66 research outputs found
Universality in movie rating distributions
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 formation.
Surprisingly, not the normal distribution achieves the best fit over histograms
obseved on the web, but distributions with fat tails which decay as power-laws
with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the
Levy skew alpha-stable distributions seem to depend on the deviation from an
average movie (with mean about 7.6). 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.Comment: 8 pages, 5 figures, accepted for publicatio
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