Universality in movie rating distributions
Jan Lorenz

TL;DR
This paper analyzes user rating histograms for movies, revealing they follow stable, double- or triple-peaked distributions well modeled by Levy skew alpha-stable distributions, indicating a universal pattern in opinion formation.
Contribution
It demonstrates that movie rating distributions are best approximated by Levy skew alpha-stable distributions, highlighting a universal pattern in opinion dynamics and challenging the normal distribution assumption.
Findings
Rating histograms are double- or triple-peaked with smooth central peaks.
Levy skew alpha-stable distributions fit the data better than normal distributions.
Distribution skewness correlates with deviation from average movie ratings.
Abstract
In this paper histograms of user ratings for movies (1,...,10) 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,...,9 and the distribution in these bins looks smooth `Gaussian-like' while changes at the extremes (1 and 10) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of L\'evy skew alpha-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 avriables 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…
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