Crowding out the truth A simple model of misinformation polarization and meaningful social interactions Fabrizio GermanoVicen c G omezFrancesco Sobbrio

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Crowding out the truth? A simple model of misinformation,

polarization and meaningful social interactions∗

Fabrizio Germano†Vicen¸c G´omez‡Francesco Sobbrio§

October 6, 2022

Abstract

This paper provides a simple theoretical framework to evaluate the eﬀect of key parameters of ranking

algorithms, namely popularity and personalization parameters, on measures of platform engagement, mis-

information and polarization. The results show that an increase in the weight assigned to online social

interactions (e.g., likes and shares) and to personalized content may increase engagement on the social media

platform, while at the same time increasing misinformation and/or polarization. By exploiting Facebook’s

2018 “Meaningful Social Interactions” algorithmic ranking update, we also provide direct empirical support

for some of the main predictions of the model.

Keywords: Algorithmic Gatekeeper, Ranking Algorithms, Popularity Ranking, Personalized Ranking, Meaningful

Social Interactions, Engagement, Polarization, Misinformation.

∗We thank Roland B´enabou, Alexander Frug, Ga¨el Le Mens, and audiences at the 8th International Conference on Computational

Social Science in Chicago (IC2S22022) and at the 5th Economics of Media Bias Workshop (Berlin 2022) for helpful comments.

Fabrizio Germano acknowledges ﬁnancial support from Grant PID2020-115044GB-I00//AEI/10.13039/501100011033 and from the

Spanish Agencia Estatal de Investigaci´on (AEI), through the Severo Ochoa Programme for Centres of Excellence in R&D (Barcelona

School of Economics CEX2019-000915-S). Francesco Sobbrio is grateful to Nando Pagnoncelli and IPSOS for allowing access to the

data of the Polimetro.

†Department of Economics and Business, Universitat Pompeu Fabra, and BSE, fabrizio.germano@upf.edu

‡Department of Information and Communications Technologies, Universitat Pompeu Fabra, Barcelona, vicen.gomez@upf.edu

§Department of Economics and Finance, Tor Vergata University of Rome and CESifo, francesco.sobbrio@uniroma2.it

arXiv:2210.02248v1 [cs.SI] 5 Oct 2022

1 Introduction

Recent revelations by whistle-blowers at Facebook have once again brought to the attention of the public the

risks and dangers associated with the algorithms of digital platforms to manage their informational content.1

The algorithms used by social media like Facebook, Twitter or Instagram or by search engines like Google and

Bing decide what information to show to users and, importantly, also in what order to show it. Indirectly, they

determine what information is more or less relevant for any given user. A rapidly growing body of empirical

research has documented how social media platforms may foster polarization and misinformation (Allcott et al.,

2020; Di Tella et al., 2021; Levy, 2021) sometimes associated with a tangible impact (Bursztyn et al., 2019;

M¨uller and Schwarz, 2020, 2021; Amnesty International, 2022). In particular, there are journalistic and academic

claims suggesting that such adverse eﬀects may be a consequence of the way proﬁt-maximizing social media

platforms design their algorithms (CNN, 2021; Lauer, 2021), namely with the objective of ensuring a high level

of engagement (Liao et al., 2017).

In this paper, we provide a theoretical framework—and related empirical evidence—to assess whether it is

indeed the case that algorithmic rules that tend to be desirable from the perspective of social media platforms

may instead lead to detrimental eﬀects for their users and, more broadly, for the health of democracies. We

build on and extend our previous work (Germano et al., 2019; Germano and Sobbrio, 2020) to develop a model

where a platform ranks news items (e.g., posts, tweets, etc.), while individuals sequentially access the platform to

decide which news items to click and possibly “highlight” (e.g., like, share, comment or retweet). At the center

of our model, there is an endogenous ranking algorithm that decides the order of news items to be displayed to

a given user. In particular, the ranking evolves according to the popularity of news items, which is a weighted

combination of the clicks and highlights received by that news item. Simply put, the more people click and the

more people highlight a news item, the higher the probability that the news item will go up in the ranking and

will be then displayed in a higher-order position. The model also allows for assessing the role of personalization,

that is, when the platform provides a diﬀerent ranking of the news items to diﬀerent individuals.

To preserve tractability, the choices of an individual over which news items to click and highlight are modeled

as driven by behavioral traits that are rooted in ample empirical evidence. In terms of clicking choices, we assume

that with some positive probability individuals have some preference for choosing conﬁrmatory news (Gentzkow

and Shapiro, 2010; Yom-Tov et al., 2013; White and Horvitz, 2015; Flaxman et al., 2016) and, at the same time,

also for news items that are higher ranked (Pan et al., 2007; Novarese and Wilson, 2013; Glick et al., 2014; Epstein

and Robertson, 2015). In terms of highlights, we assume that with some probability individuals highlight a news

item, provided it is suﬃciently close to their prior beliefs (Garz et al., 2020) and the more so the more extreme

their prior beliefs are (Bakshy et al., 2015; Grinberg et al., 2019; Pew, 2019; Hopp et al., 2020).

Armed with this theoretical framework, we then proceed to assess the impact of popularity-driven and per-

sonalized rankings on (i) platform engagement (deﬁned in terms of the overall number of clicks and highlights);

(ii) misinformation (deﬁned as the average distance between the information content present in the news items

chosen by individuals and the true state of the world) and (iii) polarization (deﬁned as the average distance

between the information content present in the news items chosen by individuals belonging to diﬀerent groups).

The paper provides insights on whether and when ranking algorithms may lead to a trade-oﬀ between platform

and user welfare. First, we show that increasing the weight given to highlights in the popularity ranking might

be desirable from the platform’s perspective as it increases engagement. Yet, it is detrimental from a public

policy perspective as it also leads to higher levels of misinformation—crowding-out the truth—and polarization.

For completeness, we also show that such trade-oﬀ would not be present if the propensity to highlight a “like-

minded” news item was not higher for people with more extreme priors. This diﬀerence is relevant as previous

research (Bakshy et al., 2015) has shown that in the case of “hard” (e.g, national, political) news, the propensity

1See, for example, https://www.wsj.com/articles/the-facebook-files-11631713039

to highlight contents is indeed higher for individuals with more extreme prior whereas the same does not apply

to “soft” news (e.g., entertainment). Accordingly, our results suggest that the trade-oﬀ between engagement

and misinformation/polarization is not much of a concern in the case of “soft” news while it might instead be

particularly relevant in the case of political news. For what concerns personalization, the results show that a

trade-oﬀ between engagement and polarization is always present regardless of whether the propensity to highlight

content is correlated with extreme priors or not. That is, increasing the degree of personalization in the ranking

algorithm is conducive to a higher level of engagement yet also to a higher degree of polarization.

In terms of the empirical relevance of our theoretical insights, ﬁrst, we point out how the detrimental impact

of personalization on political polarization implied by our model is very much in line with the empirical literature

on this issue (e.g., Levy 2021; Dujeancourt and Garz 2022; Husz´ar et al. 2022). Most importantly, we also

provide direct evidence on the impact of increasing the weight given by platforms to highlighted content. In

particular, we leverage a rich survey dataset from Italy and exploit Facebook’s “Meaningful Social Interaction”

(MSI) algorithmic ranking update implemented in January 2018, which signiﬁcantly boosted the weight given to

comments and shares in the Facebook’s ranking algorithm.2We estimate a Diﬀerences-in-Diﬀerences empirical

model comparing the ideological extremism and aﬀective polarization of people interviewed after the Meaningful

Social Interaction (MSI) algorithm was introduced (i.e., January-June 2018) and that use internet to form an

opinion relative to those of people also using internet to form an opinion who were interviewed before such a

change (i.e., June-December 2018) and at the same time relative to people interviewed after such change in the

algorithm who were not using internet as one of the main sources to form an opinion. The results conﬁrm some of

the key theoretical predictions of the model: namely Facebook’s 2018 MSI update led to an increase in ideological

extremism and aﬀective polarization in Italy.3

To the best of our knowledge, this is the ﬁrst paper to explore both theoretically and empirically how an

algorithmic boost given to highlighted content may aﬀect platform engagement and social welfare. The model

generalizes and extends the ones of Germano et al. (2019) and Germano and Sobbrio (2020). The present setting

diﬀers in several key aspects. First, signals are drawn from a continuous distribution: individuals observe whether

an item reports like-minded news, but then need to actually click on the item in order to learn the actual signal

(and update their beliefs accordingly). Second, we allow for a broader set of clicking behavior by individuals than

just conﬁrmatory or ranking-driven types. Third, most importantly, the present model also allows individuals

to highlight news items and explores how such action might impact platform engagement, misinformation and

polarization. Fourth, we implicitly endogenize the ranking weights assigned by digital platforms when considering

which highlight and personalization weights would maximize engagement. Last but not least, we evaluate the

impact of ranking algorithms along diﬀerent metrics meant to be informative for social welfare (including measures

of platforms and consumers’ welfare).

Our model is complementary to the one of Acemoglu et al. (2022) who focus on endogenous social networks

and fact-checking.4In particular, as in our model, Acemoglu et al. (2022) show that platforms have an incentive

to increase personalization (more homophilic communication patterns) as this increases platform engagement. In

their setting, this is detrimental in terms of social welfare as it increases the level of misinformation. Instead,

in our case, more personalization increases polarization yet it does not aﬀect the overall level of misinformation,

since our model does not embed the issue of fact-checking and cannot therefore capture such an eﬀect. At the

same time, because we explicitly model the endogenous dynamic ranking used by social media platforms, we

are instead able to provide insights on the incentives—and possible perverse eﬀects on social welfare—of such

platforms to boost the weight given to content highlighting in their ranking algorithm. More generally, our paper

2See https://www.facebook.com/business/news/news-feed-fyi-bringing-people-closer-together.

3The theoretical predictions of the model pointing out the role of social media algorithms in fostering misinformation, are also

consistent with Vosoughi et al. (2018) providing evidence that false stories spread faster than true ones on Twitter. Similarly, Mosleh

et al. (2020) points out the presence of a negative correlation between the veracity of a news item and its probability of being shared

on Twitter.

4See also Azzimonti and Fernandes (2022) for a model of diﬀusion of misinformation on social media via internet bots.

relates to the literature analyzing the eﬀects of ranking algorithms on democratic outcomes. This literature

encompasses communication scholars (Hargittai, 2004; Granka, 2010; Napoli, 2015), computer scientists (Cho et

al., 2005; Menczer et al., 2006; Pan et al., 2007; Glick et al., 2014; Flaxman et al., 2016; Bakshy et al., 2015;

Liao et al., 2017; Tabibian et al., 2020), economists (Levy and Razin, 2019; Germano and Sobbrio, 2020; van

Gils et al., 2020; Acemoglu et al., 2022), legal scholars (Goldman, 2006; Grimmelmann, 2009; Sunstein, 2009),

media activists (Pariser, 2011), psychologists (Epstein and Robertson, 2015), political scientists (Putnam, 2001;

Hindman, 2009; Lazer, 2015; Tucker et al., 2018), and sociologists (Tufekci, 2015, 2018).

2 The Model

At the center of the model is a digital platform characterized by its ranking algorithm, which ranks and directs

individuals to diﬀerent news items (e.g., websites, Facebook posts, tweets), based on the popularity of individuals’

choices. Such news items may be used by individuals to obtain information on an unknown cardinal state of the

world θ∈R(e.g., net beneﬁts of vaccines, consequences of inaction on global warming, optimal foreign policy

intervention, etc.). The ranking of each news item is inversely related to its popularity, where the popularity is

determined by the number of clicks and the number of “highlights” received by a given item (e.g., likes received

by a Facebook post/number of shares, like/retweets of a tweet, etc.). Each click has a weight of one, and each

“highlight” has an additional weight of η≥0. In the following subsections we provide a formal and detailed

description of the diﬀerent elements of our model.

2.1 News items and Individuals

There are M > 2 news items, each of which carries an informative signal on the state of the world ym∈R,

and which is drawn randomly and independently from N(θ, σ2

y) (we use g(y) to denote the corresponding density

function). There are Nindividuals, each of whom receives a private informative signal on the state of the world

xn∈R, which is drawn randomly and independently from N(θ, σ2

x) (we use f(x) to denote the corresponding

density function).

To model individuals’ clicking behavior, we further assume there is a benchmark b

θ∈R—non-informative

with respect to θ—which allows individuals to sort news items into “like-minded” or not. That is, we assume

that, leaving aside the order of news items provided by the ranking algorithm, individuals are able to see whether

a news item is reporting a “like-minded” information or not. Yet they need to click on the news item in order

to see the actual signal ym. This assumption is meant to capture a rather typical situation, where individuals

observe the “coarse” information provided in the landing page by the platform (e.g., infer the basic stance of a

news item, whether Left or Right, pro or anti something, from the website title, Facebook post intro, ﬁrst tweet

in a thread, etc.), yet, in order to learn the actual content of the news (i.e., the cardinal signal ym) and update

her beliefs, the individual has to click on the news item.

We formally translate this setting into assuming that an individual is able to observe whether her own

signal xnand the news items’ signals ymare above or below b

θ. Accordingly, for each individual, the signal xn

has an associated binary signal indicating whether such signal is above or below b

θ: sgn(xn)∈ {−1,1}, where

sgn(xn) = −1 if xn<b

θand sgn(xn) = 1 if xn≥b

θ. Similarly, for each news item, the signal ymhas an associated

binary signal sgn(ym)∈ {−1,1}, where sgn(ym) = −1 if ym<b

θand sgn(ym) = 1 if ym≥b

θ.

From this we can compute M−and M+as the set of news items with binary signal respectively −1 and

1 (by slight abuse of notation, we also use M−and M+to denote the number of news items in M−and M+

respectively).

That is, given the individual’s signal xn, the benchmark b

θallows the individual to sort news items into

“like-minded” or not before actually clicking or reading. For most of the paper, we focus on the case where the

benchmark separates signals in roughly symmetrical groups, i.e. b

θ≈θ.5

At the same time, individuals have to actually click on news item min order to learn its cardinal signal ym.

In particular, we assume that, absent ranking eﬀects, the individual’s choice about which news item to click on

depends on her “clicking type” (τc

n). To encompass all possible clicking behaviour, we consider three clicking

types:

•conﬁrmatory type (τc

n=τC): clicks with propensity γCon a news item with the same sign as her own signal

sgn(xn), with 1/2< γC<1, and with propensity 1 −γCon one of opposite sign;

•exploratory type (τc

n=τE): clicks with propensity γEon a news item with the same sign as her own signal

sgn(xn), with 0 < γE<1/2, and with propensity 1 −γEon one of opposite sign;

•indiﬀerent (purely ranking-driven) type (τc

n=τI): clicks with equal propensity γI= 1/2 = 1 −γIon an

outlet of either sign.

The three types occur with probabilities, respectively, pC≥0, pE≥0 and pI≥0, such that pC+pE+pI= 1.

Similar to the literature on political economy that parametrizes the fraction of diﬀerent types of voters (e.g., Krasa

and Polborn 2009; Krishna and Morgan 2011; Galasso and Nannicini 2011), the model does not micro-found the

individuals’ clicking choices. At the same time, it is easy to see that the conﬁrmatory type might be driven

by a preference for like-minded news (Mullainathan and Shleifer, 2005; Bernhardt et al., 2008; Gentzkow and

Shapiro, 2010; Sobbrio, 2014; Gentzkow et al., 2015).6Similarly, the exploratory type might be the by-product of

incentives to cross-check diﬀerent information sources (Rudiger, 2013; Athey et al., 2018). Finally, the indiﬀerent

type allows us to consider the role of individuals with a high attention bias or search cost (Pan et al., 2007; Glick

et al., 2014; Novarese and Wilson, 2013).7Notice that we specify these three diﬀerent types to encompass all

possible clicking behaviour (conﬁrmatory, exploratory, ranking-driven), yet the key insights of the model will hold

true even if we were to focus only on one or two of such types.

The binary signal sgn(xn) together with the individual’s clicking type τc

n∈Tc≡ {τC, τE, τI}determine the

propensity with which individual nwill click on an item m, absent ranking:

ϕn,m =









γk

[m]if τc

n=τk,sgn(xn) = sgn(ym), k =C, E, I

1−γk

[m]if τc

n=τk,sgn(xn)6= sgn(ym), k =C, E, I,

(1)

where [m] = M−if sgn(ym) = −1 and [m] = M+if sgn(ym) = 1.

2.1.1 Individual choice over which news items to click on

We now generalize the individual choice function to take into account the fact that individuals see the news items

presented in a given order, following the ranking rn= (rn,m)m∈M, where rn,m is the rank of news item mas seen

by individual n. We assume that individuals have an attention bias calibrated by the parameter β > 1, with the

interpretation that, a news item of equal sign but placed one position higher in the ranking has a likelihood βtimes

larger to be clicked on than the one in the lower position. Together with the propensity to click absent ranking,

these jointly determine the probability with which individuals click on news items. We deﬁne the probability of

5Say, |b

θ−θ|<min σx

4,σy

4. In Appendix.3.2, we discuss the case, where b

θand θare far apart. Appendix.3.1 discusses the case

where individuals have heterogeneous benchmarks b

θn.

6See Yom-Tov et al. (2013); Flaxman et al. (2016); White and Horvitz (2015) for empirical evidence on conﬁrmation bias by users

of digital platforms.

7We assume clicking types to be independent from the individual’s prior xn. Nonetheless, when formalizing the individual’s choice

over which news items to “highlight”, we assess how polarization is impacted when the choice to “highlight” is correlated with the

individual’s prior beliefs.

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Crowdingoutthetruth?Asimplemodelofmisinformation,polarizationandmeaningfulsocialinteractions*FabrizioGermanoVicencGomezFrancescoSobbrio§October6,2022AbstractThispaperprovidesasimpletheoreticalframeworktoevaluatetheeectofkeyparametersofrankingalgorithms,namelypopularityandpersonalizationparamete...

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Crowding out the truth A simple model of misinformation polarization and meaningful social interactions Fabrizio GermanoVicen c G omezFrancesco Sobbrio

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