Three degrees of influence
Three Degrees of Influence is a theory in the realm of social networks, proposed by Nicholas A. Christakis and James H. Fowler in 2007. It has since been explored by scientists in numerous disciplines using diverse statistical, psychological, sociological, and biological approaches.
Christakis and Fowler explored the influence of social connections on behavior. They described how social influence does not end with the people to whom a person is directly connected. People influence their friends, who in turn influence their friends, and so on; hence, a person's beliefs and actions can influence people he or she has never met, to whom he or she is only indirectly tied. Christakis and Fowler posited that diverse phenomena "ripple through our network, having an impact on our friends (one degree), our friends’ friends (two degrees), and even our friends’ friends’ friends (three degrees). Our influence gradually dissipates and ceases to have a noticeable effect on people beyond the social frontier that lies at three degrees of separation." They posited a number of reasons for this decay, and they offered informational, psychological, and biological rationales.
This argument is basically that peer effects need not stop at one degree of separation. However, across a broad set of empirical settings, using both observational and experimental methods, they observed that the effect seems, in many cases, to no longer be meaningful at a social horizon of three degrees.
Using both observational and experimental methods, Christakis and Fowler examined phenomena from various domains, such as obesity, happiness, cooperation, voting, and various public health beliefs and behaviors. Investigations by other groups have subsequently explored many other phenomena in this way (including crime, social learning, etc.).
Influence dissipates after three degrees (to and from friends’ friends’ friends) for three reasons, Christakis and Fowler propose:
- Intrinsic decay—corruption of information, or a kind of "social friction" (like the game telephone).
- Network instability—social ties become unstable (and are not constant across time) at a horizon of more than three degrees of separation.
- Evolutionary purpose—we evolved in small groups where everyone was connected by three degrees or fewer (an idea receiving subsequent support ).
Initial studies using observational data by Christakis and Fowler suggested that a variety of attributes (like obesity, smoking, and happiness), rather than being individualistic, are casually correlated by contagion mechanisms that transmit such phenomena over long distances within social networks. Certain subsequent analyses have explored limitations to these analyses (subject to different statistical assumptions); or have expressed concern that the statistical methods employed in these analyses cannot fully control for other environmental factors; or have noted that the statistical estimates arising from some approaches may not always have straightforward interpretations; or have argued that the statistical methods may not always account for homophily processes in the creation and retention of relationships over time.
But other scholarship using sensitivity analysis has found that the basic estimates regarding the transmissibility of obesity and smoking cessation, for example, are quite robust, or has otherwise replicated or supported the findings. Additional, detailed modeling work published in 2016 showed that the GEE modeling approach used by Christakis and Fowler (and others) was quite effective for estimating social contagion effects and in distinguishing them from homophily. This paper concluded, "For network influence, we find that the approach appears to have excellent sensitivity, and quite good specificity with regard to distinguishing the presence or absence of such a 'network effect,' regardless of whether or not homophily is present in network formation. This was true for small cohorts (n = 30) and larger cohorts (n = 1000), and for cohorts that displayed lesser and greater realism in their distribution of friendships." Another methodological paper concluded that it is indeed possible to bound estimates of peer effects even given the modeling constraints faced by Christakis and Fowler —even if parametric assumptions are otherwise required to identify such effects using observational data (if substantial unobserved homophily is thought to be present).
Additional support for the modeling approach used by Christakis and Fowler provided by other authors has continued to appear. From a theoretical perspective, it has been shown  that this property naturally emerges as the outcome of the interplay between social influence, or learning dynamics, and complex networks. These studies employ emblematic models used to study the diffusion of information, opinions, ideas and behaviors on a wide range of network topologies, showing also under which conditions violations of the "three degrees of influence” can be expected including of the three-degrees-of-influence property. Additional analytic approaches to observational data have also been supportive, including matched sample estimation, and reshuffling techniques. The reshuffling technique validated the "edge directionality test" as an identification strategy for causal peer effects; this technique was first proposed by Christakis and Fowler as a tool for estimating such effects in network analysis in their 2007 obesity paper.
Christakis and Fowler reviewed critical and supportive findings regarding the three degrees of influence phenomenon and the analytic approaches used to discern it with observational data in 2013.
In addition, subsequent experimental studies (by many research groups, including Christakis and Fowler) have found strong causal evidence of behavioral contagion processes that spread beyond dyads (including out to two, three, or four degrees of separation) using randomized controlled experiments, including one experiment involving 61,000,000 people that showed spread of voting behavior out to two degrees of separation. A 2014 paper also confirmed the spread of emotions beyond dyads, as proposed in 2008 by Christakis and Fowler, using another massive online experiment. The "three degrees of influence" property has also been noted by other groups using observational data regarding criminal networks.
Diverse lines of work have also explored the specific biopsychosocial mechanisms for the boundedness of contagion effects, some of which had been theorized by Christakis and Fowler. Experiments by Moussaid et al evaluated the spread of risk perception, and documented inflection at approximately three degrees. Another set of experiments documented the impact of information distortion, noting that "despite strong social influence within pairs of individuals, the reach of judgment propagation across a chain rarely exceeded a social distance of three to four degrees of separation.... We show that information distortion and the overweighting of other people’s errors are two individual-level mechanisms hindering judgment propagation at the scale of the chain." And experiments with fMRI scans in a sociocentrically mapped network of graduate students, published in 2018, showed that neural responses to conceptual stimuli were similar between friends, with a nadir at three degrees of separation, providing further biological evidence for this theory.
The theory has also been used to develop validated algorithms for efficient influence maximization.
The idea of network influence raises the question of free will, because it suggests that people are influenced by factors which they cannot control and which they are not aware of. Christakis and Fowler claim in their book, Connected, that policy makers should use knowledge about social network effects in order to create a better society with a more efficient public policy. This applies to many aspects of life, from public health to economics. For instance, when resources are scarce, they note that it might be preferable to immunize individuals located in the center of a network in preference to structurally peripheral individuals. Or, it might be much more effective to motivate clusters of people to avoid criminal behavior than to act upon individuals or than to punish each criminal separately. Their subsequent work has explored how to use social contagion to foster the spread of desirable innovations in rural villages.
- "The hidden influence of social networks Nicholas Christakis on TED.com".
- Connected Preface+chapter1
- Morgan, TJH; et al. (2015). "Experimental evidence for the co-evolution of hominin tool-making teaching and language". Nature Communications. 6: 6029. Bibcode:2015NatCo...6.6029M. doi:10.1038/ncomms7029. PMC 4338549. PMID 25585382.
- Christakis, Nicholas A.; Fowler, James H. (2007). "The Spread of Obesity in a Large Social Network over 32 Years". The New England Journal of Medicine. 357 (4): 370–379. CiteSeerX 10.1.1.581.4893. doi:10.1056/NEJMsa066082. PMID 17652652.
- Christakis, Nicholas A.; Fowler, James H. (2008). "The Collective Dynamics of Smoking in a Large Social Network". The New England Journal of Medicine. 358 (21): 2249–2258. doi:10.1056/NEJMsa0706154. PMC 2822344. PMID 18499567.
- Christakis, Nicholas A.; Fowler, James H. (2008). "Dynamic spread of happiness in a large social network: longitudinal analysis over 20 years in the Framingham Heart Study". British Medical Journal. 337 (337): a2338. doi:10.1136/bmj.a2338. PMC 2600606. PMID 19056788.
- Christakis, Nicholas A.; Fowler, James H. (2009). Connected:The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Co. ISBN 978-0316036146.
- Cohen-Cole, Ethan; Fletcher, Jason M. (2008). "Detecting implausible social network effects in acne, height, and headaches: longitudinal analysis". British Medical Journal. 337: a2533. doi:10.1136/bmj.a2533. PMC 2600605. PMID 19056789.
- Cohen-Cole, Ethan; Fletcher, Jason M. (2008). "Is obesity contagious? Social networks vs. environmental factors in the obesity epidemic" (PDF). Journal of Health Economics. 27 (5): 1382–1387. doi:10.1016/j.jhealeco.2008.04.005. PMID 18571258.
- Lyons, Russell (2011). "The Spread of Evidence-Poor Medicine via Flawed Social Network Analysis". Statistics, Politics, and Policy. 2 (1). arXiv:1007.2876. doi:10.2202/2151-7509.1024.
- Noel, Hans; Nyhan, Brendan (2011). "The 'unfriending problem': The consequences of homophily in friendship retention for causal estimates of social influence". Social Networks. 33 (3): 211–218. arXiv:1009.3243. doi:10.1016/j.socnet.2011.05.003.
- Shalizi, Cosma R.; Thomas, Andrew C. (2011). "Homphily and Contagion Are Generically Confounded in Observational Social Network Studies". Sociological Methods & Research. 40 (2): 211–239. arXiv:1004.4704. doi:10.1177/0049124111404820. PMC 3328971. PMID 22523436.
- VanderWeele, Tyler J. (2011). "Sensitivity Analysis for Contagion Effects in Social Networks". Sociological Methods & Research. 40 (2): 240–255. doi:10.1177/0049124111404821. PMC 4288024. PMID 25580037.
- Christakis, NA; Fowler, JH (2013). "Social Contagion Theory: ExaminingDynamic Social Networks and Human Behavior". Statistics in Medicine. 32 (4): 556–577. doi:10.1002/sim.5408. PMC 3830455. PMID 22711416.
- Ali, MM; Amialchuk, A; Gao, S; Heiland, F (2012). "Adolescent Weight Gain and Social Networks: Is There a Contagion Effect?". Applied Economics. 44 (23): 2969–2983. doi:10.1080/00036846.2011.568408.
- Steeg, A. Galstyan (2012). "Statistical Tests for Contagion in Observational Social Network Studies". Journal of Machine Learning Research: 563–571.
- Zachrison, Kori (2016). "Can Longitudinal Generalized Estimating Equation Models Distinguish Network Influence and Homophily? An Agent-Based Modeling Approach to Measurement Characteristics". BMC Medical Research Methodology. 16 (1): 174. doi:10.1186/s12874-016-0274-4. PMC 5192582. PMID 28031023.
- Gonzalez-Pardo, A.; Cajias, R.; Camacho, D. (2014). "An Agent Based Simulation of Christakis-Fowler Social Model". Recent Developments in Computational Collective Intelligence. Studies in Computational Intelligence. 513: 69–77. doi:10.1007/978-3-319-01787-7_7. ISBN 978-3-319-01786-0.
- Pinheiro, Flávio L.; Santos, Marta D.; Santos, Francisco C.; Pacheco, Jorge M. (2014). "Origin of Peer Influence in Social Networks" (PDF). Physical Review Letters. 112 (9): 098702. doi:10.1103/physrevlett.112.098702. hdl:1822/64002. PMID 24655286.
- Aral, Sinan; Muchnik, Lev; Sunararajan, Arun (2009). "Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks". Proceedings of the National Academy of Sciences. 106 (51): 21544–21549. Bibcode:2009PNAS..10621544A. doi:10.1073/pnas.0908800106. PMC 2799846. PMID 20007780.
- Anagnostopoulos, Aris; Kumar, Ravi; Mahdian, Mohammad (2008). Influence and Correlation in Social Networks. Proceedings of the 14th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. pp. 7–15. CiteSeerX 10.1.1.227.5676. doi:10.1145/1401890.1401897. ISBN 9781605581934.
- Centola, Damon (2010). "The Spread of Behavior in an Online Social Network Experiment". Science. 329 (5995): 1194–1197. Bibcode:2010Sci...329.1194C. CiteSeerX 10.1.1.701.3842. doi:10.1126/science.1185231. PMID 20813952.
- Fowler, James H.; Christakis, Nicholas A. (2010). "Cooperative behavior cascades in human social networks". Proceedings of the National Academy of Sciences. 107 (12): 5334–5338. arXiv:0908.3497. Bibcode:2010PNAS..107.5334F. doi:10.1073/pnas.0913149107. PMC 2851803. PMID 20212120.
- Aral, Sinan; Walker, Dylan (2011). "Creating Social Contagion Through Viral Product Design: A Randomized Trial of Peer Influence in Networks". Management Science. 57 (9): 1623–1639. doi:10.1287/mnsc.1110.1421.
- Rand D, Arbesman S, and Christakis NA,"Dynamic Social Networks Promote Cooperation in Experiments with Humans," PNAS:Proceedings of the National Academy of Sciences 2011; 108: 19193-19198
- Kim, David A; Hwong, Alison R; Stafford, Derek; Hughes, D Alex; O'Malley, A James; Fowler, James H; Christakis, Nicholas A (2015-07-11). "Social network targeting to maximise population behaviour change: a cluster randomised controlled trial" (PDF). The Lancet. 386 (9989): 145–153. doi:10.1016/S0140-6736(15)60095-2. ISSN 0140-6736. PMC 4638320. PMID 25952354.
- Bond, RM; Fariss, CJ; Jones, JJ; Kramer, ADI; Marlow, C; Settle, JE; Fowler, JH (2012). "A 61-million-person experiment in social influence and political mobilization". Nature. 489 (7415): 295–298. Bibcode:2012Natur.489..295B. doi:10.1038/nature11421. PMC 3834737. PMID 22972300.
- Kramer, ADI; Guillory, JE; Hancock, JT (2014). "Experimental evidence of massive-scale emotional contagion through social networks" (PDF). Proceedings of the National Academy of Sciences. 111 (24): 8788–8790. Bibcode:2014PNAS..111.8788K. doi:10.1073/pnas.1320040111. PMC 4066473. PMID 24889601.
- Wildeman, Christopher; Papachristos, Andrew V. (2014). "Network Exposure and Homicide Victimization in an African American Community". American Journal of Public Health. 104 (1): 143–150. doi:10.2105/ajph.2013.301441. PMC 3910040. PMID 24228655.
- Moussaid, M; Brighton, H; Gaissmaier, W (2015). "The amplification of risk in experimental diffusion chains" (PDF). Proceedings of the National Academy of Sciences. 112 (18): 5631–5636. arXiv:1504.05331. Bibcode:2015PNAS..112.5631M. doi:10.1073/pnas.1421883112. PMC 4426405. PMID 25902519.
- Moussaid, M (2017-04-18). "Reach and Speed of Judgment Propagation in the Laboratory" (PDF). Proceedings of the National Academy of Sciences. 114 (16): 4117–4122. doi:10.1073/pnas.1611998114. PMC 5402452. PMID 28373540.
- Parkinson, Carolyn; Kleinbaum, Adam M.; Wheatley, Thalia (2018-01-30). "Similar neural responses predict friendship". Nature Communications. 9 (1): 332. Bibcode:2018NatCo...9..332P. doi:10.1038/s41467-017-02722-7. ISSN 2041-1723. PMC 5790806. PMID 29382820.
- Qin, Yadong; Ma, Jun; Gao, Shuai (2015-06-08). Efficient Influence Maximization Based on Three Degrees of Influence Theory. Web-Age Information Management. Lecture Notes in Computer Science. 9098. pp. 465–468. doi:10.1007/978-3-319-21042-1_42. ISBN 978-3-319-21041-4.
- Shakya, Holly (2017). "Exploiting social influence to magnify population-level behaviour change in maternal and child health: study protocol for a randomised controlled trial of network targeting algorithms in rural Honduras". BMJ Open. 7 (3): e012996. doi:10.1136/bmjopen-2016-012996. ISSN 2044-6055. PMC 5353315. PMID 28289044.