Dynamics of ranking

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.

12 pages, 3 figures. SI: 40 pages, 22 figures

References in corpus (8)

• Understanding individual human mobility patterns
• The Building Blocks of Economic Complexity
• The Product Space Conditions the Development of Nations
• Diffusion of scientific credits and the ranking of scientists
• The Chaperone Effect in Scientific Publishing
• Dynamics of ranking
• Rank diversity of languages: Generic behavior in computational linguistics
• Consensus ranking for multi-objective interventions in multiplex networks

Cited by in corpus (14)

• Dynamics of ranking
• Temporal, structural, and functional heterogeneities extend criticality and antifragility in random Boolean networks
• Universal patterns in egocentric communication networks
• Heterogeneity extends criticality
• Competition for popularity and interventions on a Chinese microblogging site
• A perturbation-based approach to identifying potentially superfluous network constituents
• Temporal patterns of reciprocity in communication networks
• Economy importance and structural robustness of the international pesticide trade networks
• Measuring Equality and Hierarchical Mobility on Abstract Complex Networks
• Status achieved in an organization -- rank dynamics
• Language statistics at different spatial, temporal, and grammatical scales
• Universality of Top Rank Statistics for Brownian Reshuffling
• Stochastic equations and cities
• Equivalence of inequality indices in the three-dimensional model of informetric impact