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.

PACS

89.20.Hh World Wide Web, Internet89.75.Da Systems obeying scaling laws