In this paper histograms of user ratings for movies (1*,...,10*) are analysed. The evolvingstabilised 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 iswell approximated under the assumption that histograms are confined and discretised probability densityfunctions of Levy skew a-stable distributions. These distributions are the only stable distributions whichcould emerge due to a generalized central limit theorem from averaging of various independent randomvariables as which one can see the initial opinions of users. Averaging is also an appropriate assumptionabout the social process which underlies the process of continuous opinion formation. Surprisingly, notthe normal distribution achieves the best fit over histograms observed on the web, but distributions withfat tails which decay as power-laws with exponent-(1 + α) (α =4/3). The scale and skewness parametersof the Levy skew a-stable distributions seem to depend on the deviation from an average movie (withmean about 7.6*). The histogram of such an average movie has no skewness and is the most narrowone. If a movie deviates from average the distribution gets broader and skew. The skewness pronouncesthe deviation. This is used to construct a one parameter fit which gives some evidence of universality inprocesses of continuous opinion dynamics about taste.
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