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Cited by 669Complex Network Analysis TechniquesOpinion Dynamics and Social InfluenceComplex Systems and Time Series Analysis

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The “majority illusion” in social networks

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Lerman, Kristina, Yan, Xiaoran, Wu, Xin-Zeng·2016·PLOS ONE
DOI 10.1371/journal.pone.0147617PMC PMC4757419
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Abstract

Individual's decisions, from what product to buy to whether to engage in risky behavior, often depend on the choices, behaviors, or states of other people. People, however, rarely have global knowledge of the states of others, but must estimate them from the local observations of their social contacts. Network structure can significantly distort individual's local observations. Under some conditions, a state that is globally rare in a network may be dramatically over-represented in the local neighborhoods of many individuals. This effect, which we call the "majority illusion," leads individuals to systematically overestimate the prevalence of that state, which may accelerate the spread of social contagions. We develop a statistical model that quantifies this effect and validate it with measurements in synthetic and real-world networks. We show that the illusion is exacerbated in networks with a heterogeneous degree distribution and disassortative structure.

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Fig 1 An illustration of the “majority illusion” paradox. The two networks are identical, except for which three nodes are colored. These are the “active” nodes and the rest are “inactive.” In the network on the left, all “inactive” nodes observe that at least half of their neighbors are “active,” while in the network on the right, no “inactive” node makes this observation.
Fig 1 An illustration of the “majority illusion” paradox. The two networks are identical, except for which three nodes are colored. These are the “active” nodes and the rest are “inactive.” In the network on the left, all “inactive” nodes observe that at least half of their neighbors are “active,” while in the network on the right, no “inactive” node makes this observation.CC BY · PubMed Central
Fig 2 “Majority illusion” in scale-free networks. Plots show the magnitude of the illusion in scale-free networks as a function of degree–attribute correlation ρkx and for different values of degree assortativity rkk. Each network has 10,000 nodes and degree distribution of the form p(k)∼k−α. The fraction of active nodes in all cases is 5%. The lines represent calculations using the statistical model of Eq (5).
Fig 2 “Majority illusion” in scale-free networks. Plots show the magnitude of the illusion in scale-free networks as a function of degree–attribute correlation ρkx and for different values of degree assortativity rkk. Each network has 10,000 nodes and degree distribution of the form p(k)∼k−α. The fraction of active nodes in all cases is 5%. The lines represent calculations using the statistical model of Eq (5).CC BY · PubMed Central
Fig 3 “Majority illusion” in random networks. Magnitude of the illusion in Erdős-Rényi-type random networks as a function of degree–attribute correlation ρkx and for different values of degree assortativity rkk. Each network has 10,000 nodes with 〈k〉 = 5.2 (top row) or 〈k〉 = 2.5 (bottom row), and different fractions of active nodes. The lines represent calculations using the statistical model of Eq (5).
Fig 3 “Majority illusion” in random networks. Magnitude of the illusion in Erdős-Rényi-type random networks as a function of degree–attribute correlation ρkx and for different values of degree assortativity rkk. Each network has 10,000 nodes with 〈k〉 = 5.2 (top row) or 〈k〉 = 2.5 (bottom row), and different fractions of active nodes. The lines represent calculations using the statistical model of Eq (5).CC BY · PubMed Central
Fig 4 “Majority illusion” in real-world networks. Magnitude of the illusion in real-world networks as a function of degree–attribute correlation ρkx for different fraction of active nodes P(x = 1). The lines represent calculations using the statistical model of Eq (5). The plots are arranged in order of degree assortativity, from highest (a) to lowest (f). Blue circles correspond to the fraction of active nodes P(x = 1) = 0.3, red triangles to P(x = 1) = 0.2, green squares to P(x = 1) = 0.1, and black crosses to P(x = 1) = 0.05.
Fig 4 “Majority illusion” in real-world networks. Magnitude of the illusion in real-world networks as a function of degree–attribute correlation ρkx for different fraction of active nodes P(x = 1). The lines represent calculations using the statistical model of Eq (5). The plots are arranged in order of degree assortativity, from highest (a) to lowest (f). Blue circles correspond to the fraction of active nodes P(x = 1) = 0.3, red triangles to P(x = 1) = 0.2, green squares to P(x = 1) = 0.1, and black crosses to P(x = 1) = 0.05.CC BY · PubMed Central
Fig 5 Gaussian approximation. Symbols show the empirically determined fraction of nodes in the paradox regime (same as in Figs 2 and 3), while dashed lines show theoretical estimates using the Gaussian approximation.
Fig 5 Gaussian approximation. Symbols show the empirically determined fraction of nodes in the paradox regime (same as in Figs 2 and 3), while dashed lines show theoretical estimates using the Gaussian approximation.CC BY · PubMed Central

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Research works printed but not linked: 2

  1. AD Berkowitz, 2005, An overview of the social norms approach, Changing the culture of college drinking: A socially situated health communication campaign, 193
  2. B Latané, 1969, Bystander ‘Apathy’, American Scientist, 57, 244

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Metadata

Authors
Lerman, K., Yan, X., & Wu, X.-Z.
Affiliations
University of Southern California (US)
Corresponding author
Lerman, Kristina
ORCID
Venue
PLOS ONE
Publisher
Public Library of Science (PLoS)
Published
2016-02-17
Volume
11
Issue
2
Pages
e0147617
ISSN
1932-6203 (ISSN-L)
DOI
10.1371/journal.pone.0147617
PMC
PMC4757419
OpenAlex
W1552468722
Cited by
669
References
51
Citations by year
2026: 11 · 2025: 13 · 2024: 15 · 2023: 26 · 2022: 22 · 2021: 135 · 2020: 123 · 2019: 119 · 2018: 94 · 2017: 78 · 2016: 30
FWCI
60.61
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS ONE (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1217605)
  • Defense Advanced Research Projects Agency (W911NF- 12-1-0034)
  • Advanced Research Projects Agency
  • Air Force Office of Scientific Research (FA9550-, FA9550-10-1-, FA9550-10-1-0569)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
Keywords
social networks, prevalence estimation, social contagion, network structure, degree heterogeneity, disassortative mixing, statistical models
MeSH terms
Humans, Illusions, Normal Distribution, Social Networking

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