Physics > Physics and Society
[Submitted on 27 Apr 2021 (v1), last revised 11 Apr 2022 (this version, v2)]
Title:Dynamics of ranking
View PDFAbstract: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.
Submission history
From: Gerardo Iñiguez [view email][v1] Tue, 27 Apr 2021 19:22:11 UTC (1,439 KB)
[v2] Mon, 11 Apr 2022 14:46:00 UTC (1,638 KB)
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