A finitary characterization of the Ewens sampling formula

The clustering of agents i is subject to many economic interpretations, often described by the Ewens Sampling Formula (ESF). In contrast with the usual complex derivations, our approach is finitary in the sense that we provide a probabilistic description of a system of n individuals considered as a closed system, a population, where individuals can change attributes over time. The probability is understood as the fraction of time the system spends in the considered partition. As the ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way.