The happiness paradox: your friends are happier than you
Bollen et al. EPJ Data Science
The happiness paradox: your friends are happier than you
Johan Bollen 0
Bruno Gonçalves 2
Ingrid van de Leemput 1
Guangchen Ruan 0
0 School of Informatics and Computing, Indiana University , Bloomington, IN , USA
1 Environmental Sciences, Wageningen University , Wageningen , The Netherlands
2 Center for Data Science, New York University , New York , USA
Most individuals in social networks experience a so-called Friendship Paradox: they are less popular than their friends on average. This effect may explain recent findings that widespread social network media use leads to reduced happiness. However the relation between popularity and happiness is poorly understood. A Friendship paradox does not necessarily imply a Happiness paradox where most individuals are less happy than their friends. Here we report the first direct observation of a significant Happiness Paradox in a large-scale online social network of 39,110 Twitter users. Our results reveal that popular individuals are indeed happier and that a majority of individuals experience a significant Happiness paradox. The magnitude of the latter effect is shaped by complex interactions between individual popularity, happiness, and the fact that users strongly cluster by similar level of happiness. Our results indicate that the topology of online social networks, combined with how happiness is distributed in some populations, may be associated with significant psycho-social effects.
subjective well-being; social media; social network; friendship paradox; sentiment analysis; natural language processing; data science
We are a profoundly social species . The ability to establish face-to-face, physical,
relationships in a rich social environment is paramount to our happiness and individual
well-being [–]. However, technology is now playing an increasing role in forming our
networks of social relationships. Nearly /th of the world’s population and over /rd of
the US population  use some form of social media which enables individuals to maintain
virtual social networks that extend beyond geographical, economic, cultural, and
Evidence has been accumulating that online social networking is associated with
elevated levels of loneliness, anxiety, displeasure, and dissatisfaction [–]. The reason for
this apparent contradiction is unknown, but it may be found in universal social network
connectivity patterns. Surprisingly, measured in number of connections, most people will
have fewer friends than their own friends do on average. This phenomenon, commonly
referred to as the Friendship Paradox [, ], has been attributed to an inherent structural
bias in social network that favors popular individuals: they are by definition more likely
to belong to someones social circle, thereby elevating local levels of popularity. One may
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
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Figure 1 A Happiness paradox, like a Friendship paradox, could result from skewed degree
distributions. (A1) Like the examples above, most social networks are characterized by very skewed degree
distributions: a few individuals have very many connections, while most individuals have only few
connections. The number of connections are marked within each node. Those with many connections are by
definition more likely to be someone’s friend. As a result their higher number of connections can increase the
average degree of given friendship neighborhoods throughout the network (marked above each node)
leading to a Friendship paradox (red nodes) in which most individuals nodes are less popular than the
average of their friends. (A2) When popular individuals are also more likely to be happy, their Happiness
becomes more prevalent, raising average happiness levels throughout the friendship circles in the network.
A Happiness paradox may result in which most individuals are less happy than their own friends on average.
Individuals may cluster based on their Happiness or even the degree to which they experience a Happiness
speculate that if an individual compares their own popularity to that of their friends, this
effect may, in some cases, lead to increased levels of dissatisfaction (see Figure ).
The effects of this Friendship Paradox may extend beyond popularity. If popular
individuals tend to be happier, their elevated happiness will become more prevalent as well. This
may in turn lead to a Happiness Paradox, where most individuals are less happy than their
friends on average (see Figure ). In fact, the latter may contribute more directly to the
negative psycho-social effects of social networking since it affects how individuals assess
their own Subjective Well-being, i.e. general happiness or life satisfaction [, ], relative
to that of others [, ].
At this point, however, it has not been established whether () popular individuals are
indeed happier and () a Happiness Paradox does in fact occur in social networks. Given
the magnitude of social media adoption, these are questions of global importance that may
affect the well-being of billions of individuals.
Here we present the first large-scale longitudinal study of happiness and popularity levels
for a network of , Twitter users that are connected by ‘friendship’ relations.
To generate a friendship network among Twitter users we start with an initial set of
,, randomly chosen users (years -), for which we downloaded the full
list of users that they ‘follow’ or that they are ‘followed’ by . Reciprocal ‘Follow’ and
‘Following’ ties are taken as an indication of a friendship and mutual interaction
relation between the two individuals . We selected the Largest Connected Component
of the resulting network. The resulting network consists of , individuals that share
We automatically assess each individual’s Subjective Well-Being (SWB), on a scale of
[–, +] according to a procedure outlined in . For each user we collected the ,
most recently submitted tweets, serving as a comprehensive longitudinal record
pertaining to the individual user. We subject this entire timeline, not its individual tweets, to a
sentiment analysis  based on the OpinionFinder (OF) subjectivity lexicon . The
procedure consists of counting the number of words that are members of either the set
of highly positive or highly negative words in the OF subjectivity lexicon, and calculating
their fractional difference (number of positive words-negative words over all OF words in
the timeline). Aggregating this information for all Tweets in an individual Twitter record,
we determine the individual’s overall Subjective Well-Being.
The OF toolkit, although different from the above described application of its
subjectivity lexicon, was ranked th out of tools in a large-scale survey of - and -way
sentiment classification tasks against a variety of data sets . Its accuracy in scoring
individual tweets ranged from . to ., mostly approximating, and sometimes exceeding,
that of top rated tools such as VADER or AFINN, with coverage levels from . to .,
depending on the specific data set against which OF was tested. We stress that our
procedure uses the OF Subjectivity Lexicon against an entire month timeline of up to ,
tweets by the same individual Twitter user, not individual tweets. Hence the reported
coverage values are expected to be a significant underestimation relative to our application.
In addition, we exclude users with SWB values of exactly zero.
Finally, we restrict our analysis to individuals with more than friends in order to
exclude individuals with excessively low social activity and those that have non-zero SWB,
i.e. that have shared some subjective information. This reduces our final cohort to ,
subjects that are connected by reciprocal friendship relations, have at least friends, and
have non-zero SWB values.
We quantify an individuals ‘Happiness’ as their SWB value and quantify their
‘Popularity’ as their number of network friends counted in our bidirectional social network of
reciprocal connections. Simply put, we deem an individual ‘Happy’ when they have high
SWB values and ‘Popular’ when they have many friends. The Happiness and Popularity
values of all subjects are then used to determine:
. the fraction of individuals that has lower popularity than their friends on
. the fraction of individuals that has lower happiness than their friends on
. the correlation between individual happiness and popularity, R (Happiness,
We assess the magnitude of the Friendship Paradox in our network by calculating the
fraction of the number of users ui ∈ U whose Popularity, denoted D(ui) (degree of ui)
is lower than the average Popularity D¯ of their nearest neighbors (or ‘friends’) Nui ⊂ U
vs. the total number of individuals in the network U . This yields the magnitude of the
Friendship Paradox as:
The magnitude of the Happiness Paradox can be obtained in a similar way to how we
measure the Friendship Paradox. We simply calculate the fraction of users ui ∈ U whose
Happiness, denoted H(ui) (SWB value of ui), is lower than the average Happiness H¯ of
their nearest neighbors, Nui , vs. the total number of individuals in the network U :
A Friendship or Happiness Paradox for our sample is indicated by P and H values larger
than %, i.e. a majority of individuals have lower Popularity or Happiness than their
friends, on average.
To assess the correlation between Happiness and Popularity we calculate Pearson’s R
between the SWB values and log(degree) of all subjects in our cohort. The use of log(degree)
is meant to compensate for the very skewed distribution of degree values in our network.
We assess the robustness of our results by performing a bootstrapping procedure in
which we randomly sample % of subjects and their network connections with
replacement , times to assess the distribution of our paradox indicators for different samples
of our network. Furthermore, we validate the statistical significance of our results by
comparing them to a null-model where we reshuffle the SWB values across all individuals in
our network. In this way, we are able to maintain the same identical distribution of SWB
values and network structure, while completely eliminating any possible correlation that
might be present. The null-model was bootstrapped , times and, as expected, it
eliminated the Happiness paradox.
Finally, we determine the sensitivity of our results to reductions of the sample due to
the ‘minimum friends threshold’ by recalculating all Happiness Paradox magnitudes for
values of the threshold ranging from to .
As shown in Table , we find that P = ., % CI [., .], indicating a very
significant Friendship Paradox across all subjects, meaning that the great majority of users are
less popular than their friends are on average. We also find a modest but robust value of
H = .%, % CI [., .], indicating the presence of a Happiness Paradox. Hence
a majority of subjects is indeed less happy than their friends on average. Our null-model
indicates the absence of a Happiness paradox when the effects of network structure on
Happiness levels are removed by random re-assignment. The lower magnitude of the
Happiness Paradox could result from the rather low, yet robust, correlation between Happiness
and Popularity (Pearson’s R = ., % CI [., .]).
As shown in Figure the joint distribution of individual Happiness levels and mean
neighbor happiness in our sample is distinctly bi-modal. There exists some evidence that
Subjective Well-Being itself can be distributed in a bimodal fashion across several
cultures and nations  matching previous observations by . In this case, bi-modality
also occurs at the level of our friendship network which separates subjects into distinct
groups: Happy subjects with Happy friends (the ‘Happy’ group) and Unhappy subjects with
Unhappy friends (the ‘Unhappy’ group). This result follows earlier reports of happiness
being homophilic or assortative in social networks [, , ]. Note that this phenomenon
Table 1 Magnitude of Friendship Paradox, Happiness Paradox (compared to null-model
produced by randomly re-assigning SBW values across all subjects), and
Happiness-Popularity correlation coefficient (Pearson’s R) for all subjects (N = 39,110)
Figure 2 Overview of the magnitude of the Happiness and Friendship paradox for the sample of
Twitter subjects; individuals positioned above the diagonal experience a Happiness or Friendship
paradox. (B1) Happiness Paradox: Distribution of individual Happiness (x-axis) vs. average Happiness of one’s
friend’s average (y-axis). Happiness is measured in terms of longitudinal Subjective Well-Being (SWB) scores.
Subjects above the red paradox line experience lower happiness (SWB) than their friends’ average. The
distribution of SWB scores places a majority of subjects well above the diagonal Paradox line. Ellipses indicate
the boundaries of 2 Gaussian Mixture Model components used to demarcate a Happy (red) and Unhappy
(blue) groups of subjects. Paradox magnitudes are expressed in terms of the percentage of users who
experience lower happiness than their friends. The 95% confidence intervals are calculated by a 5,000-fold
bootstrapping of a 10% sample to determine the sensitivity of our results to random network sampling
variations. (B2) and (B3) Friendship Paradox: Distribution of individual Popularity (x-axis) vs. average Popularity
of one’s Friends (y-axis). Popularity is measured in terms of log(degree) in the Friendship network. Subjects
above the red paradox line experience lower popularity than their friends on average. As shown, we find
significant Happiness and Friendship Paradoxes for all users, but Happy users experience a stronger
Friendship Paradox whereas Unhappy users experience a stronger Happiness Paradox.
is not the result of the distribution of our SWB values, but is determined by network
connections; i.e. unhappy people tend to have unhappy friends and happy people tend to have
Since a Happiness Paradox specifically compares individual happiness to the average
happiness of one’s friends, this homophilic bi-modality must be factored into our analysis.
By performing a separate analysis for Happy and Unhappy groups of users, we attempt to
equalize the effects of neighbor happiness across the two groups.
As shown in Figure we use a Gaussian Mixture Model (GMM) to demarcate our Happy
and Unhappy groups. We determine the location and distribution of two separate
Gaussian components in the distribution of individual happiness vs. mean friend happiness and
demarcate both groups by simply determining whether the SWB value of a subject and
the mean SWB values of their neighbors fall within standard deviations from the
center of either one of the components (illustrated by the ellipses in Figure ). We thereby
split our sample in groups of subjects: a group of Happy individuals with Happy friends
Figure 3 Bootstrapped estimates of the correlation between Happiness and Popularity, and the
magnitude of the Friendship and Happiness Paradox for Happy and Unhappy subjects. Top: Estimated
Pearson’s R correlation coefficients (95% Confidence Intervals in brackets) between individual Happiness
(Subjective Well-Being) vs. individual Popularity (log degree) for All subjects: 0.109 [0.077, 0.140], Happy group:
0.126 [0.081, 0.171], and unhappy group: -0.047 [–0.08, –0.013]. Middle: Distribution of Friendship Paradox
values for all subjects 0.943 [0.937, 0.949], happy group: 0.958 [0.951, 0.964], and unhappy group 0.888
[0.869, 0.906]. Bottom: Distribution of Happiness Paradox values for all subjects: 0.585 [0.581, 0.589], happy
group: 0.578 [0.573, 0.582], and unhappy group 0.666 [0.657, 0.674].
cedure assumes a Gaussian density distribution which roughly matches the quantiles of
the empirical density as shown by the contour lines of Figure , so that both Gaussian
components capture % of our sample. These groups are well-separated in the
underlying social network. Of all edges adjacent to individuals in the Happy group only .%
connect to individuals in the Unhappy group. Vice versa, of all edges adjacent to
individuals in the Unhappy group only .% connect to individuals in the Happy group.
We re-run our analysis for the Happy and Unhappy groups separately. The results are
summarized in Figures and .
These results reveal that the Happy group experiences a strong Friendship Paradox but
a weak, yet very robust Happiness Paradox. The Unhappy group experiences a weaker
Friendship Paradox, but a significantly stronger Happiness Paradox than the Happy group,
in spite of subjects being surrounded by less Happy friends.
To determine whether the strong Happiness Paradox for the unhappy group, in spite of
its lower correlation between Popularity and Happiness, may be related to interpersonal
effects, we examine the relation between individual happiness and the average happiness
of ones neighbors. As visually indicated by the distribution of individuals in Figure , the
strength of the relationship between a subjects’ Happiness and the average Happiness of
their friends may differ between the Happy and Unhappy group. The results of a linear
regression predicting mean neighbor SWB from a user’s own SWB values match the visual
tilt of the separate GMM components. For the Happy group we find F(, ,) = ,,
p < . with an adjusted R = .. The resulting regression equation is Mean Neighbor
SWB = . + . (own SWB). For the Unhappy Group we find F(, ,) = ,,
p < . with an adjusted R = .. Here, the resulting regression equation is Mean
Neighbor SWB = . + . (own SWB). An ANCOVA analysis to predict Average
Neighbor SWB from the interaction between a user’s own SWB and their membership of
the Happy or Unhappy group results in F(, ,) = ,, p < . with an adjusted
R = .. On the basis of this last result we reject the null-hypothesis that the
regression slopes between own SWB and mean neighbor SWB are equal between the Happy
and Unhappy group. This outcome suggests that unhappy users may be more strongly
affected by the lower happiness of their friends, possibly explaining why this group exhibits a
stronger Happiness Paradox in the absence of a strong correlation between Popularity and
Happiness. However, we caution that further investigation is warranted on this matter.
Finally, to determine the sensitivity of our analysis to the choice of our minimum
neighbors threshold (the minimum number of neighbors a user must have to be included in
our sample), we recalculate Happiness paradox values for all threshold values between
and . We use the same GMM component locations for every calculation to provide
an equal basis for comparison. As shown in Table and Figure , we find that requiring
a minimum threshold of neighbors for each individual in our data constitutes a
Figure 4 Minimum neighbor threshold vs.
percentage of sample retained. In our calculation
of the Happiness Paradox we apply a minimum
neighbor threshold for each user, i.e. a minimum
number of neighbors the individual must have to be
included in our sample, to (1) reduce the chances of
including defunct, automated, or particularly socially
inactive users and (2) ensure that a mean neighbor
degree or SWB is calculated on the basis of no less
than 15 data points. This threshold leads to a
reduction of our sample. This graph visualizes the
magnitude of the reduction at chosen threshold
value of 15 and all other values between 1 and 200.
Values provided in Table 2.
Figure 5 Happiness paradox values for Happy and Unhappy group at different minimum neighbor
threshold values, with 95% confidence intervals. Overlayed are the remaining sample size for the same
threshold values. The gray area indicates paradox value below 50%, i.e. no happiness paradox. We find a
significant happiness paradox, under all but the most extreme values of the minimum neighbor threshold.
icant reduction of our sample, but we still retain more than % of the entire sample. In
exchange for this reduction, we attempt to increase the chances of removing noise caused
by socially inactive, and possibly automated or defunct accounts. The value of this
threshold is notably much lower than recent estimations of the online Dunbar number .
The results of our sensitivity analysis, shown in Figure , indicate that the magnitude of
the happiness paradox is largely independent from our choice of threshold, with the
exception of extremely large values, i.e. where less than % of the original sample remains and
only individuals with more than friends are included, thus approaching the Dunbar
limit . We find a significant happiness paradox for the Unhappy group for all values of
the minimum neighbor threshold indicating that this result is largely independent from
We find that a majority of both Happy and Unhappy social media users will experience a
significant Popularity and Happiness Paradox, i.e. they will be less popular and less happy
than their friends on average. One may speculate that previous observations reporting
decreased happiness among social media users may be associated with a widespread inflated
perception of the happiness of one’s friends. Although happy and unhappy groups of
subjects are both affected by a significant happiness paradox, unhappy subjects seem most
strongly affected. This is counter-intuitive for two reasons. First, the correlation between
happiness and popularity is lowest for individuals in the unhappy group. A happiness
paradox can result from a friendship paradox when popularity and happiness are correlated,
since more popular and thus more prevalent individuals will increase the average
happiness of ones circle of friends. As a result, the unhappy group, with the lowest correlation
between popularity and happiness, should experience the lowest happiness paradox.
Second, the strong assortativity of happiness in our social network reduces the prevalence of
happy subjects in the social network circle of unhappy subjects. Therefore, it should be
easier for individuals in this group to surpass the average happiness of their friends. Our
results show that neither is the case. We speculate that a possible explanation may lie in
the stronger relation between the happiness of individuals in this group and the overall
happiness of their friends. This effect may point to an alternate origin for the occurrence
of a Happiness paradox; instead of resulting from the greater prevalence of popular and
happy individuals, in some cases, a happiness paradox may result from the complex social
interactions between individuals and their friends, e.g. through mood contagion [–]
and potentially verbal commiseration and mirroring.
Our results suggest that social media use may be associated with increased levels of
social dissatisfaction and unhappiness if individuals are subject to unfavorable comparison
between their own happiness and popularity to those of their friends. Happy social media
users may think their friends are much more popular and slightly happier than they are
while unhappy social media users will likely have unhappy friends that will still seem much
happier and more popular than they are on average.
However, our study has limitations. First, the assessment of Subjective Well-Being from
social media using text analysis algorithms may not be perfectly reliable. However, given
the large number of individuals in our dataset, the absence of consistent directional bias,
and the magnitudes of the observed effects, we expect this will not affect the validity of our
observations. Future improvements in sentiment and mood analysis, and ground truth
obtained from user surveys, may increase the reliability of our SWB estimates. Second, given
the large role that social media plays in the social lives of billions of individuals, we
speculate that these environments may induce longitudinal changes in the public social behavior
and may over time alter the very nature of social relations themselves . Further
analysis will be required to determine the extent and significance of these changes, and how
they affect the propensity of online users to experience the effects of a Friendship and
Happiness Paradox over time. Lastly, we stress that our study is, by definition,
observational in nature. We do not and can not make any claims with respect to the causal nature
of the relationships between Subjective Well-Being, popularity, mood contagion, and
social network use. This will require an extensive program of experimental verification over
extended periods of time which we are planning.
Bruno Gonçalves thanks the Moore and Sloan Foundations for support as part of the Moore-Sloan Data Science
Environment at NYU. Johan Bollen thanks the Defense Advance Research Projects Agency (NGS2 2016 #D17AC00005)
and the National Science Foundation (SMA-SBE: 1636636) for their support.
JB designed and executed the experimental methodology, performed the data analysis, and wrote the manuscript.
IL performed data analysis, advised on methodological and analytical issues, and co-authored the manuscript.
BG collected the data, advised on methodological and analytical issues, and co-authored the manuscript. GR collected
and processed the raw data. All authors reads and approved the final manuscript.
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