235–245.
Morrison, D. G. (1979). Purchase intentions and pur-chase behavior. Journal of Marketing, 43, 65–74.
16 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Morwitz, V. G., Steckel, J. H., & Gupta, A. (2007).When do purchase intentions predict sales? Inter-national Journal of Forecasting, 23, 347–364.
Mullainathan, S., Schwartzstein, J., & Shleifer, A.(2008). Coarse thinking and persuasion. QuarterlyJournal of Economics, 123, 577–619.
Oaksford, M., & Chater, N. (2007). Bayesian ratio-nality: The probabilistic approach to human rea-soning. New York, NY: Oxford University Press.
Osgood, C. E., & Tannenbaum, P. H. (1955). Theprinciple of congruity in the prediction of attitudechange. Psychological Review, 62, 42–55.
Parikh, P. (2010). Language and equilibrium. Cam-bridge, MA: MIT Press.
Pearl, J. (1988). Probabilistic reasoning in intelligentsystems: Networks of plausible inference. Colum-bus, OH: Morgan Kaufmann.
Pechmann, C. (1990). How do consumer inferencesmoderate the effectiveness of two-sided messages.NA - Advances in Consumer Research, 17, 337–341.
Petty, R. E., & Cacioppo, J. T. (1979). Issue involve-ment can increase or decrease persuasion by en-hancing message-relevant cognitive responses.
Journal of Personality and Social Psychology, 37,1915–1926.
Petty, R. E., & Cacioppo, J. T. (1986). The elabora-tion likelihood model of persuasion. In L. Berkow-itz (Ed.), Advances in experimental social psychol-ogy (Vol. 19, pp. 123–205). Cambridge, MA:Academic Press.
Petty, R. E., & Cacioppo, J. T. (1996). Attitudes andpersuasion: Classic and contemporary ap-proaches: Boulder, CO: Westview Press.
Staats, A. W., & Staats, C. K. (1958). Attitudesestablished by classical conditioning. Journal ofAbnormal and Social Psychology, 57, 37–40.
Wasserstein, R. L., Schirm, A. L., & Lazar, N. A.(2019). Moving to a world beyond “p ) 0.05.” TheAmerican Statistician, 73, 1–19.
Wyer, R. S., Jr., & Goldberg, L. (1970). Aprobabilistic analysis of the relationships amongbelief and attitudes. Psychological Review, 77,100–120.
Zenker, F. (2013). Bayesian argumentation: Thepractical side of probability. In F. Zenker (Ed.),Bayesian argumentation (pp. 1–11). New York,NY: Springer.
Appendix
Simulation of Subgroup Patterns
Here, we split participants up into groupsbased on the pattern of how they respond (interms of attitude change) to different star rat-ings when the retailer is the manufacturer.Four patterns are possible, as the response can(A) be increasing in rating (3 ) 4 ) 5; 710participants), (B) have an inverted-U pattern(3 ) 4 ( 5; 61 participants), (C) be decreas-ing in rating (3 ( 4 ( 5; 54 participants), or(D) have a U pattern (3 ( 4 ) 5; 27 partic-ipants). In Figure A1, we plot the averageresponses for participants in each of thesefour groups. This reveals cases in whichhigher ratings have both positive and negativeeffects depending on the condition. Figure A2
displays corresponding hand-tuned simula-tions (with parameters in Table A1) from anextension of the model in which value isequal to the expected quality minus a penaltybased on how likely the reviews are to befake, E(q | r) % +P(f $ 1 | r), where + is aparameter capturing the distaste for fraud.Only the data in Group D is fundamentally atodds with the theory and unable to be cap-tured naturally, as the downward trend goingfrom three stars to four stars is not mirroredby an increase in P(fake), and the possibledifference in attitude change between condi-tions is not recapitulated in beliefs. Encour-agingly, this is the smallest group of the four.
(Appendix follows)
17PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Figure A1. Effect of star rating and manufacturer identity on attitude change and beliefsabout fake reviews, with participants split by pattern of attitude change. Bayesian 95%credible intervals shown based on Cauchy (0, 10) prior. See the online article for the colorversion of this figure.
(Appendix continues)
18 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Figure A2. Simulated effect of star rating and prior on attitude change and beliefs about fakereviews, split by pattern of attitude change. Parameters provided in Table A1. See the onlinearticle for the color version of this figure.
(Appendix continues)
19PARADOXICAL EFFECTS OF PERSUASIVE MESSAGES
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
Received February 12, 2019Revision received March 11, 2020
Accepted March 12, 2020 !
Table A1Parameter Values From Simulations in Figure A2
Simulation parameters
Pattern P(r $ 3 | f $ 1) P(r $ 4 | f $ 1) P(r $ 5 | f $ 1) Low P(f $ 1) High P(f $ 1) +
A 0.05 0.30 0.65 0.10 0.15 2B 0.00 0.20 0.80 0.10 0.30 1C 0.05 0.32 0.63 0.10 0.25 4D 0.00 0.40 0.60 0.15 0.20 5
20 BHUI AND GERSHMAN
Thi
sdo
cum
ent
isco
pyri
ghte
dby
the
Am
eric
anPs
ycho
logi
cal
Ass
ocia
tion
oron
eof
itsal
lied
publ
ishe
rs.
Thi
sar
ticle
isin
tend
edso
lely
for
the
pers
onal
use
ofth
ein
divi
dual
user
and
isno
tto
bedi
ssem
inat
edbr
oadl
y.
