Spheres of Legislation: Polarization and Most Influential Nodes in Behavioral Context

  • Andrew C. Phillips
  • Mohammad T. IrfanEmail author
  • Luca Ostertag-Hill
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 882)


Game-theoretic models of influence in networks often assume the network structure to be static. In this paper, we allow the network structure to vary according to the underlying behavioral context. This leads to several interesting questions on two fronts. First, how do we identify different contexts and learn the corresponding network structures using real-world data? We focus on the U.S. Senate and apply unsupervised machine learning techniques, such as fuzzy clustering algorithms and generative models, to identify different spheres of legislation as context and learn an influence network for each sphere. Second, how do we analyze these networks in order to gain an insight into the role played by the spheres of legislation in various interesting constructs like polarization and most influential nodes? To this end, we apply both game-theoretic and social network analysis techniques. In particular, we show that game-theoretic notion of most influential nodes brings out the strategic aspects of interactions like bipartisan grouping, which typical centrality measures fail to capture. We also show that for the same set of senators, some spheres of legislation are more polarizing than others.


Influence in networks Machine learning and networks Computational game theory Graphical games 



This research was partially supported by NSF grant IIS-1910203. We sincerely thank Dr. Stephen Majercik (Bowdoin College) for reading an earlier draft of this paper and giving us many valuable suggestions. We are also thankful to Drs. Honorio and Ortiz for letting us use their codes [15] and to the anonymous reviewers for their suggestions.


  1. 1.
    Bakshy, E., Messing, S., Adamic, L.A.: Exposure to ideologically diverse news and opinion on facebook. Science 348(6239), 1130–1132 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefGoogle Scholar
  3. 3.
    Chen, W., Collins, A., Cummings, R., Ke, T., Liu, Z., Rincon, D., Sun, X., Wang, Y., Wei, W., Yuan, Y.: Influence maximization in social networks when negative opinion may emerge and propagate. In: Proceedings of the Eleventh SIAM International Conference on Data Mining, pp. 379–390 (2011)Google Scholar
  4. 4.
    Christakis, N.A., Fowler, J.H.: The spread of obesity in a large social network over 32 years. N. Engl. J. Med. 357(4), 370–379 (2007). Scholar
  5. 5.
    Christakis, N.A., Fowler, J.H.: The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358(21), 2249–2258 (2008). Scholar
  6. 6.
    Clinton, J., Jackman, S., Rivers, D.: The statistical analysis of roll call data. Am. Polit. Sci. Rev. 98(2), 355–370 (2004)CrossRefGoogle Scholar
  7. 7.
    Conover, M.D., Ratkiewicz, J., Francisco, M., Gonçalves, B., Menczer, F., Flammini, A.: Political polarization on Twitter. In: Fifth International AAAI Conference on Weblogs and Social Media (2011)Google Scholar
  8. 8.
    Farina, C.R.: Congressional polarization: terminal constitutional dysfuction. Colum. L. Rev. 115, 1689 (2015)Google Scholar
  9. 9.
    Garcia, D., Abisheva, A., Schweighofer, S., Serdült, U., Schweitzer, F.: Ideological and temporal components of network polarization in online political participatory media. Policy Internet 7(1), 46–79 (2015)CrossRefGoogle Scholar
  10. 10.
    Gerrish, S.M., Blei, D.M.: How they vote: issue-adjusted models of legislative behavior. Adv. Neural Inf. Process. Syst. 25(1), 2762–2770 (2012)Google Scholar
  11. 11.
    Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Granovetter, M.: Threshold models of collective behavior source. Am. J. Sociol. 83(6), 1420–1443 (1978). Scholar
  13. 13.
    Guerra, P.C., Meira Jr., W., Cardie, C., Kleinberg, R.: A measure of polarization on social media networks based on community boundaries. In: 7th International AAAI Conference on Weblogs and Social Media (2013)Google Scholar
  14. 14.
    Gómez, S., Jensen, P., Arenasl, A.: Analysis of community structure in networks of correlated data. Institut des Systèmes Complexes 1(1), 2–3 (2009)Google Scholar
  15. 15.
    Honorio, J., Ortiz, L.: Learning the structure and parameters of large-population graphical games from behavioral data. J. Mach. Learn. Res. 16, 1157–1210 (2015).
  16. 16.
    Irfan, M.T., Gordon, T.: The power of context in networks: ideal point models with social interactions. In: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, pp. 910–918. International Foundation for Autonomous Agents and Multiagent Systems (2018)Google Scholar
  17. 17.
    Irfan, M.T., Ortiz, L.E.: A game-theoretic approach to influence in networks. In: Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, pp. 688–694 (2011).
  18. 18.
    Irfan, M.T., Ortiz, L.E.: On influence, stable behavior, and the most influential individuals in networks: a game-theoretic approach. Artif. Intell. 215, 79–119 (2014). Scholar
  19. 19.
    Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2010)CrossRefGoogle Scholar
  20. 20.
    Kearns, M., Littman, M., Singh, S.: Graphical models for game theory. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pp. 253–260 (2001)Google Scholar
  21. 21.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2003)Google Scholar
  22. 22.
    Kempe, D., Kleinberg, J., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP) (2005)Google Scholar
  23. 23.
    Leskovec, J., Adamic, L.A., Huberman, B.A.: The dynamics of viral marketing. ACM Trans. Web (TWEB) 1(1), 5 (2007)CrossRefGoogle Scholar
  24. 24.
    Li, Y., Chen, W., Wang, Y., Zhang, Z.L.: Influence diffusion dynamics and influence maximization in social networks with friend and foe relationships. In: Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, pp. 657–666. ACM (2013)Google Scholar
  25. 25.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1: Statist, pp. 281–297 (1967).
  26. 26.
    McCarty, N., Poole, K.T., Rosenthal, H.: Polarized America: The Dance of Ideology and Unequal Riches. MIT Press, Cambridge (2016)Google Scholar
  27. 27.
    Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  28. 28.
    Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)CrossRefGoogle Scholar
  29. 29.
    Poole, K.T., Rosenthal, H.: A spatial model for legislative roll call analysis. Am. J. Polit. Sci. 29(2), 357–384 (1985). Published by: Midwest Political Science Association St. Political Science 29(2), 357–384 (2008)CrossRefGoogle Scholar
  30. 30.
    Ross, T.J.: Fuzzy Logic with Engineering Applications, 2nd edn. Wiley, Hoboken (2004)zbMATHGoogle Scholar
  31. 31.
    Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, New York (1994)CrossRefGoogle Scholar
  32. 32.
    Waugh, A.S., Pei, L., Fowler, J.H., Mucha, P.J., Porter, M.A.: Party polarization in congress: a network science approach. arXiv preprint arXiv:0907.3509 (2009)
  33. 33.
    Zhang, Y., Friend, A.J., Traud, A.L., Porter, M.A., Fowler, J.H., Mucha, P.J.: Community structure in congressional cosponsorship networks. Phys. A Stat. Mech. Appl. 387(7), 1705–1712 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Andrew C. Phillips
    • 1
  • Mohammad T. Irfan
    • 1
    Email author
  • Luca Ostertag-Hill
    • 1
  1. 1.Bowdoin CollegeBrunswickUSA

Personalised recommendations