2004), ”A finitary characterization of the Ewens sampling formula

The clustering of agents in the market is a typical problem dealt with by the new approaches to macroeconomic modeling, that describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering has a lot of economical interpreta-tions [3], that are often described by Ewens Sampling Formula (ESF). This formula can be traced back to Fisher as “species sampling”, and its main use was restricted to Genetics for a long time. Contrary to the usual complex derivations [17], we suggest a finitary characterization of the ESF pointing to real economic processes. Our approach is finitary in the sense that we probabilize a system of n individuals considered as a closed system, a population, where individuals can change attributes as time moves on. The intuitive meaning of the probability is the frac-tion of time the system spends in the considered state of clustering. As ESF is an equilibrium distribution satisfying the detailed balance, some cumbersome properties are derived in a simple way.