Dynamics of ranking

TL;DR

This paper investigates how rankings in various systems evolve over time, revealing that the stability of rankings depends on the flux of new elements and that simple stochastic mechanisms can explain different dynamic regimes.

Contribution

It introduces a comprehensive analysis of ranking dynamics across diverse systems and proposes a minimal model capturing key empirical behaviors.

Findings

High flux leads to unstable lower ranks but stable top ranks.

Displacement and replacement are key mechanisms in ranking changes.

Two regimes of ranking behavior: rapid changes and slow diffusion.

Abstract

Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from socioeconomic policy to knowledge extraction. A century of research has found regularities when temporal rank data is aggregated. Far less is known, however, about how rankings change in time. Here we explore the dynamics of 30 rankings in natural, social, economic, and infrastructural systems, comprising millions of elements and timescales from minutes to centuries. We find that the flux of new elements determines the stability of a ranking: for high flux only the top of the list is stable, otherwise top and bottom are equally stable. We show that two basic mechanisms - displacement and replacement of elements - capture empirical ranking dynamics. The model uncovers two regimes of behavior; fast and large rank changes, or slow diffusion. Our results indicate that the balance between robustness and adaptability in ranked systems might be governed by simple random processes irrespective of system details.