Status achieved in an organization -- rank dynamics

Abstract: A new model of an evolution of ranks of employees due to staff turnover in an organization is designed. If the rank is determined only by the performance, the rank shift of incumbents due to the turnover is proportional to the initial rank: the status of high staff is reduced only slightly. This effect that has been observed in the literature. However, if the status also depends on some other variable, the positions of high staff may be greatly deteriorated. In that case, the effect depends nonlinearly on the time $\tau$ between subsequent replacements of staff.