Content Sharing in a Social Broadcasting Environment:

Evidence from Twitter

Zhan Shi

†

Huaxia Rui

‡

Andrew Whinston

Abstract

The rise of social broadcasting technologies has greatly facilitated open access to

information worldwide, not only by powering decentralized information production and

consumption, but also by expediting information diﬀusion through social interactions

like content sharing. We study users’ voluntary information sharing in the context of

Twitter, the predominant social broadcasting site, by modeling both the technology

and user behavior. We collect a detailed dataset about the oﬃcial content-sharing

function on Twitter, called retweet, and document the statistical relationships between

the users’ social network characteristics and their retweeting acts. We then estimate

a more structural model using conditional Maximum Likelihood Estimation (MLE)

method. The empirical results convincingly support our hypothesis that weak ties are

more likely to engage in the social exchange process of content sharing. Speciﬁcally, we

ﬁnd that after an author posts a median quality tweet (as deﬁned in the sample), the

likelihood that a unidirectional follower will retweet is 3.1% higher than the likelihood

that a bidirectional follower will.

Keywords: Information Diﬀusion, Content Sharing, Social Broadcasting, Twitter,

Weak Tie

We thank Rion Snow from Twitter, our editors, the four anonymous reviewers, as well as the attendees

to our panel at SXSW Interactive 2011 and our session at WISE 2010, for useful comments and suggestions.

†

The University of Texas at Austin, Department of Economics, Austin, TX 78712, email: zs@utexas.edu

‡

The University of Texas at Austin, Department of Information Systems, Risk and Operations Manage-

ment, McCombs School of Business, Austin, TX 78712, email: huaxia@utexas.edu

The University of Texas at Austin, Department of Information Systems, Risk and Operations Manage-

ment, McCombs School of Business, Austin, TX 78712, email: abw@uts.cc.utexas.edu

1 Introduction

At 10:24 p.m. EST, May 1, 2011, one hour and eleven minutes before the formal announce-

ment of Osama Bin Laden’s death by U.S. President Barack Obama, the following message

was posted on Twitter by Mr. Keith Urbahn,

So I’m told by a reputable person they have killed Osama Bin Laden...

The post quickly attracted attention and got forwarded by Mr. Urbahn’s subscribers on

Twitter, and within two minutes, there were already more than 300 reactions to it. In the

following hour, tens of thousands more users in the Twitter world were passing this message,

and the ﬁnal number of people who got exposed to the information before the formal White

House announcement was even higher.

This example not only shows the sheer power of Twitter as a fast-growing social medium,

but also demonstrates that, the emerging social media can beat even their mainstream com-

petitors in terms of speed, ﬂexibility, and reach, especially in tracking events as they unfold

in real time.

The unique advantage of websites like Twitter in disseminating news comes

from their distinctive technological infrastructure. Although Twitter and a number of other

similar online services, such as Tumblr and Sina Weibo, are usually referred to as micro-

blogging or social networking sites, these labels fail to capture their whole essence — that

these websites each are simultaneously a broadcasting service and a social network. Like

content from most traditional mass media, user-generated content on these sites is accessible

by the public and is broadcasted through directed subscription. The subscription relation-

ships, as the only kind of user relationship, constitute the accompanying social network. The

coexistence of a broadcasting service and a social network makes the combination of facets

easily distinguishable from each one’s respective standalone peers. On the one hand, the

broadcasting service diﬀers from traditional mass media like TV or radio in its decentralized

structure and its social ingredient; it represents the full spectrum of communications, from

headline news to personal and private communications (Wu et al. 2011). On the other hand,

the social network, derived from content-subscription relationships, also signiﬁcantly diﬀers

from traditional online social networks, which typically map real-world friendships or con-

nections. For example, the social network on Twitter is quite open and loose compared to

the social network on Facebook because the follower–following relationship on Twitter can

@keithurbahn, http://twitter.com/keithurbahn.

Indeed, this capability has been proven again and again during events such as the 2009 Iran election,

the 2011 Middle East Revolution, and the 2012 Chinese political scandal.

be established unilaterally and usually cuts across long (real-world) social distances. This

combination gives these technologies unique advantages in facilitating information diﬀusion

and justiﬁes assigning them to a new category, which we call social broadcasting networks.

This view is also explicitly or implicitly shared by many computer and information scientists.

For example, Kwak et al. (2010) suggested that Twitter more closely resembles an informa-

tion sharing site than a traditional social network. Bakshy et al. (2011) noted that “unlike

other user-declared networks, Twitter is expressly devoted to disseminating information.”

Social broadcasting networks have blurred the traditional boundary between social networks

and news media by adding the “social” ingredient into the cycle of information production,

exchange, and consumption (Kwak et al. 2010, Wu et al. 2011, Socialﬂow 2011).

As exempliﬁed by the Bin-Laden case, information diﬀusion in social broadcasting net-

works critically relies on social interactions, such as content sharing. Indeed, without the

voluntary relaying of Mr. Urbahn’s message by numerous Twitter users, that single post

might never have triggered an avalanche of reactions and reached an audience far beyond

Mr. Urbahn’s own subscribers.

Content sharing is a critical mechanism of information dif-

fusion in social broadcasting networks and is vital to a network’s proper functioning and

thriving. When interesting or important information does not get passed on, the social

broadcasting network fails to reach its full potential as a news medium; meanwhile, excess

transmission of redundant or trivial information creates information overload and lowers the

value of a social broadcasting network to the users. Understanding the information relaying

process is thus both interesting and important. The objective of this paper is to make an

early step in this direction by examing the sharing decision-making process at the individual

level. As suggested, one deﬁning feature of social broadcasting networks is that they possess

a large volume of weak interpersonal relationships. Thus, our central goal in this article is

to address the following research question:

Research Question How does the strength of the interpersonal tie moderate people’s vol-

untary content sharing behavior in a social broadcasting network?

Exploring the question might further reveal people’s motivation in passing on information.

Users’ voluntary content sharing is a social exchange process (Blau 1964) that involves

the content’s creator, the sharer, and the sharer’s subscribers. To develop and test a theoret-

ical model explaining how tie strength moderates people’s decisions to engage in the social

According to social media company SocialFlow, Keith Urbahn wasn’t the ﬁrst to speculate Bin Laden’s

death after the news was released about the presidential address. However, Keith Urbahn’s tweet proved to

be a watershed in people’s discussion on Twitter regarding the presidential address.

exchange, we draw on two streams of prior research: the literature on tie strength and the

literature on people’s pro-social behavior.

Plenty of literature has looked at the implications of tie strength in a variety of social or

economic settings. For example, Granovetter (1973) did the pioneering work on the role that

weak ties played when people search for jobs, the result of which is famously summarized as

the strength of weak ties

(SWT). The arguments of SWT suggest the importance of weak ties

(i.e., ties with acquaintances, rather than close friends) in enabling novel information to ﬂow

across two densely knit groups of close friends. Levin and Cross (2004) proposed and tested

a model of dyadic knowledge exchange taking into account trust and tie strength between

the two parties. Their results also suggested that weak ties provide access to nonredundant

information. Bapna et al. (2012) studied the link between strength of social ties and trust

in an online social network using data from a Facebook application. They found that for

the average user social tie strength as measured by actively interacting with someone else is

positively linked to trust.

Researchers have also extensively studied people’s motivation of sharing knowledge in

online environment where explicit ﬁnancial compensation is often absent (Wasko and Faraj

2005, Bock et al. 2005, Chiu et al. 2006, Olivera et al. 2008). However, most of the pre-

vious studies focus on sharing behavior in the form of helping others (often strangers) solve

problems by contributing one’s own knowledge. Bock et al. (2005) surveyed 154 managers

from 27 Korean organizations and found that anticipated reciprocal relationships aﬀect in-

dividual’s attitudes toward knowledge sharing. Chiu et al. (2006) also found that social

interaction ties, reciprocity, and identiﬁcation increased individuals’ quantity of knowledge

sharing by surveying 310 members of one professional virtual community in Taiwan. Olivera

et al. (2008) developed a framework for understanding contribution behaviors and delineated

three mediating mechanisms : awareness, searching and matching, and formulation and de-

livery. The sharing behavior we study is people’s voluntary information relaying decision,

which is a quite diﬀernt type of contribution. Wasko and Faraj (2005) applied theories of col-

lective action to examine how individual motivations and social capital inﬂuence knowledge

contribution in electronic networks. Using survey data and archival data from one electronic

network supporting a professional legal association, they found that people contribute their

knowledge when they perceive that it enhances their professional reputations, when they

have the experience to share, and when they are structurally embedded in the network.

The current paper can be viewed as an extension of Wasko and Faraj (2005) in the sense

that we are also examing people’s contribution behavior on a electronic network. However,

this paper departs from previous IS literature in two important ways. In terms of data and

method, we use micro-level data and a two-stage discrete choice model to study a relatively

new form of sharing behavior–relaying information contributed by others–on a social broad-

casting network which is also a new form of virtual community. In terms of theory, we

integrate SWT with the general framework of social exchange to develop a new theoretical

model to examine the relationship between network characteristics and retweeting behavior.

Our theoretical model posits that one’s motivation for engaging in the social exchange

process of content sharing is the latent beneﬁt of perceived reputation enhancement resulting

from consumption of the shared content by one’s subscribers. The majority part of the latent

beneﬁt comes from the subscribers and thus is positively associated with the perceived

novelty of the content to the sharer’s subscribers, which in turn is negatively associated

with the strength of the social tie between the content’s creator and the sharer. Empirically

testing our theory in a real-world social broadcasting network is complicated both by the

challenge of collecting micro-level data from the Internet and by the speciﬁcs of the actual

technological environment in which data are produced. To overcome these problems, we

deploy 20 servers over a 140-day period to collect a detailed dataset containing information

on both the content-sharing activity and social relationships from Twitter, and we develop a

two-stage “consumption-sharing” model to help us better understand the machine-mediated

human decision-making process. We then estimate the empirical model using conditional

Maximum Likelihood Estimation (MLE) method, the results of which convincingly support

our theory.

The remainder of this paper proceeds as follows. In Section 2, we brieﬂy introduce

Twitter as an example of social broadcasting networks and describe the technology-mediated

information-sharing mechanism on Twitter. Drawing on social and behavioral theories, we

develop our hypothesis in Section 3. After describing our dataset in Section 4, we conduct

a series of empirical analyses to test our model in Section 5, and we discuss the managerial

implications of our ﬁndings in Section 6. Finally, we conclude and discuss future research

directions in Section 7.

2 Twitter and Retweeting

Designed to be the “Short Message Service of the Internet” at start-up, Twitter was launched

in July 2006. During the 2007 South by Southwest (SxSW) festival in Austin, TX, a showcase

of Twitter impressed the highly tech-savvy attendees. Since then, Twitter has entered a phase

of rapid growth and gained popularity far beyond the technology industry insiders. As of

March 2011, Twitter had more than 200 million registered users worldwide, who in total

post an average of 150 million updates a day.

Twitter is now one of the most vibrant online

communities in the world.

Twitter: A Social Broadcasting Technology

Twitter is an example of a social broadcasting site, where a broadcasting service and a social

network organically constitute the technological infrastructure. On top of that, Twitter users

produce and consume informational content by authoring and reading tweets,

which are

text-based updates/messages of up to 140 characters. Like content on most traditional mass

media, tweets are by default open to the public, and there is no restriction on consumption.

consumer.

Twitter users are networked to each other through a following-follower relationship. A

user’s followers are those who subscribe to receive his or her tweets, and a user’s followings are

the users whose tweets he or she subscribes to receive.

This following-follower relationship

is the sole interpersonal link in the Twitter network. It is not only the pathway through

which broadcasted content traverses the Twittersphere but also the channel of person-to-

person communications, such as public reply and direct message. This relationship diﬀers

from friendship on Facebook or some other social network site in two respects: (1) the

following-follower relationship on Twitter is relatively open in the sense that A following B

does not require B’s consent, and they usually do not map to real-world friendships as the

ones on Facebook do;

and (2) perhaps more importantly, the following-follower relationship

is directed (A’s following B does not imply B’s following A) while friendship is undirected

(A’s being a friend of B implies B’s being a friend of A). The existence of a large volume of

(loose and directed) subscription relationships is thus a distinctive characteristic of a social

broadcasting network.

See http://blog.twitter.com/2011/03/numbers.html and http://en.wikipedia.org/wiki/Twitter for more

statistics.

Tweet can also be used as a verb, meaning to post. So “to tweet a tweet” means “to post an update.”

A user A does not have to follow B to consume B’s tweets. A can access B’s Twitter webpage at any

time to consume B’s tweets, which, like everyone else’s, are always publicly available. But if A follows B,

B’s tweets will be “pushed” to A in real time.

The fact that users who are connected in a social broadcasting site are usually neither friends nor even

acquaintances in the real world allows us to narrow our focus just to the online context in studying their

interactions. For instance, we do not have to worry that a favor A does for B online would be reciprocated

oﬄine.

Retweeting: Content Sharing on Twitter

Content sharing is an integral part of the Twitter experience. In addition to composing and

posting tweets themselves, Twitter users can also rebroadcast — or retweet

in Twitter’s

terminology — other users’ (most likely their followings’) tweets that they ﬁnd are of partic-

ular (informational, entertaining, etc) value.

Retweeting spreads information by exposing

new audience to the content. Meanwhile, retweeting is a special kind of sharing because a

retweet is simply a copy of the original tweet, and thus the author, content, and format of the

shared information stay exactly the same as the original tweet. Retweeting can also display

a “chain eﬀect”: not only a tweet’s author’s followers, but also sharers’ followers, and so on,

can further retweet, spreading the content onto their respective networks and amplifying the

audience of the content to a potentially massive scale (Socialﬂow 2011). Thus, retweeting is

evidently a critical mechanism of information diﬀusion on Twitter. Since it was introduced,

retweeting has been extremely popular on Twitter because of the straightforward idea and

the easy-to-use oﬃcial retweet button.

Therefore, we use retweeting in the Twittersphere

as the primary real-world example of content sharing activity.

The mechanism of retweeting is graphically illustrated in Figure 1. Hereafter, we call

the user who writes the original tweet the author, and the author is denoted R in the ﬁgure.

The other nodes represent other users who are linked to each other via the following-follower

relationship, together forming a tiny community inside the Twitter world. If two users

mutually follow each other, the edge between them is drawn in solid (e.g., R and A, and we

call A a bidirectional follower of R). Otherwise, if only one of them follows the other, the

edge between them is a dashed line, with an arrow pointing to the user followed (e.g., B

follows R but R doesn’t follow B, so that we call B a unidirectional follower of R). After R

posts an update, if no one retweets it, only R’s followers A, B, C, D, and E would receive it.

Retweet is both a verb and a noun, just as tweet is. When user A retweets a tweet t, we call the reposted

copy of t a retweet and call A a retweeter of t.

Posting others’ tweets simply by copying and pasting their tweets without mentioning the original author

is technologically possible but is not considered retweeting. Rather, it is a highly criticized misbehavior in

the Twitter community.

The oﬃcial retweet function is built into most mobile applications, as well as Twitter’s oﬃcial website.

There is no publicly available statistic on the popularity of retweeting vs. other ways of information sharing.

For example, another widely adopted way is to quote a tweet and add “RT” in front. An oﬀ-the-record

interview with a Twitter employee conﬁrmed that the oﬃcial retweeting button had been the more popular

mode of sharing.

In addition to Twitter’s dominance in the social broadcasting domain, another important reason we

focus on it is that the openness of Twitter allows us to collect a detailed, micro-level dataset to complete our

study. Section 4 describes our data collection in detail.

Figure 1: An Illustration of Retweeting

But now assume that after reading the message, users A, D, and E retweet (retweeters are

shown in ﬁlled circles), thereby making F , G, H, and K, who are not immediate followers

of R, receive a copy of the tweet. Then the new receivers could also retweet (as G and H

do in the Figure 1 example), circulating the information more broadly around the network.

One thing to note is that a retweet is also a content broadcast; because of the technology, a

sharer cannot select a subgroup of his or her followers and only retweet to this subgroup.

Using the graphic example in Figure 1 as the context, we emphasize a few things related

to our research question. First, we do not consider network dynamics (the formation and

destruction of personal relationships among the users). In this research, we take a snapshot

of the network structure, consider it as ﬁxed and exogenous, and study user behavior on top

of it. Second, in later econometric analyses, we model potential retweeters only in the ﬁrst

order (i.e., R’s immediate followers A, B, C, D, and E), but not those in the second and

higher orders (i.e., F , G, H, I, J, and K). As we explain in the data section, the reason is

that we do not have the network graph data for higher order potential sharers. Third, the

variation of user behavior we exploit is diﬀerent users’ diﬀerent reactions to a single tweet

(e.g., A, B, C, D, and E’s reactions to a tweet authored by R), rather than one single user’s

diﬀerent reactions to diﬀerent tweets (e.g., B’s reactions to diﬀerent tweets authored by R,

H, and L).

In non-broadcasting social networks, such as Facebook, users typically can post messages only to a chosen

subgroup of his or her “friends.”

3 Theoretical Model

In this section, we develop the hypothesis on how the strength of the interpersonal tie mod-

erates people’s decision of relaying others’ message. Although we often refer to Twitter as we

develop our hypothesis, our theoretical arguments are applicable to other social broadcasting

networks as well.

Content sharing is a social exchange process (Homans 1958; Blau 1964) that involves

three parties: the sharer, the content’s creator, and the group of individuals to whom the

content is shared. By choosing to relay the information, the sharer incurs the cost of sharing

without being rewarded in any explicit way. However, the other two parties explicitly beneﬁt:

The subscribers can consume the shared information, and the content’s creator reaches a

larger audience.

Social exchange theory posits that people engage in social exchange in expectation of

getting returns. When no explicit material or ﬁnancial gains are received, the latent beneﬁt

of a social exchange process can be emotional comforts or social rewards (e.g., reputation).

Indeed, “people’s positive sentiments toward and evaluations of others, such as aﬀection,

approval, and respect, are rewards worth a price that enter into exchange transactions”

(Blau 1964, p 112). Certain acts conducted by members of a community, such as sharing

knowledge, beneﬁt the collective but do not generate any immediate ﬁnancial returns to the

actors. Such behaviors are often referred to as “pro-social,” because social rewards have

been identiﬁed as an important incentive. For example, perceived reputation enhancement

is identiﬁed as an important factor in motivating sharing in the information system and

management literature (Wasko and Faraj 2005).

These early research works suggest that the latent beneﬁt for the sharer to engage in

the social exchange process might come from the perception that participation in sharing

information enhances his or her reputation either as a connected person in the network or

as a person that has the capability to ﬁlter large amounts of content and dig out valuable

pieces.

How large the latent beneﬁt can be, or the extent to which a user’s reputation can be

enhanced by sharing a message, is determined by two factors: the number of subscribers

who would receive the shared content and the extent to which the subscribers value that

piece of content. The subscribers’ valuation depends partly on the intrinsic quality of the

shared information: The higher the quality is, the more the audience values the content, and

The cost could be interpreted as the opportunity cost of choosing not to share.

hence the greater the latent beneﬁt of sharing.

Moreover, diﬀerent audiences’ valuations

of the same content (quality) should also diﬀer because they have diﬀerent preferences and

diﬀerent knowledge sets. For instance, the early tweet about the death of Osama bin Laden

should indeed have high informational value to most ordinary Twitter users. However, for

anyone inside the White House Situation Room on May 1, 2011, that tweet simply repeated

a story he or she already knew and thus was of little additional value. This case shows that

information consumers with diﬀerent backgrounds could attach unequal value to the same

piece of content, and, in particular, the novelty of information should aﬀect a particular

consumer’s valuation.

Earlier works in sociology studied the importance of weak ties in enabling the ﬂow of

novel information in a social structure. For example, Granovetter (1973) theorized the re-

lationship between the novelty of information and the strength of the social tie through

which the information is transmitted in the context of people ﬁnding jobs. Granovetter’s

results suggested that weak ties — those personal connections linking distant acquaintances

— were more likely to provide nonredundant information because strong ties link closely re-

lated persons, such as family and friends, who often possess knowledge sets similar to the job

seeker’s. Following Granovetter’s seminal work, subsequent research further demonstrated

that, in both real organizations and virtual communities, weak ties are instrumental in con-

necting diverse groups and enabling a person to access heterogeneous and thus more valuable

opinions (see, e.g., Granovetter 1982; Constant et al. 1996; Hansen 1999; Levin and Cross

2004). Adopting this view in the context of information sharing in a social broadcasting en-

vironment, we hypothesize that the strength of the social tie between the content creator and

a potential sharer mediates the sharer’s latent beneﬁt of sharing. Speciﬁcally, on average,

the weaker the tie is, the higher a potential sharer believes the subscribers would value the

information and hence the higher the expected reputation enhancement is. The implication

of this line of argument is the following hypothesized relationship between content-sharing

probability and tie strength.

Hypothesis. In social broadcasting networks, the latent beneﬁt of sharing content is nega-

tively associated with the strength of the social tie between a potential sharer and the content

creator. Thus, given a piece of content, a weak-tie subscriber is more likely to share than a

strong-tie subscriber, everything else being equal.

This hypothesis might look counter-intuitive at ﬁrst glance for readers who anticipate

that, for example in the Twitter world, a Twitter user is more likely to retweet tweets from

Because of this quality eﬀect, we cluster our observations based on each tweet in our analysis.

those who are strongly tied to her.

However, as we argued, information sharing in a social

broadcasting environment is mainly a social exchange with one’s followers. SWT suggests

that the followers of a weak-tie follower of the content’s creator should on average attach a

higher value to the content, which, we argue, serves as a larger incentive for participating

in the social exchange of forwarding information. Moreover, although our hypothesis is

consistent with SWT, it is not a simple repetition of it. SWT states only that information

obtained from one’s weak-tie connections is expected to be more valuable; it does not say

that weak ties actually promote information dissemination in anticipation of the higher

value from the information receivers. In this sense, our hypothesis extends the original

SWT ﬁndings within the social exchange theoretical framework by arguing that in social

broadcasting networks, weak ties, in expectation of higher social exchange returns, are more

likely to provide the path by which information is relayed. We quote the following paragraph

from Friedkin (1980):

Granovetter’s theory, to the extent that it is a powerful theory, rests on the

assumption that local bridges and weak ties not only represent opportunities for

the occurrence of cohesive phenomena ... but that they actually do promote

the occurrence of these phenomena. A major empirical eﬀort in the ﬁeld of

social network analysis will be required to support this aspect of Granovetter’s

theoretical approach ... It is one thing to argue that when information travels

by means of these ties it is usually novel, and perhaps, important information to

the groups concerned. It is another thing to argue that local bridges and weak

ties promote the regular ﬂow of novel and important information in diﬀerentiated

structures. One may agree with the former and disagree with the latter.

Our hypothesis suggests that the two things Friedkin tried to disentangle conceptually might

after all be indistinguishable practically because people’s quest for reputation enhancement

motivates them to facilitate the penetration of novel information into the social network

through weak ties.

User relationships in the Twitter environment are apparently not exactly the same as

the real-world personal relationships Granovetter initially focused on to study the strength

Such intuition might have its root in the balance theory in psychology (Heider 1958). Blau (1964, p26)

argued that a strain toward imbalance, as well as toward reciprocity, arises in social associations. If we think

of the action of retweeting as an endorsement or a favor to the content creator, then a user’s retweeting a

tweet from someone who does not follow that user represents a greater imbalance than if that tweet were

from someone who follows that user. In other words, from the perspective of the social exchange between

the sharer and the content creator, a strong tie entails a stronger sense of obligation.

of weak ties. Hence, to adapt our hypothesis in the Twitter world and test it with data,

we need to empirically operationalize the strength of social ties in the Twitter network. We

do this based on the observed relationship types and assume that reciprocal relationships

are on average stronger than nonreciprocal ones. This assumption leads to the following

assumption, which is key to our subsequent empirical analysis:

Assumption. A unidirectional link between two Twitter users is expected to be weaker than

a bidirectional one, in the sense of “tie strength” established by Granovetter (1973).

For instance in the Figure 1 example, ties like D-R are expected to be weaker than those

like C-R.

Our measure of tie strength looks natural, but it nonetheless needs to be supported by

convincing theoretical arguments and empirical evidence. We provide the supporting argu-

ment of our assumption in Appendix I for interested readers. Meanwhile, we note here that

the emphasis on reciprocity is consistent with a long tradition in the sociology literature.

Davis (1970) suggests that mutual choices indicate a strong tie while asymmetric pairs in-

dicate weak ties.

Granovetter also pointed out that the strength of a tie is a combination

of several factors, including mutual conﬁding and reciprocal services (Granovetter 1973).

Friedkin (1980) measured tie strength among faculty members in seven biological science

departments of a single university based on whether a discussion about current research is

reciprocated or not reciprocated.

Based on the assumption, our hypothesis, adapted in the Twitter world, becomes an

empirically testable one:

Hypothesis. On expectation, a unidirectional follower is more likely to retweet than a

bidirectional follower.

For instance, in Figure 1, ex ante we expect D is more likely to retweet R’s tweet than

C is. We develop our econometric model based on both these theoretical discussions and the

technological speciﬁcs of the Twitter environment. Before discussing the model, we describe

our data in Section 4.

Davis measured interpersonal relations on a three-point ordinal scale: mutual positives are the most

positive, mutual negatives are least positive, and asymmetric pairs are intermediate. In sociometry, these

correspond to mutual choices (i chooses j and j chooses i), mutual nonchoices (i does not choose j, and j

does not choose i), and unreciprocated (i chooses j but j does not choose i, or j chooses i but i does not

choose j).

Tweets Database

http://www.twitter.com/toptweets

Retweets Database

Net-Graph Database

Twitter API

“pick-tweet”

picks 1 tweet per day

“fetch-retweeters”

runs once per hour

“fetch-graph”

crawls network data

Figure 2: Data Collection Workﬂow

4 Data

We deployed 20 servers to collect data by querying Twitter’s application programming in-

terface (API).

Data Collection

Figure 2 shows the data collection workﬂow and is a useful illustration for helping readers to

understand the details of our data collection process, described in the following paragraphs.

From July 22, 2010 to December 2, 2010, at 0:05 each day, our “pick-tweet” program fetched

Twitter’s toptweets webpage, which usually showed 17 to 18 popular tweets in the Twitter-

sphere at the visiting time.

Sorting these tweets into chronological order, our program

then checked, one by one, the number of followers a tweet’s author had and inserted into

our tweets database the ﬁrst one it found whose author had less than 1,500 followers; the

http://dev.twitter.com

Top Tweets is an oﬃcial Twitter account, which is a “new algorithm that ﬁnds tweets that are catching the

attention of other users.” The algorithm is proprietary, so we cannot give a deﬁnition for a “popular tweet.”

Twitter’s Chief Scientist, Abdur Chowdhury, explained, “the algorithm looks at all kinds of interactions

with tweets, including retweets, favorites, and more to identify the tweets with the highest velocity beyond

expectations.”

rest were discarded. If all the authors had more than 1,500 followers, the program wouldn’t

insert any tweet on that day. In other words, our program picked either 1 tweet or 0 tweets

every day over this period of time.

After a tweet entered our tweets database, another “fetch-retweeters” program began to

track and fetch its retweeting data and would do so constantly during the subsequent ﬁve

days.

At 10 minutes past each clock hour over the 5 days, the program queried Twitter

API to get the user IDs of the retweeters (those in ﬁlled circles in the Figure 1 example).

The retweeter IDs were obtained in the order of the time at which the user retweeted.

As retweeting data came in, another “fetch-graph” program worked on collecting relevant

network graph information. Speciﬁcally, for each tweet, we were interested in its author (R

in Figure 1), the author’s followers (A, B, C, D, E in Figure 1), and the tweet’s (ﬁrst-order)

retweeters (A, D, E in Figure 1); we called this set of Twitter users our focal set. For each

user in the focal set, our program collected the IDs of both the followings and followers and

stored the data in our network graph database. For some users in the focal set, access to their

following-IDs and follower-IDs was restricted because they explicitly disallowed third-party

access to their data. We used a “protected” ﬂag to indicate this privacy protection status,

with the ﬂag = 1 meaning no public data access. With the retweeting data and network

graph data in hand, we produced a real-world analog of Figure 1 (see Figure 10 in Appendix

II). The ﬁgure shows the spread of the ﬁrst tweet in our database.

We designed our data collection strategy around one important binding constraint: Twit-

ter API allowed only 150 visits/queries per IP per hour,

and our computational capacity

was limited. One API visit would return only a limited amount of information, so to ﬁnish

one “job” (e.g., getting the entire set of a user’s following-IDs) could require a number of

The “pick-tweet” program did not run properly on a few days during our data collection period because

technical problems (e.g., server failure) occurred on either the Twitter side or our side. On those days, no

tweets were added to our database.

The decision to track retweeting activities for ﬁve days was made on the basis of our judgment about

how long a retweeting process of one tweet could stay active. The log ﬁle written by the “fetch-retweeters”

program showed that most retweeting activities of a tweet happened within just one or two days of when

it was ﬁrst posted. Tracking for ﬁve days thus seemed conservative enough to ensure that any truncated

sample problem (a large number of retweets occurring after our tracking period) was unlikely.

One important technical constraint was that Twitter API provided IDs for only the 800 most recent

retweeters, so that if more than 800 users retweeted a tweet between two queries, our program was not able

to get the complete set of retweeters. In addition, we found no publicly available way to verify the number

of retweeters our program had missed. We took a conservative approach to deal with this situation: Unless

we were sure we had fetched the complete set of retweeters for a tweet, we discarded that tweet from our

database.

This REST API rate limit was as of the second half of 2010: https://dev.twitter.com/docs/rate-limiting.

Tweet level t index of tweets/authors

the number of followers of author t

the number of observations for tweet t

the total number of retweeters of tweet t

Follower level ti index of author t’s followers, i ∈ {1, 2, . . . , n

}

binary outcome, = 1 if follower ti retweeted tweet t

binary variable, = 1 if follower ti is a unidirectional follower of t (weak tie)

the number of ti’s followings

the number of ti’s followers

the number of times ti’s followings retweeted tweet t (before ti did if y

= 1)

Table 1: Notations

queries (e.g., the actual number of visits required would depend on the number of followings

the user had). As discussed in the previous paragraph, we had to collect all following-IDs

and follower-IDs for all users in the focal set; moreover, we had to ﬁnish collecting the data

as quickly as possible to avoid potential signiﬁcant changes in their following-follower rela-

tionships. This 150-visits limit was the reason why we decided to select only one tweet per

day, select only tweets whose authors had fewer than 1,500 followers, and track retweeting

activity only once per hour, and why we decided not to collect network graph data of follow-

ers’ followers (G in Figure 1).

Deciding otherwise would have prevented us from ﬁnishing

the workload for one tweet before the next tweet came into our database.

Data Description and Statistics

We provide a list of notations in Table 1.

Tweets, authors, and the number of observations

By the end of the 140-day data collection course, we had successfully completed data

collection for 65 tweets. We index the tweets in order of posting time by an integer, t, ranging

from 1 to 65. The tweets were all authored by diﬀerent users, so we also denote the author

of tweet t author t, for simplicity of notation.

As a result, we do not have the “second-order” retweeters’ network characteristics and we do not include

the “second-order” retweeters in later econometric analyses. Studying their retweeting decisions can be a

future research topic.

Among the 65 tweets, 3 are in Spanish, 1 is in Italian, 1 is in Portugese, and the remaining are in English.

None of the authors is celebrity, partly because of our 1,500-follower constraint. The textual contents range

from breaking news and comments on news to political jokes and witty quotes.

min max mean median

total 87 1497 457 370

non-protected 54 1189 375 324

Table 2: Number of Observations per Tweet

The two plots in Figure 3 show the distributions of the tweets by month of post and

by hour of post, respectively. The sample frequency of tweets by hour of post is roughly

consistent with the distribution of total volume of tweets posted in each clock hour in the

entire Twitter world. The left subplot of Figure 4 shows the distribution of the number of

followers an author had (n

) and the distribution of the total number of retweeters a tweet

gained (ν

). Note that for a tweet, ν

could be larger than n

because retweeters’ followers

who were not immediate followers of the author could also have retweeted. The right subplot

of Figure 4 is a scatter-plot of the 65 tweets on the n

-ν

plane. More or less surprisingly,

our sample shows no positive correlation between the number of followers an author had and

the total number of retweeters her tweet gained (a linear ﬁtting line shows weakly negative

slope). However, this simple result is actually consistent with Bakshy et al. (2011), which

also ﬁnds that the number of an author’s followers is in general a poor predictor of the size

of the retweet cascade.

Because our objective is to model a follower’s binary decision of whether to retweet, n

the number of followers that author t had is also the number of observations in cluster t.

From this place onward, we exclude users for whom we could not collect following/follower

IDs (ﬂag “protected” = 1) and users with zero following/followers (assuming they were

either new registrants or inactive members). As a result, the total number of observations

(N =

∑

t=1

) in our sample declined from 29,681 to 24,403, a decrease of 17.78%. Table

2 gives the basic descriptive statistics of n

before and after dropping the observations, and

Figure 5 shows the number of pre-dropping vs. post-dropping observations in more detail.

Variables

We now summarize the key variables used in the econometric model. For a tweet t, we

use y

, i ∈ {1, 2, . . . , n

} to index whether each of its observations (i.e., author t’s followers)

retweeted tweet t. The deﬁnitions of the key variables can be found in Table 1. These

variables are either directly observed or constructed from observed ones. We provide the

descriptive statistics of these variables in Table 3 and the correlations between them in

Jul Aug Sep Oct Nov Dec

Count

(a) Tweets Distribution - Month

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Count

(b) Tweets Distribution - Hour

Figure 3: Distributions of Tweets by Month of Post and by Hour of Post

0-200 200-400 400-600 600-800 800-10001000-1500

Count

Range

(a) Distribution of Tweets over # of Followers (unshaded) and # of Retweeters (shaded)

followers

retweeters

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400

# of Retweeters

# of Followers

(b) # of Followers/Retweeters Scatter Plot

Figure 4: Distribution of Number of Author’s Followers and Number of Retweeters

200

400

600

800

1000

1200

1400

1600

31 34 57 26 35 64 61 17 10 44 62 56 41 37 6 23 15 9 32 58 48 18 11 60 43 30 28 51 7 3 36 53 54 19 5 33 13 65 59 47 22 24 27 14 2 55 25 4 16 12 52 50 39 1 21 63 42 8 38 40 46 29 20 45 49

Obs

: # of Observations (Protected v.s. Non-protected)

non-protected

protected

Figure 5: Number of Observations per Tweet

mean std 5% 15% 50% 85% 95%

retweet dummy 0.0427 0.2022 - - - - -

unid’l dummy 0.7598 0.4272 - - - - -

# of followings 1574 9046 25 69 347 1714 3297

# of followers 3304 73124 5 22 190 1117 4970

# of repetition 3.2845 7.5216 1 1 1 4 11

Table 3: Descriptive Statistics

retweet dummy 1.0000

unid’l dummy 0.0072 1.0000

# of followings -0.0225 -0.0921 1.0000

# of followers -0.0065 -0.0338 0.4436 1.0000

# of repetition 0.0493 -0.1508 0.2002 0.1400 1.0000

Table 4: Correlations

Table 4.

Let y

∑

i=1

be the number of retweeters among author t’s followers (note that

̸= ν

), and yr

= y

could then be naturally interpreted as the retweeting rate of

t. Figure 6 shows the retweeting rate across the tweets with a 95% error bar. That the

rate varies quite a lot is not surprising given the signiﬁcant heterogeneity across the tweets

(i.e., the intrinsic quality). Hence, we should consider tweet-speciﬁc eﬀects when modeling

retweeting behavior. Over the whole sample (i.e., tweets pooled together), the retweeting

rate is 0.0427, and the 95% conﬁdence interval is (0.0402, 0.0452).

is the binary indicator of unidirectional relationship, which is also our main opera-

tionalization of a weak tie in econometric analysis. The simple correlation of y

and w

positive. w

∑

i=1

is the number of author t’s followers who were not followed back by t.

= w

is thus the fraction of t’s unidirectional followers. We plot wr

in Figure 7, which

shows that for most of the tweets in our sample, wr

is in the range (0.5, 0.9). Over the whole

sample, the fraction is wr = 0.7598, and its 95% conﬁdence interval is (0.7545, 0.7652).

Because we selected popular tweets, this retweeting rate does not generalize to the entire tweet space.

We also compute the fraction of unidirectional links among all 110,583,366 relationships observed in our

database (not only those between authors and their followers); the percentage is 75.2%, which is surprisingly

close to wr. In other words, this ﬁnding says that, on average, one out of four edges in the Twitter world

is bidirectional. Kwak et al. crawled the entire Twitter network in July 2009 and computed this rate to

-0.05

0.05

0.1

0.15

0.2

0.25

0.3

0.35

42 50 13 58 53 60 19 33 59 2 10 30 49 47 4 25 43 7 63 24 38 3 41 12 44 36 45 22 21 23 8 16 51 54 9 55 32 57 28 65 27 6 52 11 18 39 48 46 5 20 15 26 37 40 56 34 64 14 35 29 1 17 31 61 62

Ratio

, Retweeting Rate

retweeting rate, 95% error bar

Figure 6: Retweeting Rate Across Tweets

Some basic descriptive statistics of the number of followings (V

) and the number of

followers (W

) can be found in Table 3. The median values of both V

and W

are much

smaller than their respective mean values, so both distributions are positively skewed and

have long right tails (i.e., the majority of the users had tens or hundreds of followings and

followers, but a handful of them might have had up to hundreds of thousands of followings

or even millions of followers). Similar statistics can be found in Kwak et al. (2010) and Wu

et al. (2011), but the median numbers are much bigger in our study than in their articles

because we exclude observations with zero followings/followers. The Pearson’s correlation of

V and W is 0.4436, as shown in Table 4, and both V and W are negatively correlated with

is the number of times someone among ti’s followings (re)tweeted t (including author

t’s original tweet). m

also has a heavily positively-skewed distribution: More than half of

the observations received the tweet just once (i.e., none of their followings retweeted). Over

the whole sample, the mean is equal to 3.28, and the standard deviation is equal to 7.53.

We observe that m

is positively correlated with V

, the number of followings a user has,

because m

is by deﬁnition the size of a subset of followings. m

is negatively correlated with

, meaning bidirectional followers are likely to receive more retweets than unidirectional

ones.

be 77.9%; thus we see more bidirectional links one year after their research. This increment might be an

interesting metric for researchers who study network formation.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

30 59 42 1 47 17 63 41 44 7 32 51 57 62 19 4 60 48 29 15 58 31 10 26 2 38 35 5 55 16 36 33 11 43 34 37 54 25 9 23 3 24 64 56 28 20 22 61 13 6 12 18 14 65 53 50 8 45 21 49 39 52 46 40 27

Ratio

: Weak-Tie Rate

weak-ties rate, 95% error bar

Figure 7: Weak-Tie Rate Across Tweets

5 Empirical Model and Results

In this section we use our retweet dataset to perform empirical tests on our hypothesis.

Instead of using standard reduced-form econometric methods for binary response (e.g., probit

or logit), we take a more structural approach, modeling both the user behavior and special

features of social broadcasting technology. We then use MLE technique to estimate the

empirical model and present the results.

5.1 Conditional MLE

We model a two-stage, consumption-retweeting process, in which consumption is the nec-

essary ﬁrst step for retweeting. We ﬁrst describe the two stages and derive the likelihood

function that would be used in our ﬁnal conditional MLE analysis. We then show the results

and discuss our ﬁndings.

Stage One: Consumption

The ﬁrst stage models whether a follower of author t, say, ti, after receiving a tweet, actually

consumes it. Figure 8 illustrates the technological aspect of this stage. The horizontal line

stands for ti’s home timeline or Twitter feed, which is a stream of received tweets for ti to

consume (read), including retweets, listed in chronological order. Note that not only the

original tweet t but also ti’s followings’ retweets of it, if any, appear in ti’s timeline. The

rt 0

rt 1

rt 2

rt 3

rt 4

Figure 8: (Re)Tweets Entering a Twitter User’s Timeline

downward pointing arrows show the times at which a total of ﬁve (re)tweets of t enter the

feed. Between these ﬁve (re)tweets, other tweets are also posted by ti’s followings.

In reality, few Twitter users can or will monitor their Twitter feed continuously. We

assume every time they start reading their feeds, they consume only a limited number of

tweets. In the example shown in Figure 8, the upward pointing arrows indicate the times,

and τ

, when user ti launches her Twitter application. Because the tweets are listed in

chronological order, tweets posted at times close to the τ s are more likely to be consumed.

For simplicity, we use a thick horizontal segment to indicate a “period of attention” of length

L, inside which tweets posted are consumed. In doing so, we implicitly assume that users do

not discriminate between tweets authored by diﬀerent people. The only factor determining

whether a tweet catches the user’s attention is whether it enters the timeline during a certain

period preceding the time a user checks tweets.

Therefore, the cognitive limit restricts a user ti from reading every single tweet she

receives. In Figure 8, tweets that enter into the timeline in the interval (τ

, τ

− L) are

outside any of the periods of attention and would not be consumed by ti. When a tweet t

gets retweeted by ti’s followings, it enters the timeline multiple times, thus increasing the

likelihood that t falls into one of the periods of attention (e.g., rt3 in the ﬁgure). If neither

the original tweet t nor the retweets fall into some period of attention, then it is not consumed

and hence would not be retweeted by ti.

Unfortunately, whether tweet t is actually consumed by ti is unobserved. Our task

for this stage is to build a probabilistic model to capture the likelihood that ti consumes

t, conditional on observed variables. Based on previous discussions about the technology,

whether ti consumes tweet t is determined by three factors: (1) m

, the number of times

This “random-reading” modeling assumption is only a rough approximation of the real consumption

stage. In reality, great variation exists in how people use Twitter and read their Twitter feed. However,

because most people receive a large amount of tweets, of which they are “able” to consume only a portion, we

believe that without detailed data on individual Twitter usage, “random-reading” is an appropriate modeling

approximation for us to use.

t appears in ti’s timeline; (2) the frequency with which ti checks her Twitter feed; and (3)

L, which is determined by the number of tweets ti can read in each consumption and the

number of tweets ti receives per unit of time, which we assume to be a linear function of

(i.e., the more people a user follows, on average, the more tweets she receives over a

ﬁxed time span). Therefore, we propose the condition for ti to consume t be the following

equation:

> a

, (1)

where b is a positive constant and 1/(bV

) measures L.

The unobserved variable a

can

be interpreted as an inverse measure of the frequency with which ti checks her Twitter feed,

and is assumed to be independent of both V

and m

. The left side of equation (1) can

be seen as the scaled frequency with which t appears in the timeline, and the right side as

a user-speciﬁc threshold. If a user does not check her feed very often, so that she gets a

high draw of a

, then the scaled frequency needs to be high for the tweet to be consumed,

and vice versa. To derive the likelihood function, we further assume that a

is log-normally

distributed in the population:

log a

|t ∼ log a

∼ N (a, σ

). (2)

So we can rewrite equation (1) as

−log b + log m

− log V

> log a

−

a + log b

log m

−

log V

log a

− a

where the term on the right side is a standard normal distribution. Thus, the ex ante

probability that ti consumes tweet t, conditional on receipt, is

= p(−

a + log b

log m

−

log V

log a

− a

)

= Φ(−

a + log b

log m

−

log V

(3)

where Φ is the cumulative distribution function (CDF) of the standard normal distribution.

The outcome of this stage is unobserved, so we cannot estimate the parameters in which we

are interested just on the basis of equation (3).

Or more generally, we can assume L =

, where z

is the number of tweets ti can read in each

consumption and bV

, b > 0, is the number of tweets received by ti per unit of time. We can still get (1) by

dividing both sides by z

and absorbing the unobserved z

into a

Stage Two: Retweeting

Recall that a follower ti retweets only if ti consumes the tweet himself. If a user’s ﬁrst stage

outcome is a failure (he does not consume t), then his ﬁnal outcome would automatically

be not retweeting, y

= 0. In other words, y

= 1 implies success at both stages. Unlike

the ﬁrst stage, where success is determined by the broadcasting technology and chance, the

second stage outcome depends on the decision made by the user.

At the second stage, the users who have consumed the tweets each decide whether

to retweet. The decision is made on the basis of a subjective cost-beneﬁt analysis. As

discussed in Section 3, the latent beneﬁt of retweeting depends on both the number of

followers the content is retweeted to, W

, and the mean valuation the followers attach to

the tweet, which we denote α

. Thus, we write the latent beneﬁt α

. We expect ti’s

followers’ mean valuation, α

, to be moderated by the strength of the social tie connecting

author t and potential retweeter ti. Finally, for the retweeting act to happen, the latent

beneﬁt should exceed the user-speciﬁc reservation utility or cost, denoted c

. Therefore,

after using logarithmic transformation, the necessary and suﬃcient condition of retweeting

upon consumption can be written (with a slight abuse of the notation α and c):

+ δw

+ β log W

> c

, (4)

where c

, like a

, is unobserved, and α, sub-indexed by t, is allowed to diﬀer across the

tweets, capturing tweet-speciﬁc eﬀect.

Technically, we further assume c

is distributed normally among the population. We

also allow the unobservables at the two stages to be correlated:

|t ∼ c

∼ N (c, σ

), Cor(c

, a

) = ρ. (5)

We can rewrite equation (4) as

−

log W

− c

where the right side is a standard normal distribution. Therefore, the conditional probability

of retweeting can be written as follows:

= p( −

log W

− c

−

a + log b

log m

−

log V

log a

− a

(6)

also includes the author-speciﬁc eﬀect, since in our sample the tweets are all by diﬀerent authors.

Two-Stage Model For MLE

At this point, we put the two stages together. Equations (2), (3), (5), and (6) represent

all the necessary elements for conducting the MLE analysis. The likelihood of observing

outcome y

= 1 for tweet t and follower ti is the product of p

and p

, and the likelihood of

observing y

= 0 is 1−p(y

= 1). In terms of econometrics, not all the structural parameters

are identiﬁed. For example, we can identify δ/σ

, but not δ and σ

separately. Fortunately,

for our research purpose, we care most about the signs of the parameters rather than their

absolute value. In the example, δ/σ

has the same sign as δ ; thus, identifying the ratio is

good enough for understanding w’s partial eﬀect. Therefore, for simplicity of notation, we

rearrange the terms, rescale the parameters following the standard practices in probit and

logit models, and obtain our benchmark speciﬁcation:

p(y

= 1) = p

= p(e + b

log m

+ b

log V

> a

)

= p(α

+ δw

+ β log W

> c

|e + b

log m

+ b

log V

> a

)

, c

∼ N (0, 1)

Cor(a

, c

) = ρ

θ = {e, b

, b

, α

, . . . , α

, δ, β, ρ},

(7)

where θ is a vector of parameters to estimate. α

— with t ranging from 1 to T — absorbs

the constant term and captures the tweet-speciﬁc eﬀects. δ is the coeﬃcient of the weak-tie

indicator, which is of our primary interest. b

, b

, and β determine the partial eﬀects of the

other social network characteristic variables.

Results

With equation (7) in hand, we estimate the parameters using the conditional MLE method.

We report the results in Table 5.

We estimate a total of six diﬀerent speciﬁcations, the ﬁrst

ﬁve of which are described in detail in the following paragraphs. The last one is discussed in

the next subsection. In all speciﬁcations, we use dummy variables to capture tweet-speciﬁc

eﬀects,

s, and we do not report these ﬁxed eﬀects because they are less important in our

*, **, and *** indicate 0.1%, 1% and 5% signiﬁcance levels, respectively.

Technically, we can directly use dummy variables to control for ﬁxed eﬀects without appealing to more

sophisticated econometric speciﬁcations because we have a large number of observations for every tweet. See

Figure 5.

analysis.

All standard errors are computed to be robust to tweet clustering.

Model 1 is a simple probit of y

on the four key variables: w

, m

, V

, and W

. Model

2 corresponds to equation (7), with an additional restriction that a

⊥ c

, which implies

ρ = 0. Model 3 strictly follows the benchmark equation (7), allowing correlation between a

and c

. Models 4 and 5 slightly modify model 3: Model 4 includes the interaction term of

and W

in the retweeting equation; model 5 includes w

in the consumption equation.

We observe that the ﬁtted likelihood increases from model 1, 2 to 3, {4, 5}, as we grad-

ually relax the model restriction by adding richer structures and more variables. Across the

ﬁve columns, we ﬁnd consistent support for a positive m

coeﬃcient (repetition of retweets)

and a negative V

coeﬃcient (the number of followings). All estimates are signiﬁcant with

99.9% conﬁdence level. Therefore, the results are consistent with the model prediction de-

scribed in Section 5.1, and in particular with equation (3).

The unidirectional-relationship/weak-tie indicator is found to have a signiﬁcantly posi-

tive eﬀect on the (conditional) retweeting probability. In the benchmark model (model 3),

its coeﬃcient is positive at the 0.1% signiﬁcance level. The w

coeﬃcient becomes less sig-

niﬁcant, but is still positive at the 5% signiﬁcance level, when we allow an interaction eﬀect

of tie-strength and the number of followers (model 4) or when we put the weak-tie indicator

into both the consumption and retweeting equations (model 5). These results show that,

in the retweeting equation, the positive sign of the weak-tie coeﬃcient is robust; thus, they

support our hypothesis: Weak ties are more likely than strong ties to relay information to

their social network neighbors.

In model 4, where we include the weak-tie dummy w

in both the consumption and

retweeting equations, we ﬁnd that, although its eﬀect on retweeting probability is positive

and signiﬁcant, its eﬀect on consumption probability is negative but insigniﬁcant. This result

shows that messages generated from stronger ties might be more likely to be read than those

from weaker ties. However, the diﬀerence in likelihood is not statistically signiﬁcant. It

supports our assumption that users generally do not discriminate between tweets received

from strong ties and tweets received from weak ties. We believe the separation of the diﬀerent

eﬀects that weak ties have on the two probabilities, as model 4 reveals, shows the merit of our

two-stage econometric model. It indeed uncovers more structure in the retweeting process

than a reduced-form probit regression.

In all models, the number of followers has a signiﬁcantly positive coeﬃcient. This rev-

We do not control for follower ﬁxed eﬀects because, for each tweet, all followers/observations are by

deﬁnition distinct, and when we pool tweets together, among all the 24,403 observations, 24,002 are unique.

elation by our econometric models is a new one because, as shown in Table 4, the simple

correlation between y

and W

is negative. This result thus supports our argument in the

theory section that the number of subscribers is positively associated with the latent beneﬁt

of retweeting.

5.2 Theoretical Model Revisited

From model 1 to model 5, we consistently ﬁnd that, conditional on the consumption of a

piece of information, weak-tie users are more likely to share information with their social

network neighbors. In the theory section, we argued the reason is that a weak-tie follower’s

followers would on average value the information more than a strong-tie follower’s followers;

thus, the latent beneﬁt from the social exchange of content sharing is greater for a weak-tie

follower than for a strong-tie follower, everything else being equal.

In a social broadcasting environment, two possible explanations remain for the higher

mean valuation of the shared content from a weak-tie follower’s followers:

1. New audience eﬀect: Because of the social broadcasting technology (in which whatever

is posted or shared is broadcast to all followers), the possibility exists that the infor-

mation has already been circulated to more of a strong-tie follower’s followers than

to a weak-tie follower’s followers.

Holding the total number of a potential sharer’s

followers constant, the expected number of followers who are new to the information

is larger for a weak-tie follower. Therefore, a weak-tie follower can reach a larger new

audience, and hence the sharing gives a greater social exchange beneﬁt.

2. Informational value eﬀect: The information to be shared is intrinsically more valuable

to a weak-tie follower’s followers than to a stronger-tie follower’s followers. Therefore,

a weak-tie follower is more willing to share it because the sharing is expected to yield

higher social exchange beneﬁt.

3. A third possibility is that both of these two eﬀects exist.

We test the three possibilities in model 6 by adding two empirically constructed followers-

overlap measures into the second-stage retweeting equation. Mathematically, we deﬁne two

One important observation is that a strong-tie follower’s followers are more likely to be simultaneously

following the author than a weak-tie follower’s followers. Readers can refer to Appendix I for an empirical

test.

versions of an overlap index of followers:

W 1

√

W 2

min{W

, W

}

where

, W

, and W

are the number of mutual followers author t and user ti shared, the

number of followers author t had, and the number of followers ti had, respectively. OI

W 1

and OI

W 2

basically measure how “similar” user ti’s followers and author t’s followers are:

The larger the index is, the more similar the two sets of followers are. The indexes are

also used in Appendix I, where we test whether unidirectional relationships are weaker than

bidirectional ones. Readers can refer to Appendix I to see more discussion on the indexes.

We include OI

W 1

and OI

W 2

to capture the new audience eﬀect, the ﬁrst explanation. If

it is indeed a driver of the result, we expect OI

W 1

and OI

W 2

collectively to have a negative

eﬀect on retweeting probability: If a user has a large number of followers who also follow

the author, then he or she should be less willing to share the information. Moreover, if the

new audience eﬀect is the sole driver, then the weak-tie indicator w

should have no eﬀect

on retweeting probability once we include the two indexes.

If we ﬁnd the two indexes have

negative coeﬃcients and the weak-tie indicator still has a positive coeﬃcient, then we should

conclude that both the informational value eﬀect and the new audience eﬀect exist.

The result of model 6 shows that the coeﬃcients of the two indexes are indeed negative.

Although the second version of the overlap index, OI

W 2

, separately is insigniﬁcant, collec-

tively they are signiﬁcant with 99.9% conﬁdence level. The magnitude of the coeﬃcient of

decreases from model 3, but, it is still positive at 0.1% signiﬁcance level. These two

ﬁndings together support the third possibility: Both the informational value eﬀect and the

new audience eﬀect exist.

Assume the two indexes have perfectly captured the new audience eﬀect.

Probability of Retweeting Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Coeﬀ. Coeﬀ. Coeﬀ. Coeﬀ. Coeﬀ. Coeﬀ.

(z-value) (z-value) (z-value) (z-value) (z-value) (z-value)

: Probability of Consumption upon Receipt

log m

# of Repetitions 0.174*** 0.494*** 0.340*** 0.340*** 0.338*** 0.434***

(8.21) (4.81) (4.37) (4.37) (4.47) (5.86)

log V

# of Followings -0.170*** -0.639*** -0.472*** -0.473*** -0.475*** -0.566***

(-9.19) (-10.38) (-5.14) (-5.05) (-5.02) (-7.23)

Weak tie -0.076

(-0.46)

: Probability of Retweeting upon Consumption

Weak tie 0.218*** 0.284*** 0.220*** 0.237* 0.249** 0.175***

(5.13) (5.57) (5.52) (2.14) (3.22) (4.11)

log W

# of Followers 0.087*** 0.115*** 0.101*** 0.103*** 0.102*** 0.131***

(5.41) (6.32) (7.46) (4.95) (7.21) (6.83)

log W

Weak tie × -0.003

# of Followers (-0.17)

W 1

Overlap Index -2.131*

of Followers I (-2.44)

W 2

Overlap Index -0.429

of Followers II (-1.33)

ρ Correlation - -0.836*** -0.835*** -0.834*** -0.606*

(p-value) (0.000) (0.000) (0.000) (0.034)

# of Observations 24,403 24,403 24,403 24,403 24,403 24,403

Pseudo Log-Likelihood -3,953.823 -3,921.876 -3,913.125 -3,913.112 -3,913.010 -3,892.148

Table 5: Result of Maximum Likelihood Estimation

6 Managerial Implications

Impression vs. Consumption

Internet display advertisement is often priced based on cost per impression or cost per

action (e.g., cost per purchase, cost per click). However, it is important to realize that an

ad being displayed is not equivalent to an ad being consumed. In other words, between

the stage of impression and action is a stage of consumption, which does not necessarily

occur after an impression because Internet users are often overloaded with information. The

popularization of social broadcasting technologies, or social media as a whole, has greatly

facilitated decentralized information production, which further leads to an explosion of user-

generated content.

Then the question arises: Of the content being produced, how much

is actually being consumed? One answer to this practical, important question suggests the

possibility of another way of pricing for display advertisement: cost per ad consumption.

This approach has largely been ignored in the literature because ascertaining whether an

Internet user actually reads or watches an ad is diﬃcult. Indeed, neither the content creator

nor any third-party can observe whether an individual has consumed a piece of content

supplied to him or her.

What our empirical model contributes is that the estimation of the ﬁrst stage equation

= Φ(e + b

log m + b

log V ),

provides a simple but useful way to approximate the probability of consuming a piece of

content for an average Twitter user with certain social network characteristics. Essentially,

our model solves this problem in the Twitter context by exploiting the fact that observed

interaction with content can be used to infer unobserved consumption. Given that the

number of impressions is usually known or can be easily obtained, one then can calculate

the expected number of consumptions for a piece of published content.

Inﬂuence

Measuring a user’s social inﬂuence in an online community is of great interest to managers

who want to leverage the power of social media. On Twitter, a user is often regarded as

being inﬂuential when many people retweet her tweets. Indeed, the depth of penetration

Taking Twitter as an example, as of May 2011, the average volume of tweets posted per day had reached

150 million (i.e., more than 1,700 tweets per second.)

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 1000 2000 3000 4000 5000

Prob

: Number of Followers

: Probability of Retweeting upon Consumption, w=0 vs w=1, Median Quality Tweet in Sample

(5, p=0.027)

(5, p=0.045)

(190, p=0.060)

(190, p=0.091)

(4970, p=0.111)

(4970, p=0.158)

w = 1

w = 0

Figure 9: The Probability of Retweeting a Tweet upon Consumption

and breadth of reach of one’s words in an online community are important aspects of social

inﬂuence. Our model measures the role that social network characteristics play in the infor-

mation diﬀusion process. Combined with the probability of consumption, we can compute

the expected total number of consumers of a user’s tweet based on his or her social network

characteristics, which may serve as a starting point for measuring his or her social inﬂuence.

One important implication of our study is that having more followers does not directly

translate into greater social inﬂuence. In particular, the strength of social ties between a user

and her followers should have an important moderating role, because it can greatly aﬀect the

followers’ willingness to forward her messages. To see this more intuitively, we plot the ﬁtted

retweeting probabilities in Figure 9 for w = 0 (solid curve) and w = 1 (dashed curve), ﬁxing

at the median value in our sample. The diﬀerence between the conditional probabilities

of retweeting for a unidirectional follower and for a bidirectional follower is signiﬁcant. For

example, when W , the number of followers, equals 190, the median number in our sample,

the conditional likelihoods of retweeting are 6.0% for a bidirectional follower and 9.1% for a

unidirectional follower. The latter is more than 50% higher in percentage.

7 Conclusion

An important question in the ﬁeld of information systems is how information or knowledge is

disseminated in an online community (with or without an organizational form). Large-scale

empirical studies to address this question have traditionally been challenging because of the

diﬃculty of obtaining detailed micro-level data. To the best of our knowledge, this paper

is the ﬁrst such study in the information systems ﬁeld, where publicly available data from

Twitter is used to explore people’s voluntary information relay process.

Using a carefully designed data collection process and a series of econometric analyses,

we ﬁnd that information is more likely to be retweeted through weak ties on Twitter. This

result is complementary to Granovetter’s ﬁnding, which advocates for the important role of

weak ties in carrying novel information (Granovetter 1973). The implications of our ﬁnding

are far-reaching. On the one hand, our theory, which is based on two highly inﬂuential

sociological theories – the social exchange theory and the strength of weak tie theory –

and is supported by the latest data from one of today’s largest online social networks,

reveals the important role that weak ties play in facilitating information dissemination in

the social network through people’s voluntarily information relay behavior. On the other

hand, the interesting connection between tie strength and retweeting behavior indicates the

importance of incorporating tie strength when measuring personal inﬂuence on Twitter,

which is a question of fundamental importance to both researchers and practitioners.

As one of the ﬁrst in the information systems ﬁeld to bring together the huge amount

of public data on Twitter with sociological theories to study information diﬀusion in so-

cial broadcasting networks, the paper is not without its limitations. First, the tweets in

our dataset were not randomly sampled. By using this dataset to study the eﬀect of tie

strength in information sharing, we implicitly assumed that tweet “quality” changes every-

one’s retweeting probability only uniformly. Relaxing this assumption requires additional

work (including obtaining a new dataset) to test whether our results hold when the quality

of tweets is moderate or low. Second, we measured tie strength using a binary variable

based on whether a link is unidirectional or bidirectional. Measuring tie strength based on

the amount of conversation between two Twitter users would be an alternative approach.

Third, we used only an author’s immediate followers and omitted higher-order potential

followers in empirical analyses. As we discussed in the data section, this was due to the

diﬃculty of collecting network graph data for all higher-order potential retweeters. In fu-

ture research one could try to overcome the diﬃculty by, possibly, sampling these users.

Fourth, we observed only one snapshot of the social network and thus modeled it as ﬁxed

and exogenous. Future research can examine the interplay of user behavior and the dynamics

of underlying network structure. Another possibility for extending the current study is to

include more user-speciﬁc variables (e.g., demographic information) and tweet-speciﬁc vari-

ables (e.g., constructed from natural language processing) into the econometric model. Of

course, these extensions pose new challenges in terms of data collection and data processing.

Nevertheless, they are certainly interesting directions to pursue in the future.

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Appendix I

In this appendix, we discuss our operationalization of weak ties used in our empirical anal-

yses. We deﬁne tie strength based on the following-follower relationships observed in the

Twitter network, and speciﬁcally, we claim that unidirectional relationships are on average

weaker than bidirectional ones. We want to stress a few points regarding this assumption.

First, we are not claiming that a bidirectional relationship in the Twitter world is a strong

tie in the absolute sense. Twitter users, even if they are mutually connected online, often

barely know each other in the real world, so to a certain extent, the claim that almost all

ties on Twitter are weak is a fair one to make. The hypothesis only emphasizes the ordinal

strength of the two tie types, and the comparison is carried out in the sense of probabilistic

expectation. The reason why reciprocity makes a diﬀerence is that frequent learning or reg-

ular interaction is more likely to happen when a reciprocal relationship exists. By reading

each other’s posts, a pair of users can more easily develop mutual understanding about each

other’s topics of interest and expertise, and sometimes even about detailed aspects of each

one’s personal life. Over time, even though the pair are unknown to each other in the real

world, they could probably become very familiar with each other’s activities and habits in

the online community. Of course, reciprocal following does not guarantee such relationship

development (which is why we emphasize the probabilistic nature of the hypothesis). How-

ever, without it, the relationship development is unlikely. Moreover, our operationalization

is consistent with the previous sociological literature. Granovetter (1973) pointed out the

importance of reciprocity by deﬁning that “the strength of a tie is a (probably linear) com-

bination of the amount of time, the emotional intensity, the intimacy (mutual conﬁding),

and the reciprocal services which characterize the tie.” In Friedkin (1982), asymmetrical con-

tact between college professors was classiﬁed as a weak tie, and a reciprocal connection was

classiﬁed as a strong tie. Marlow et al. (2009) also applied similar deﬁnitions in analyzing

friendships on Facebook.

We perform an empirical test on the hypothesis, using the network graph data we col-

lected. Note that we know not only the number of followings (followers) a user has, but also

whom the followings (followers) are (i.e., we observe the IDs of the user’s immediate social

neighbors in our database). This information should give us more knowledge about, and in

the meantime the ability to build important metrics of, a user’s network characteristics. In

particular, knowing the IDs of two users’ social neighbors, we can compare how “similar”

their social neighborhoods are. In deriving his theory, Granovetter in his 1973 paper claimed

that the stronger the social tie between two persons, the larger the overlap of their friend-

ship circles. Applying this statement in the Twittersphere, under our assumption, we would

V 1

V 2

W 1

W 2

-0.042*** -0.069*** -0.034*** -0.064***

F (2322.21) (1476.43) (3837.34) (2158.65)

p-value 0.00 0.00 0.00 0.00

Table 6: Results of ANOVA Tests

expect that two users who mutually follow each other, on average, have a larger overlap in

their followings (followers) than two who don’t. Our test is based on this prediction. Opera-

tionally, we do so by empirically verifying whether w

= 0 positively correlates with a higher

“similarity” between user ti and author t’s followings (followers). We measure “similarity”

by computing two overlap indexes of followings (followers) of author t and user ti:

V 1

√

V 2

min{V

, V

}

, (8)

where

, V

, and V

are the number of mutual followings author t and user ti shared, the

number of followings author t had, and the number of followings i had, respectively (Onnela

et al. 2007 deﬁned a similar “neighborhood overlap”). Similarly, we can deﬁne and compute

overlap indexes of followers (OI

W 1

, OI

W 2

) by changing V to W in equation (8). Note that

the two numerators in equation (8) are the same:

. The diﬀerence between OI

V 1

and

V 2

is in the denominators, or in the way by which we scale down

based on the number

of followings ti has. Both indexes are in the range [0, 1] because

≤ min{V

, V

}. The

larger the indexes are, we say the more “similar” the two sets of followings are. When t and

ti have no mutual followings shared, both indexes equal 0. When t and ti have exactly the

same sets of followings, OI

V 1

= 1. When ti’s followings represent a subset/superset of t’s

followings, OI

V 2

= 1.

We investigate wether diﬀerent w

values lead to signiﬁcantly diﬀerent overlap indexes

by running a series of ANOVA tests, the results of which are given in Table 6. In all four

tests, we control tweet-speciﬁc eﬀects. As the regression coeﬃcients in the ﬁrst row show, we

ﬁnd that a unidirectional relationship (w

= 1) is indeed associated with a smaller overlap

in social neighborhoods. The F statistics and p-values indicate this diﬀerence is signiﬁcant

at 0.1% level, no matter which index we use. Therefore, bidirectional relationships are

associated with higher transitivity in social neighborhoods. The results thus support our

hypothesis that unidirectional relationships are, on average, weaker than bidirectional ones.

Appendix II

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Figure 10: The Spread of a Single Tweet (idx=1) in Our Sample