The formation and stability of social hierarchies is a question of general relevance. Here, we propose a simple model for establishing social hierarchy via pair-wise interactions between individuals and investigate its stability. In each interaction or fight, the probability of "winning" depends solely on the relative societal status of the participants, and the winner has a gain of status whereas there is an equal loss to the loser. The interactions are characterized by two parameters. The first parameter (δ) represents how much can be lost, and the second parameter (α) represents the degree to which even a small difference of status can guarantee a win for the higher-status individual. Depending on the parameters, the resulting status distributions reach either a continuous unimodal form or lead to a totalitarian end state with one dominant high-status individual and all other individuals having zero status. However, we find that in the latter case long-lived intermediary distributions often exist, which can give the illusion of a stable society. Moreover, by implementing a simple, but realistic rule that restricts interactions to sufficiently similar-status individuals, the stable or long-lived distributions acquire high-status structure corresponding to a dominant class. We compare our model predictions to human societies using household income as a proxy for societal status and find agreement over their entire range from the low-to-middle-status parts to the characteristic high-status "tail". We discuss the model as a conceptual framework for understanding the origin of social hierarchy and the factors leading to the preservation or deterioration of the societal structure .