Learning from Viral Content Krishna DasarathaKevin He First version August 20 2022

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Learning from Viral Content∗

Krishna Dasaratha†Kevin He‡

First version: August 20, 2022

This version: August 3, 2023

Abstract

We study learning on social media with an equilibrium model of users interacting with shared

news stories. Rational users arrive sequentially, observe an original story (i.e., a private signal)

and a sample of predecessors’ stories in a news feed, and then decide which stories to share.

The observed sample of stories depends on what predecessors share as well as the sampling

algorithm generating news feeds. We focus on how often this algorithm selects more viral

(i.e., widely shared) stories. Showing users viral stories can increase information aggregation,

but it can also generate steady states where most shared stories are wrong. These misleading

steady states self-perpetuate, as users who observe wrong stories develop wrong beliefs, and

thus rationally continue to share them. Finally, we describe several consequences for platform

design and robustness.

Keywords: social learning, selective equilibrium sharing, social media, platform design, en-

dogenous virality

∗We thank Leonie Baumann, Michel Benaïm, Aislinn Bohren, Tommaso Denti, Glenn Ellison, Mira Frick, Drew

Fudenberg, Co-Pierre Georg, Ben Golub, Ryota Iijima, Bart Lipman, George Mailath, Suraj Malladi, Chiara Margaria,

Meg Meyer, Evan Sadler, Philipp Strack, Heidi Thysen, Fernando Vega-Redondo, Rakesh Vohra, Yu Fu Wong, and

numerous seminar participants for valuable comments and discussions. Byunghoon Kim, Stephan Xie, and Tyera

Zweygardt provided excellent research assistance. We gratefully acknowledge ﬁnancial support from NSF Grants

SES-2214950 and SES-2215256.

†Boston University. Email: krishnadasaratha@gmail.com

‡University of Pennsylvania. Email: hesichao@gmail.com

arXiv:2210.01267v2 [econ.TH] 4 Aug 2023

1 Introduction

In recent years, viral content on social media platforms has become a major source of news and

information for many people. What content users consume often depends on the news feeds created

by platforms like Twitter, Facebook, and Reddit. Which stories go viral and which disappear is

jointly determined by the algorithms generating these feeds and users’ actions on the platforms

(e.g., sharing, retweeting, or upvoting stories).

How does the design of the news feed aﬀect how users learn on such platforms? Consider a

platform deciding how much to push widely shared (or highly upvoted) content into users’ news

feeds. On the one hand, a news feed that primarily shows users widely shared stories can create

a social version of the conﬁrmation bias: incorrect but initially popular stories spread widely and

determine people’s beliefs, even though they are contradicted by most of the information that arrives

later. One might expect such feedback loops with naive users, but we show they can also arise in

an equilibrium model with rational users. The idea is that when stories supporting an incorrect

position are shared more, subsequent users tend to see these incorrect stories in their news feeds

due to the stories’ popularity, and hence form incorrect beliefs through Bayesian updating. If users

derive utility from sharing accurate content and thus share stories that agrees with their beliefs,

they will rationally share these false stories and further increase their popularity. Users have less

exposure to the true stories: even if these stories are more numerous, they are shared less than the

false stories and therefore shown less by the news-feed algorithm.

But on the other hand, selecting news stories based on their popularity may help aggregate more

information. Seeing a particular story in a news feed that selects widely shared content gives a user

more information than the realization of a single signal. The popularity of this story also tells the

user about the past sharing decisions of their predecessors, and thus lets the user draw inferences

about the many stories that these predecessors saw in their news feeds. In some circumstances,

seeing just a few stories in a news feed that emphasizes viral content can lead to strong Bayesian

beliefs about the state of nature. This can happen even if individual stories are imprecise signals

about the state, since sophisticated users can use the selection of these stories to infer much more

about sharing on the platform.

This work examines the trade-oﬀs in choosing how much to feature viral content in a news feed

and studies how this design choice aﬀects social learning on the platform. There is an active public

discussion about how news feeds shape society’s beliefs. Some commentators have blamed the

wide spread of misinformation about issues ranging from public health to politics on social media

platforms pushing viral but inaccurate content into users’ feeds. We contribute to this discussion

by developing an equilibrium model of people learning from news feeds and sharing news stories

on a platform. We characterize learning outcomes under diﬀerent news-feed designs, taking into

account rational users’ responses to diﬀerent designs and to other people’s equilibrium sharing

patterns. The model also allows provides insights about speciﬁc applied questions, such as how the

platform will optimally design its news feed to maximize its objective and the robustness of the

platform to manipulation by a malicious attacker.

In our model, a large number of users arrive in turn and learn about a binary state. Each user

receives a conditionally independent binary signal about the state (which we call a news story)

and observes a sample of stories from predecessors (which we call a news feed). These stories

are sampled using a news-feed algorithm that interpolates between choosing a uniform sample of

the past stories and choosing each story with probability proportional to its popularity (i.e., the

number of times it has been shared). Users are Bayesians and know the news-feed algorithm, so

they appropriately account for selection in the stories they see.1Users then choose which of these

news-feed stories to share. We assume users prefer to share stories that match the true state, given

their endogenous beliefs. This simple utility speciﬁcation, which one might think is conducive to

learning, can nevertheless generate rich learning dynamics including persistent learning failures.

The platform’s design choice in our model is a virality weight λthat captures the weight placed

on popularity when generating news feeds: higher λcorresponds to a news-feed algorithm that shows

more viral stories. The evolution of content on the platform is described by a stochastic process in

[0,1] we call viral accuracy, which measures the relative popularity of the stories that match the

true state in each period. We show viral accuracy almost surely converges to a (random) steady-

state value, which depends on the randomness in signal realizations and in news-feed sampling. In

equilibrium, there is always an informative steady state where most stories in news feeds match

the state. But when the virality weight is high enough, there can also be a misleading steady

1An alternative approach would be to assume users are naive and fail to account for this selection. Many of the

main forces we highlight in our equilibrium framework would also appear in this behavioral model.

state in equilibrium, where most stories in news feeds do not match the state (so viral accuracy

is less than 1

2). At a misleading steady state, users tend to see false stories, and therefore believe

in the wrong state and share these false stories. The misleading steady states correspond to the

socially-generated conﬁrmation bias described above.

These misleading steady states emerge when λcrosses a threshold, which we call the critical

virality weight λ∗. Misleading steady states exist in equilibrium when virality weight is at or

above this threshold, but not below it. A key ﬁnding is that this emergence is discontinuous: at

the threshold virality level λ∗where the misleading steady state ﬁrst appears, the probability of

learning converging to this bad steady state is strictly positive. As a consequence, the accuracy

of content on the platform jumps downward at this threshold. Below the critical virality weight,

however, the unique informative steady state becomes monotonically more accurate as λincreases.

This result formalizes the intuition mentioned above that a more viral news feed helps aggregate

more information. A platform choosing λtherefore faces a trade-oﬀ between facilitating more

information aggregation and preventing the possibility of a misleading steady state in equilibrium.

Since misleading steady states only appear when virality weight exceeds the threshold λ∗, com-

parative statics of this threshold with respect to other parameters tell us which platform features

make it more susceptible to misleading steady states. Platforms are more susceptible when news

stories are not very precise, when news feeds are large, and when users share many stories. That

is, misleading steady states arise on platforms that let users consume and interact with too much

social information relative to the quality of their private information from other sources.

We give two consequences of our results for platform design. First, we ask what virality weight

a platform would choose to maximize a broad class of objectives, including users’ equilibrium utility

from sharing stories on the platform. Because of the discontinuous change in the set of equilibrium

steady states around the critical virality weight λ∗, the optimal choice of λeither converges to this

threshold or lies strictly above it as the number of users grows. We then discuss when a platform

is robust to malicious attackers who manipulate its content. If a platform chooses λsuﬃciently

below the threshold λ∗, a large amount of manipulation is required to produce a misleading steady

state. We provide a simple explicit lower bound on this amount, which we interpret as a robustness

guarantee.

At a technical level, our paper applies mathematics techniques on stochastic approximation to

an equilibrium model where agents respond optimally to the evolution of a stochastic process. The

same techniques have been used in economics to study dynamics under behavioral heuristics (e.g.,

Benaïm and Weibull (2003) in evolutionary game theory or Arieli, Babichenko, and Mueller-Frank

(2022) in naive social learning). Even for a ﬁxed strategy, the system we study can often converge

to multiple steady states and there is no closed-form expression for the probabililty of reaching a

given steady state. Understanding outcomes under equilibrium sharing rules is even more complex.

To make progress despite this complexity, we show that outcomes under a speciﬁc simple strategy

(sharing stories that match a majority of one’s observations) tell us about the equilibrium outcomes

(which cannot be characterized directly). In particular, a misleading steady state exists when users

choose equilibrium sharing strategies if and only if one exists when users follow this simple strategy.

1.1 Related Literature

We ﬁrst discuss how our model relates to a recent literature on learning from shared signals. Several

papers have looked at diﬀerent models of news sharing or signal sharing. As we discuss in detail

below, the existing work focuses on the dissemination of a single signal, or on settings where signals

are shared once with network neighbors but not subsequently re-shared. Our model diﬀers on

these two dimensions. First, we consider a platform where many signals about the same state

circulate simultaneously. These signals interact: a user’s social information consists of the multiple

stories that they see in their news feed, so the probability that they share a given story depends

on whether the other stories corroborate it or contradict it. Second, we allow signals to be shared

widely through a central platform algorithm that generates news feeds for all users. A signal can

become popular due to early agents’ sharing decisions and get pushed into a later agent’s news feed,

and this later agent can re-share the same signal. The combination of these two model features

generates the social version of conﬁrmation bias that we outlined earlier.

Bowen, Dmitriev, and Galperti (2023) study a model where signals are selectively shared at most

once with network neighbors, but agents are misspeciﬁed and partially neglect this selection. This

bias leads to mislearning, and it also generates polarization in social networks with echo chambers.

By contrast, we focus on rational agents who make endogenous sharing decisions in equilibrium.

Bowen et al. (2023) note that:

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LearningfromViralContent∗KrishnaDasaratha†KevinHe‡Firstversion:August20,2022Thisversion:August3,2023AbstractWestudylearningonsocialmediawithanequilibriummodelofusersinteractingwithsharednewsstories.Rationalusersarrivesequentially,observeanoriginalstory(i.e.,aprivatesignal)andasampleofpredecessors’st...

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