Self-organization and time-stability of social hierarchies

Abstract

The formation and stability of social hierarchies is a question of general relevance. Here, we propose a simple generalized theoretical 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 represents how much can be lost, and the second parameter 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 high-status individual and all other individuals having status approaching zero. However, we find that in the latter case long-lived intermediary distributions often exist, which can give the illusion of a stable society. As we show, our model allows us to make predictions consistent with animal interaction data and their evolution over a number of years. 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 distinct high-status class. Using household income as a proxy for societal status in human societies, we find agreement over their entire range from the low-to-middle-status parts to the characteristic high-status “tail”. We discuss how the model provides a conceptual framework for understanding the origin of social hierarchy and the factors which lead to the preservation or deterioration of the societal structure.

Unveiling dimensions of stability in complex ecological networks

“…Acronym [equation in (time scale) SI Appendix, section 10] Description Reactivity (initial) R 0 [6], MR 0 [11] Maximum instantaneous rate at which perturbations can be amplified.…”

“…S tability has been a core topic of research in complex systems across disciplines. From socioeconomic models of political regimes (1,2), to financial systems (3)(4)(5), social organizations (6,7), or biological systems of genetic regulatory circuits (8,9), the study of dynamical stability keeps drawing the attention of the scientific community. This interest has been particularly prominent in ecology, where it has fuelled decades of research (10)(11)(12)(13)(14)(15)).…”

Emergence of hierarchy in networked endorsement dynamics

“…Empirical studies have indicated the presence of a "winner effect": An individual who participates in a favorable interaction, such as winning a fight or receiving an endorsement, increases their likelihood of being favored in future interactions (10,11). Both theoretical work (12)(13)(14)(15)(16)(17)(18)(19)(20) and controlled experiments in humans (21) suggest that winner effects are sufficient (though not necessary) to form stable hierarchies. Mechanistic explanations of winner effects vary.…”

Emergence of Hierarchy in Networked Endorsement Dynamics

“…Empirical studies have indicated the presence of a winner effect: an individual who participates in a favorable interaction, such as winning a fight or receiving an endorsement, increases their likelihood of being favored in future interactions [Chase et al, 1994;Hogeweg and Hesper, 1983]. Both theoretical work [Bonabeau et al, 1995[Bonabeau et al, , 1996Hemelrijk, 1999;Ben-Naim and Redner, 2005;Miyaguchi et al, 2020;Pósfai and D'Souza, 2018;Hickey and Davidsen, 2019;Vehrencamp, 1983;Sánchez-Tójar et al, 2018] and controlled experiments in humans [Salganik et al, 2006] suggest that winner effects are sufficient (though not necessary) to form stable hierarchies. Mechanistic explanations of winner effects vary.…”