This work constitutes the first direct measurement of a Happiness paradox in social networks, rather than its theoretical derivation from hypothetical network attributes and properties. Our results suggest that previous observations of decreased happiness among social media users may result directly from 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 are 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 one’s 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. 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 [23, 24, 25] and potentially verbal commiseration and mirroring.
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, no indication 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 expect that these environments may induce longitudinal changes in the public’s 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.
In spite of these limitations our results provide a strong indication that widespread social media use may lead to increased levels of social dissatisfaction and unhappiness since individuals will be prone to unfavorably compare their own happiness and popularity to that of others. Happy social media users will likely 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. We caution against the widespread use of social media given the likelihood that it decreases the happiness and well-being of particularly the most vulnerable groups in society.
BG thanks the Moore and Sloan Foundations for support as part of the Moore-Sloan Data Science Environment at NYU.
References and Notes
-  C. L. Apicella, F. W. Marlowe, J. H. Fowler, N. A. Christakis, Nature 481, 497 (2012).
-  R. Dunbar, Neurosci Biobehav Review 34, 260 (2010).
-  A. Steptoe, A. Shankar, P. Demakakos, J. Wardle, Proceedings of the National Academy of Sciences 110 (2013).
-  S. Pinker, The Village Effect: Why Face-to-Face Contact Matters (Atlantic Books, 2015).
-  A. Perrin, Report: Pew Research Center (2015).
-  M. Burke, C. Marlow, T. Lento, Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’10 (ACM, New York, NY, USA, 2010), pp. 1909–1912.
-  E. Kross, et al., PLoS ONE 8, e69841 (2013).
-  M. Tromholt, M. Lundby, K. Andsbjerg, M. Wiking, The facebook experiment: does social media affect the quality of our lives?, Tech. rep., The Happiness Institute (2015).
-  L. Mitchell, M. R. Frank, K. D. Harris, P. S. Dodds, C. M. Danforth, PLoS ONE 8, e64417 (2013).
-  S. L. Feld, American Journal of Sociology 96, 1464–1477 (1991).
-  N. O. Hodas, F. Kooti, K. Lerman, Proceedings of the Seventh International AAAI Conference on Weblogs and Social Media (AAAI Press, 2013).
-  F. Kooti, N. O. Hodas, K. Lerman, Proceedings of the Eighth International AAAI Conference on Weblogs and Social Media (AAAI Press, 2014).
-  H.-H. Jo, Y.-H. Eom, Phys. Rev. E 90, 022809 (2014).
-  Y.-H. Eom, H.-H. Jo, Sci. Rep. 4 (2014).
-  A. J. Oswald1, S. Wu, Science 327, 576.
-  A. B. Krueger, A. A. Stone, Science 346, 42 (2014).
-  D. R. Posel, D. M. Casale, Social Indicators Research 104, 195 (2011).
-  A. de la Garza, G. Mastrobuoni, A. Sannabe, K. Yamada, The Relative Utility Hypothesis With and Without Self-reported Reference Wages, Carlo Alberto Notebooks 159, Collegio Carlo Alberto (2010).
-  J. Bollen, B. Gonçalves, G. Ruan, H. Mao, Artificial Life 17, 237 (2011).
-  B. Stiller, et al., Measuring national well-being－proposed well-being indicators－, Tech. rep., The Commission on Measuring Well-being, Japan (2010).
-  M. McPherson, L. Smith-Lovin, J. M. Cook, Annual Review of Sociology 27, 415 (2001).
-  J. H. Fowler, N. A. Christakis, British Medical Journal 337 (2008).
-  A. D. I. Kramer, J. E. Guillory, J. T. Hancock, Proceedings of the National Academy of Sciences 111 (2014).
-  E. Ferrara, Z. Yang, PLoS ONE 10 (2015).
-  E. Ferrara, Z. Yang, PeerJ Computer Science 1:e26 (2015).
-  R. Dunbar, Philos Trans R Soc Lond B Biol Sci 367, 2192 (2012).
-  B. Gonçalves, N. Perra, A. Vespignani, PLoS One 6, e22656 (2011).
The Friendship Network
To generate a friendship network among Twitter users we started with an initial set of users, 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 relation between the two individuals . This resulted in a network of node connected by reciprocal edges. We further remove subjects with less than friends in order to improve the reliability of calculating the mean degree and mean SWB values of an individuals’ friends. This reduces our final cohort to subjects connected by reciprocal friendship relation.
We then assess the magnitude of the Friendship Paradox in our network by calculating the fraction of users whose Popularity, denoted is lower than the average Popularity of their nearest neighbors (or “friends”) , denoted , vs. the total number of individuals in the network . This yields the magnitude of the Friendship Paradox as:
When the magnitude of we conclude that the majority of users experiences a Friendship.
For each of the users that fulfill all the requirements listed above, we further collect their complete Twitter history based on which we can assess the SWB of each individual. With this information hand, the magnitude of the Happiness Paradox can be obtained in a way similar to the way in which we measure the Friendship Paradox. We simply calculate the fraction of users whose Happiness, denoted respectively, is lower than the average Happiness of their nearest neighbours, denoted , vs. the total number of individuals in the network , or, mathematically:
To determine the significance of our results we employ a bootstrapping procedure in which we repeatedly re-sample the set of individuals in our data with replacement and re-calculate our indicators to assess the variance of results resulting from random changes in the underlying population. This procedure allows us to obtain Confidence Intervals for all indicators by determining the 5th and 95th percentile of the results obtained for each of 5000 sub-samples with replacement over the entire set of individuals.
As mentioned in the text we verify the importance of popularity-happiness correlations by comparing the results we obtained in our dataset with those of a simple null-model. We keep the structure of the network and SWB distributions intact by simply resampling the complete set of SWB values with replacement and re-calculating Eq. 2 and Eq.1. This procedure is performed 20,000 times. We report the 95% confidence intervals for the resulting distribution of paradox values.
Gaussian Mixture Components
Our data contains two data points for each user:
their own Popularity or Happiness
the average Popularity or Happiness of their friends
Each user can then be described as a point on a 2-dimensional euclidean plane spanned by their own popularity or happiness (x) and the average happiness of their group of friends (y).
In this plane, users cleanly separate in 2 clusters in
according to matching levels of popularity or happiness. To determine an objective demarcation criterion we use a Gaussian Mixture Model (GMM) to identify membership in either of the 2 groups. The GMM is trained from our empirical data by means of a standard Expectation-Maximization procedure to identify two 2D Gaussian distributions that are each characterized by a centerand co-variance to best match the distribution of individuals in . Each components carries a weight
with which to mix the 2 components to match the probability density function of the data, but we are only concerned with their location to demarcate the two groups of individuals. The gaussian parameter values obtained using the Scikit-learns sklearn.mixture package without any constraints on the covariance model are:w
|1 (Happy group)||(0.2037652, 0.21266452)||(0.00186789, 0.00046923)|
|2 (Unhappy group)||(0.00704093,0.0182976)||(0.00046923, 0.0018294)|