Lognormal distributions of user post lengths in Internet discussions - a consequence of the Weber-Fechner law?

Abstract

The paper presents an analysis of the length of comments posted in Internet discussion fora, based on a collection of large datasets from several sources. We found that despite differences in the forum language, the discussed topics and user emotions, the comment length distributions are very regular and described by the lognormal form with a very high precision. We discuss possible origins of this regularity and the existence of a universal mechanism deciding the length of the user posts. We suggest that the observed lognormal dependence may be due to an entropy maximizing combination of two psychological factors which are perceived on a non-linear, logarithmic scale in accordance with the Weber-Fechner law, namely the time spent on post related considerations and the comment length itself. This hypothesis is supported by an experimental check of text length recognition capacity, confirming proportionality of the ‘just noticeable differences’ for text lengths - the basis of the Weber-Fechner law.