  In recent years it has been increasing evidence that lognormal distributions
are widespread in physical and biological sciences, as well as in various
phenomena of economics and social sciences. In social sciences, the appearance
of lognormal distribution has been noticed, among others, when looking at body
weight, and at women's age at first marriage. Likewise, in economics, lognormal
distribution appears when looking at consumption in a western society, at
call-center service times, and others. The common feature of these situations,
which describe the distribution of a certain people's hallmark, is the presence
of a desired target to be reached by repeated choices. In this paper we discuss
a possible explanation of lognormal distribution forming in human activities by
resorting to classical methods of statistical mechanics of multi-agent systems.
The microscopic variation of the hallmark around its target value, leading to a
linear Fokker--Planck type equation with lognormal equilibrium density, is
built up introducing as main criterion for decision a suitable value function
in the spirit of the prospect theory of Kahneman and Twersky.

Physics and Society