Sentiment Paradoxes in Social Networks:
Why Your Friends Are More Positive Than You?

Sentiment analysis, also known as opinion mining, analyzes individual opinions, sentiments, and attitudes towards various entities such as individuals, products, organizations, and topics (?). Relying on advancements in natural language processing and machine learning (?), existing studies in sentiment analysis have made substantial progress towards classifying and predicting sentiments of independent individuals and groups in social networks, focusing on tasks such as content sentiment prediction and review spam detection (?).

However, existing studies have less explored sentiments among interacting users as their sentiments may be dependent. With the unavoidable peer influence in social networks (?), it is essential to consider user interactions when studying their sentiments, especially in large-scale social networks. For example, Lin et al. find that the stress levels of users are closely related to that of their friends on social media (?). A common observation with respect to sentiments of interacting users is that many users feel their friends are more positive than themselves, experiencing a sentiment paradox. There have been many discussions on why this phenomenon takes place, with psychology research linking it to human cognition biases. For example, Jordan et al. (?) show that most people have a tendency to underestimate the negative feelings of others. With many users in social networks experiencing a sentiment paradox – being less positive than their friends – can we attribute all such perceptions to human cognition biases alone? In other words, do sentiment paradoxes exist not only in user cognition, but also in reality?

Overall, the specific contributions of this paper are:

1. 1.

   Five sentiment paradoxes are identified in both undirected (friend) and directed (follower and followee) social networks and at multiple network levels (triad-, community-, and network-level). Our work shows that for most users their friends are indeed more positive than them, mostly due to the fact that more positive users are more likely to have more friends, followers, and followees;

2. 2.

   We empirically and mathematically verify each paradox, where our mathematical analysis allows us to determine whether such a paradox is expected to exist;

3. 3.

   We investigate the connections between the sentiment paradox and two other well-established network paradoxes: friendship paradox and activity paradox. Our results reveal factors that can determine the (1) existence and the (2) magnitude of sentiment paradoxes; and

4. 4.

   We demonstrate the role that the sentiment paradox that can play in practical applications, i.e., in predicting s user’s sentiments by looking at the sentiments of his or her social connections.

The remainder of the work is organized as follows. Experimental setup is presented first, followed by a formal definition for the general sentiment paradox, and sentiment paradoxes in triads and communities. Then, we investigate the connections of sentiment paradox to other network paradoxes, which helps determine the existence and magnitude of sentiment paradoxes. One application of sentiment paradoxes, i.e., user sentiment prediction, is provided next. Finally, a literature review and some conclusions are provided.

To study sentiment paradoxes at different network levels, proper data that contains user sentiments and their network information (e.g., friends or communities joined) is required.

We have collected the following data spanning more than 10 years (from 1999 to 2010) (?; ?): (i) users and their posts to obtain user sentiments; (ii) friendships and followee/follower relationships among users; and (iii) community memberships for all users. We only retain users with ten or more posts to exclude occasionally active or inactive users. We plot the post distribution of these excluded users, which is provided in the Appendix and indicates that most ($\sim$97%) of these users have posted nothing. As moods are limited (132 moods), we manually convert each mood in our dataset to its sentiment polarity (details can be seen in the Appendix): positive ($+$, e.g., cheerful, excited and happy), negative ($-$, e.g., angry, annoyed and depressed) or neutral ($0$, e.g., busy). Some statistics on our data is provided in Table 1.

Note that $S(u)\in[-1,+1]$, where $-1$ shows an extremely negative user and $+1$, an extremely positive user.

In this section, we mainly focus on a “general” sentiment paradox, which can be observed among all users of a network. We first present the definition of sentiment paradox, followed by experiments to verify its existence and mathematical proofs on whether the paradox is expected to exist.

When the magnitude is greater than 0.5, we say the sentiment paradox strongly holds in the network. When the magnitude is less than or equal to 0.5, but is still greater than the proportion of users that are more positive than their connections, and that of users that are as positive as their connections, we say the paradox weakly holds in the network.

A surprise value on the order of tens is highly significant, indicating that $p$-values are nearly zero.

Following this three-step process, we obtain the results in Table 2, where “Holds” (“Does not hold”) indicates that users are less (more) positive than their connections. “Unknown” indicates that users are as positive as their connections. In both undirected and directed networks, irrespective of using mean or the median, we make the following three observations:

1. 1.

   Sentiment paradox strongly holds within the network, as the observed sentiment paradox magnitudes (user proportions) for all networks are greater than 0.5;

2. 2.

   The observed paradox magnitude values are all higher than the expected paradox magnitudes; and

3. 3.

   The surprise values are on the order of tens, which indicate that the observed paradox magnitudes are all statistically significant.

Triads (a group of three connected people) are crucial components of networks, especially when investigating ideas such as structural balance (i.e., a friend of a friend is a friend), clusterability (i.e., friends form small groups) and transitivity (i.e., $A$ is a friend of $B$, $B$ is a friend of $C$, so $A$ is a friend $C$). In this section, we study sentiments among interacting users in triads. We will investigate if a sentiment paradox exists at the triad level, and aim to provide explanations on the existence (or lack) of such a paradox.

To explore if the sentiment paradox holds within triads, assume user $u_{i}$, $i=1,2,\cdots,n$ is a member of triads $t_{j}$, $j=1,2,\cdots,m$. Within each $t_{j}$, we compare the sentiment (i.e., the SWB value) of $u_{i}$ and the mean and median of that of his two connections (friends, followees, or followers). Note at the triad level, the results based on either the mean or the median should be the same because each user has no more than two connections within a triad. If in the majority of triads that $u_{i}$ is a member of, $u_{i}$ is less positive than his connections, we consider $u_{i}$ as a user exhibiting sentiment paradox at the triad level. Then, we compute the proportion of such users in the overall network, and conduct significance analysis similar to how it was conducted in last section. Note such paradox is not expected to exist, as proved in Theorem 1. However, Table 3 provides the empirical results, which can be summarized as:

On the other hand, one can think of a triad as a pair of users sharing a common neighbor. This observation motivates us to verify whether there is a sentiment paradox between users and their connections with whom users share common neighbors. Hence, we conduct an experiment similar to the one performed to validate the sentiment paradox in last section, except that we only compare sentiments between users and a subset of their connections with whom users share a triad, i.e., have at least one common neighbor. The paradox is not expected to exist either, as proved in Theorem 1. However, the empirical results in Table 3 show that:

Similar to triads, communities also play an important role in understanding social networks (?). We take a similar approach to triad-level paradoxes and study sentiments among interacting users within communities. However, we highlight that unlike triads, communities can have different sizes (i.e., number of members) and different levels of interactions among their members (i.e., different densities). Hence, in addition to investigating whether sentiment paradox exists at the community level, we also assess whether the existence or magnitude of such paradoxes depend on the size or level of connections within communities. Similar to triads, we do not expect a sentiment paradox to exist at the community-level as proved in Theorem 1.

First, we assume user $u_{i}$, $i=1,2,\cdots,n$ is involved in communities $c_{k}$, $k=1,2,\cdots,p$. For each $c_{k}$, we compare the sentiment (i.e., the SWB value) of $u_{i}$ with the mean and median of that of his connections (friends, followees, or followers) within the community. If in a majority of communities that $u_{i}$ belongs to, $u_{i}$ is less positive than his connections in the community, we denote $u_{i}$ is exhibiting the paradox. Finally, we compute the fraction of such users in the network and perform statistical significance analysis. Table 3 has the results, which we summarize as the following paradox:

Additionally, we conduct an experiment similar to the one performed to verify the common-neighbor sentiment paradox in the last section, in which we only compare sentiments between users and a subset of their connections with whom users share a community. Statistical significance is computed in the same way as before.

The results are shown in Table 3. We observe a sentiment paradox within such users. As users in our dataset mostly form communities around a common interest (one community often refers to a certain topic), we denote this paradox as the common-interest sentiment paradox:

We observe from Figure 2 that the proportion of communities within which the paradox holds becomes larger as communities become larger or denser, ultimately reaching 0.7 (and at times, over 0.9), while the expected magnitude is always around 0.5. Even when the community size or its density is very small, the observed proportion of communities where the sentiment paradox holds is always higher than the expected proportion, and the observed proportion of communities where the sentiment paradox does not hold is always lower than the expected values.

Social networks exhibit many counter-intuitive properties. We assess the connection between sentiment paradox and two of the most commonly observed network paradoxes: (1) friendship paradox and (2) activity paradox, which provides opportunities to investigate the relationships among user sentiments, social connections and activities.

Sentiment paradoxes reveal a certain relationship between users and their social connections (friends, followees, or followers) at triad-, community- and network-level, i.e., in general, users are less positive than their social connections. In this section, we demonstrate how a user’s sentiment (positive or negative) can be predicted by investigating the general sentiments of his social connections at triad-, community- and network-level. Before the elaboration, we provide the distribution of positive, negative and neutral users in Table 7.

To predict user sentiments (positive or negative), we regard it as a binary classification problem to be addressed within a supervised machine learning framework. Specifically, we represent each user as a set of machine learning features. Features are inspired by the validated five sentiment paradoxes, and the friendship paradox which has been validated to be correlated to the sentiment paradox. Features are presented in Table 6. Then, several common supervised classifiers are trained and used to predict user sentiments (positive or negative) based on ten-fold cross-validation. Results are evaluated by accuracy (ACC) and AUC value.

Table 9 provides the overall results. Results are obtained by using XGBoost (?), which performs best among supervised classifiers including logistic regression, decision trees, naïve Bayes, random forests, and Support Vector Machine (SVM) - see Table 8 for their performance comparison. Results in Table 9 indicate that (1) among single sentiment paradoxes, the general one performs best in predicting user sentiments; (2) when combining all sentiment paradoxes, it outperforms when separately using single ones; and (3) in general, using all features (five sentiment paradoxes plus the correlated friendship paradox) perform best, which can achieve 62% accuracy ratio and 60% AUC value.

Numerous studies have looked at network paradoxes, especially, friendship paradox. For example, friendship paradox has been observed in many online (e.g., Quora (?) and Twitter (?)) and offline networks (?). Kooti et al. (?) have observed and proved that friendship paradox must exist, based on the mean value, in social networks as node degrees always follow heavy-tail distributions. A recent study shows friendship paradox can help identify popular users by connecting it with friendship strength among users (?). Nettasinghe and Krishnamurthy utilize friendship paradox to design randomized polling methods for social networks (?).

In addition to friendship paradox, recent literature has focused on the explorations of other network paradoxes such as user activity paradox, happiness paradox  (?), and scientific collaboration paradox indicating that researchers always have fewer coauthors, citations, publications, and lower h-index than their collaborators (?; ?; ?). The development of these non-friendship paradoxes, however, is in an early stage, whose potential interpretations for their existence and applications have rarely investigated.

This work is motivated by the limitation of current sentiment analysis studies that have not considered interacting users in social networks, and by the phenomenon that people often consider their friends to be more positive than themselves, often attributed to human cognition biases in psychology. We present five sentiment paradoxes at the triad-, community- and network-level, all empirically and mathematically validated in undirected (i.e., with friendships) and directed (i.e., with follower and followee relationships) networks. Through studying the relations between the sentiment paradox and various characteristics of networks and users, we observe that (i) sentiment distributions determine the expected (non-) existence of sentiment paradoxes; (ii) node degrees (i.e., the number of social connections of users) is positively correlated to user sentiments; and (iii) there is no clear pattern between user sentiments and user activity. These connections (though not causal) can be responsible for the existence and magnitude of sentiment paradoxes in social networks, which cannot be solely attributed to human cognition bias as they generally exist in social networks. Additionally, we firstly demonstrate the application of our findings in predicting user sentiment prediction. In the future, we will further analyze causal relationships between user’s connections (degrees) and sentiments. Sentiment paradoxes in dynamic social networks as well as the “like’ and “comments” networks will be part of our future studies.