Universality of movie rating distributions

The histograms of user ratings (1F, . . . , 10F) on the Internet Movie Database (IMDb.com) which are in a mature state (more than 20, 000 ratings) seem to follow common rules. All are either double or triple peaked. Moreover, at most one peak can be on the central bins 2F, . . . , 9F and the distribution in these bins looks smooth `Gaussian-like' while changes at the extremes the often look abrupt. This is well approximated under the assumption that histograms are con ned 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 we see 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 t over the dataset of 1, 086 movies, but distributions with fat tails which decay as power-laws with exponent −(1+α) (α = 4 3 ). Parameters of the Lévy skew α-stable distributions seem to depend on the deviation from an average movie (with mean about 7.6F). The histogram of an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skewness appears which pronounces the deviation. This is used to construct a one parameter t which gives some evidence of universality in processes of continuous opinion dynamics about taste.