The European Physical Journal B

, Volume 71, Issue 2, pp 251–258 | Cite as

Universality in movie rating distributions

  • J. LorenzEmail author
Interdisciplinary Physics


In this paper histograms of user ratings for movies (1\(\bigstar\),...,10\(\bigstar\)) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either double- or triple-peaked. Moreover, at most one peak can be on the central bins 2\(\bigstar\),...,9\(\bigstar\) and the distribution in these bins looks smooth `Gaussian-like’ while changes at the extremes (1\(\bigstar\) and 10\(\bigstar\)) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of Lévy skew α-stable distributions. These distributions are the only stable distributions which could emerge due to a generalized central limit theorem from averaging of various independent random variables as which one can see the initial opinions of users. Averaging is also an appropriate assumption about the social process which underlies the process of continuous opinion formation. Surprisingly, not the normal distribution achieves the best fit over histograms observed on the web, but distributions with fat tails which decay as power-laws with exponent –(1+α) \((\alpha=\frac{4}{3})\). The scale and skewness parameters of the Lévy skew α-stable distributions seem to depend on the deviation from an average movie (with mean about 7.6\(\bigstar\)). The histogram of such an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skew. The skewness pronounces the deviation. This is used to construct a one parameter fit which gives some evidence of universality in processes of continuous opinion dynamics about taste.


89.20.Hh World Wide Web, Internet 89.75.Da Systems obeying scaling laws 


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  1. 1.
    S. Asch, Scientific American 193, 31 (1955)CrossRefGoogle Scholar
  2. 2.
    I. Lorge, D. Fox, J. Davitz, M. Brenner, Psychological Bulletin 55, 337 (1958)CrossRefGoogle Scholar
  3. 3.
    M. Sherif, C. Hovland, Social Judgment: Assimilation and Contrast Effects in Communication and Attitude Change (Yale University Press, New Haven, CT, 1961)Google Scholar
  4. 4.
    J. Forgas, European Journal of Social Psychology 7, 175 (1977)CrossRefGoogle Scholar
  5. 5.
    N. Friedkin, American Sociological Review 64, 856 (1999)CrossRefGoogle Scholar
  6. 6.
    M. Salganik, P. Dodds, D. Watts, Science 311, 854 (2006)CrossRefADSGoogle Scholar
  7. 7.
    W. Mason, F. Conrey, E. Smith, Personality and Social Psychology Review 11, 279 (2007)CrossRefGoogle Scholar
  8. 8.
    G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Advances in Complex Systems 3, 87 (2000)CrossRefGoogle Scholar
  9. 9.
    R. Hegselmann, U. Krause, Journal of Artificial Societies and Social Simulation 5, 2 (2002), Google Scholar
  10. 10.
    D. Urbig, Journal of Artificial Societies and Social Simulation 6, 2 (2003), Google Scholar
  11. 11.
    G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Journal of Artificial Societies and Social Simulation 5, (2002)Google Scholar
  12. 12.
    W. Jager, F. Amblard, Computational & Mathematical Organization Theory 10, 295 (2004)CrossRefGoogle Scholar
  13. 13.
    L. Salzarulo, Journal of Artificial Societies and Social Simulation 9, 13 (2006), Google Scholar
  14. 14.
    D. Baldassarri, P. Bearman, American Sociological Review 72, 784 (2007)CrossRefGoogle Scholar
  15. 15.
    D. Stauffer, AIP Conf. Proc. 779, 56 (2005)CrossRefADSGoogle Scholar
  16. 16.
    J. Lorenz, Int. J. Modern Physics C 18, 1819 (2007)zbMATHCrossRefADSGoogle Scholar
  17. 17.
    C. Castellano, S. Fortunato, V. Loreto, Rev. Modern Physics 81, 591 (2009)CrossRefADSGoogle Scholar
  18. 18.
    D. Turnbull, in CHI ’07: CHI ’07 extended abstracts on Human factors in computing systems (ACM, 2007), pp. 2705–2710Google Scholar
  19. 19.
    J. Lorenz, in Managing Complexity: Insights, Concepts, Applications, edited by D. Helbing (Springer, 2008)Google Scholar
  20. 20.
    C. Dellarocas, Management Science 49, 1407 (2003)CrossRefGoogle Scholar
  21. 21.
    K. Goldberg, T. Roeder, D. Gupta, C. Perkins, Information Retrieval 4, 133 (2001)zbMATHCrossRefGoogle Scholar
  22. 22.
    K. Cheung, J. Kwok, M. Law, K. Tsui, Decision Support Systems 35, 231 (2003)CrossRefGoogle Scholar
  23. 23.
    A. Umyarov, A. Tuzhilin, Leveraging aggregate ratings for better recommendations, in RecSys ’07: Proceedings of the 2007 ACM conference on Recommender systems (ACM, 2007), pp. 161–164Google Scholar
  24. 24.
    D.M. Chance, E. Hillebrand, J.E. Hilliard, Management Science 54, 1015 (2008)CrossRefGoogle Scholar
  25. 25.
    B.J. Jiang, P.Y. Chen, SSRN eLibrary (2007)Google Scholar
  26. 26.
    D. Cosley, S. Lam, I. Albert, J. Konstan, J. Riedl, Proceedings of the SIGCHI Conference on Human factors in computing systems, pp. 585–592 (2003)Google Scholar
  27. 27.
    X. Li, L.M. Hitt, Information Systems Research 19, 456 (2008)CrossRefGoogle Scholar
  28. 28.
    F. Wu, B.A. Huberman, Arxiv preprint [arXiv: 0805.3537] (2008)Google Scholar
  29. 29.
    C. Dellarocas, R. Narayan, Statistical Science 21, 277 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    C. Borghesi, J.P. Bouchaud, Quality and Quantity 41, 557 (2007)CrossRefGoogle Scholar
  31. 31.
    B. Gu, M. Lin, The Dynamics of Online Consumer Reviews, in Workshop on Information Systems and Economics (WISE) (2006)Google Scholar
  32. 32.
    I looked at all movies with more than 20 000 ratings on in March 2008. These were identified by IMDb “Power Search”-function. These were 1086 histogramsGoogle Scholar
  33. 33.
    J.P. Nolan, Stable Distributions — Models for Heavy Tailed Data (Birkhäuser, 2010), in progress, Chap. 1 online at∼jpnolanGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Chair of Systems Design, ETH Zürich, Kreuzplatz 5ZürichSwitzerland

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