Displaying things in common to encourage friendship formation: A large randomized field experiment

Abstract

Friendship formation is of central importance to online social network sites and to society, but can suffer from significant and unequal frictions. In this study, we demonstrate that social networks and policy makers may use an IT-facilitated intervention – displaying things in common (TIC) between users (mutual hometown, interest, education, work, city) – to encourage friendship formation, especially among people who are different from each other. Displaying TIC may update an individual’s belief about the shared similarity with another and reduce information friction that may be hard to overcome in offline communication. In collaboration with an online social network, we design and implement a randomized field experiment, which randomly varies the prominence of different types of things in common information when a user (viewer) is browsing a non-friend’s profile. The dyad-level exogenous variation, orthogonal to any (un)observed structural factors in viewer-profile’s network, allows us to cleanly isolate the role of individuals’ preference for TIC in driving network formation and homophily. We find that displaying TIC to viewers may significantly increase their probability of sending a friend request and forming a friendship, and is especially effective for pairs of people who have little in common. Such findings suggest that information intervention is a very effective and zero-cost approach to encourage the formation of weak ties, and also provide the first experimental evidence on the crucial role of individuals’ preference (versus structural embeddedness) in network formation. We further demonstrate that displaying TIC could improve friendship formation for a wide range of viewers with different demographics and friendship status, and is more effective when the TIC information is more surprising to the viewer. Our study offers actionable insights to social networks and policy makers on the design of information intervention to encourage friendship formation and improve the diversity of the friendship, at both an aggregate and an individual level.

Appendices

Appendix A: Tables and Figures

Table 1 Summary Statistics Overall the experiment includes about 50 million viewer-profile pairs

Fig. 9

Distribution. We group all pairs by the number of actual things in common shared between the viewer-profile and draw its distribution. Most viewer-profile pairs have one thing in common

Fig. 10

Distribution. We group all pairs by the number of actual things in common shared between the pairs and draw separate distribution for pairs with and without mutual friend

Fig. 11

Distribution of things in common when the viewer-profile pair share two things in common. Among the large number of combinations between the five types of TIC (mutual city, like, hometown, education, work), we only show distributions for the nine most commonly seen combinations. The remaining combinations consist of a very small portion of our sample

Fig. 12

Distribution of profiles per viewer (left) and Distribution of viewers per profile (right)

Fig. 13

Effects of displaying things in common. Same as Fig. 6 with an additional panel for pairs with 3 TIC

Fig. 14

Effects of displaying things in common, for pairs with and without mutual friends. Same as Fig. 7 with an additional panel for pairs with 3 TIC

Table 2 Effect of Displaying TICs on Friend Requests and Formation RR stands for relative risk and is calculated using the relative ratio in means compared to the baseline group (i.e. viewer-profile pairs with the same number of actual TICs but zero TICs at display)

Table 3 Effect of Displaying TICs on Friend Requests and Formation (Decomposed by Whether View-Profile Pairs Share Mutual Friends) RR stands for relative ratio and is calculated using the relative lift in means compared to the baseline group (i.e. viewer-profile pairs with the same number of actual TICs but zero TICs at display)

Fig. 15

Acceptance Rate Conditional on Request

Fig. 16

Effect of Displaying Thing in common on Friend Request, for male viewers and female viewers

Fig. 17

Effect of Displaying Thing in common on Friend Request, for gender combinations of viewers and profiles

Fig. 18

Effect of Displaying Thing in common on Friend Request, for viewers with different number of friends

Fig. 19

Incremental Effect of displaying both things in Common, as compared to displaying one. Following information theory, we measured the incremental information (‘surprisal’) of displaying two TIC (mutual hometown and current city), as compared displaying one, using normalized pointwise mutual information (PMI). We calculate normalized PMI using its formal definition (Church and Hanks 1990): the surprisal ($-\log _{2}(\Pr (X_{ia} = X_{ja}))$) of displaying mutual hometown plus the surprisal of displaying current city minus the joint surprisal of displaying both mutual current city and hometown, normalized by joint surprisal. The PMI measure, ranging from + 1 to -1, captures the co-occurrence likelihood and is symmetric with respect to the two TICs. An PMI with + 1 indicates 100% likelihood of co-occurrence, thus displaying both mutual hometown and current city would reveal little additional information or ‘surprisal’. In contrast, a low PMI indicates a small likelihood of co-occurrence thus displaying both TIC would would be more surprising to the viewer given that they already know one of the TIC). The empirical finding is aligned with such mechanism and further confirms the belief update process underlying the effectiveness of displaying TIC. To generate smooth curves, we fit LOESS regressions separately for the display 2 TIC and display 1 TIC conditions for each of 500 bootstrap replicates clustered on viewer. The dashed lines are the 95% bootstrap confidence intervals for the smoothed estimates of the ratio

Fig. 20

Comparison of Post-friendship Interaction score between friendship ties in control versus treatment group. We categorize all the friendship ties formed in our experiment into two groups based on whether certain TIC is shown during friendship formation process, and then calculate the difference between the groups in the volume of their post-friendship interactions (like, comment, messaging). We do not find any significant difference in the post-friendship interactions between the control and treatment group

Fig. 21

Effects of showing zero, one, or both things in common when the viewer-profile pair share two things in common. Among the large number of combinations between the five types of TIC (mutual city, like, hometown, education, work), we only show the effect of TIC display for the nine most commonly seen combinations. The remaining combinations consist of a very small portion of our sample

Appendix B: Effect of displaying different types of things in common

The availability of multiple types of things in common in our experiment also enables us, for the first time, to investigate the relative importance of a range of TIC documented in the literature (McPherson et al. 2001) in the same context. Previous studies on homophily have separately documented different things in common in social networks (Ibarra 1992; Currarini et al. 2010), but never compared the causal effect of them within the same context.

We find a variation in the effect of showing different types of things in common (Fig. 22). We focus on presenting the results for viewer-profile pairs with only one thing in common, as they represent the majority of the sample (Fig. 6). There are three categories of things in common: past experience (mutual hometown, mutual education, mutual work), current context (mutual city), common interests (overlap of page like). As shown in Fig. 22, certain type of things in common, such as mutual likes, city and hometown, may lead to a larger increase in friendship formation than other types of things in common (mutual education). Previous studies on homophily has separately documented different type of things in common across different situations (Ibarra 1992; Currarini et al. 2010; Thelwall 2009), but never compared the relative importance of them within the same context. Similar to previous studies on social influence (Aral and Walker 2014), we find that social factors such as current context (e.g. mutual city) and past experience (mutual hometown) are associated with a large impact on friendship formation. However, we also find that showing overlap of interest may also be effective: a finding that has not been established before. In this way, we contribute to the literature on the role of different type of things in common (or similarity) in facilitating interpersonal interaction (Berscheid and Reis 1998).

Fig. 22

Distribution and effects of showing specific type of things in common when the viewer-profile pair share one thing in common. Using zero things in common as a baseline, showing shared likes and hometown significantly increases the relative risk of friendship formation, while we cannot reject the null hypothesis that showing a shared city or education causes any change. 95% confidence intervals are computed from standard errors estimated using a bootstrap clustered on viewer with 500 bootstrap replicates

Fig. 23

Effect of Specific Type of Thing in common, for pairs with and without mutual friends. We group all pairs with one thing in common by the specific things in common as well as the existence of mutual friends. Using pairs with zero things in common shown as a baseline within each group, we find showing certain thing in common increases the relative risk of friendship formation, but only for people with no mutual friends and for shared likes, hometown and city

Appendix C: Methodological: correlation from observational data is opposite to the causal effect of TIC

Finally, we want to demonstrate the importance and necessity of using a randomized experiment approach to identify causal effect of showing TIC. We explicitly compare the estimates from our experiment with those from a direct correlation analysis using observational data to highlight the advantage of our method. In Fig. 24, we can see that interestingly the correlation between number of things in common and friendship formation is in the opposite direction from the identified causal effect of showing things in common: for viewer-profile pairs with mutual friends, the observed correlation suggests a very positive and significant effect of showing more things in common, i.e. pairs with more TIC is more likely to form friendship, whereas the true causal effect of TIC based on experiment results is zero; for viewer-profile pairs with no mutual friends, the observed correlation suggests a zero or even slightly negative relationship between more TIC and friendship formation, whereas the true causal effect of showing TIC is large and significant. This contrast further highlights the importance of using a randomized experiment for causal inference. As shown above, using the observed correlation in the secondary data may significantly bias the effect of displayed things in common. We can cleanly identify the causal effect from correlation only by using a proper randomization.

Fig. 24

Correlation vs Causal Effect of TIC on friendship formation. Correlation between number of things in common in a pair and the friendship formation rate (Left) is biased and opposite to the true causal effect of showing things in commons (middle and right)

Appendix D: Theoretical Contribution: Identifying the Role of Individual Preference in Things in Common (versus Structural Factor) in Network Formation

Besides practical importance, our findings from a carefully designed large-scale randomized experiment may contribute to social network literature and improve our theoretical understanding of the origin of network formation and homophily, in a few ways.

First, while strategic network formation have been studied in detail using analytical models (Bala and Goyal 2000; Jackson 2008) and simulations (Phan and Godes 2018), empirical work designed to test theories and examine the drivers of network formation is still in their infancy. Most of the empirical works on network formation (Currarini et al. 2010; Mele 2017) impose strong functional assumptions and use network structure for identification²¹. To the best of our knowledge, our study is the first randomized field experiment to directly engineer the drivers of network formation (i.e. viewer’s information about the alter as in our case). Our experiment design and framework provides a new way to examine various factors underlying network formation and the relative importance between them, in real networks and at a very large scale.

Second, as documented by a broad history of literature on homophily in social network (McPherson et al. 2001), an individual is more likely to form a friendship tie with someone that is similar to her/him in demographic and behavioral attributes (Centola 2015; Ameri et al. 2017; Goel and Goldstein 2013). However, the origin of homophily is far from clear (Kossinets and Watts 2009; Currarini et al. 2010). Recent literature hypothesizes that the homophily pattern in social network might be partially driven by individuals’ preference over similar others (termed as preference or choice homophily Currarini et al.2009), as opposed to the structural factors. However, as far as we know, no study has provided clear empirical evidence on whether and when preference for TIC would drive network formation. As the literature repeatedly acknowledge (Currarini et al. 2010; Phan and Airoldi 2015), such lack of insights is because preference factor and structural factor in network formation process are inherently confounded in observational data and extremely hard to disentangle: pairs with similar attributes are always more likely to have mutual friends. We address the challenge by designing a experiment to exogenously vary the prominence of things in common displayed during friendship formation in a real social network. The randomization is independent of structural factor therefore allows us, for the first time, to demonstrate the importance of preference in driving friendship formation. Third, we examine the relationship between preference and structural factor in network formation and find that preference over TIC matters in the absence of structural factor (mutual friend) thus can be leveraged to encourage formation of weak ties.

Finally and importantly, the variation in the treatment effect within each type of TIC (e.g. sharing mutual hometowns of different size) sheds light on the underlying mechanisms: aligned with belief update process (Ely et al. 2015), displaying TIC is more effective when the information shown is less expected, and the effect size of a certain TIC is in proportion to the ‘surprise’ it creates to the viewer (measured by bits in information theory). Our study is among the first to understand network formation and homophily from a belief update perspective. SN sites can use our information-theoretic principles to optimally select specific things in common to highlight in online friendship formation process. The information-theoretic framework may also be extended to guide the personalized design of user profile for each viewer-profile interaction.