Universal dynamics of ranking

Gerardo Iñiguez, Carlos Pineda, Carlos Gershenson, Albert-László Barabási
Virtually anything can be and is ranked; people and animals, universities and countries, words and genes. Rankings reduce the components of highly complex systems into ordered lists, aiming to capture the fitness or ability of each element to perform relevant functions, and are being used from socioeconomic policy to knowledge extraction. A century of research has found regularities in ranking lists across nature and society when data is aggregated over time. Far less is known, however, about ranking dynamics, when the elements change their rank in time. To bridge this gap, here we explore the dynamics of 30 ranking lists in natural, social, economic, and infrastructural systems, comprising millions of elements, whose temporal scales span from minutes to centuries. We find that the flux governing the arrival of new elements into a ranking list reveals systems with identifiable patterns of stability: in high-flux systems only the top of the list is stable, while in low-flux systems the top and bottom are equally stable. We show that two basic mechanisms – displacement and replacement of elements – are sufficient to understand and quantify ranking dynamics. The model uncovers two regimes in the dynamics of ranking lists: a fast regime dominated by long-range rank changes, and a slow regime driven by diffusion. Our results indicate that the balance between robustness and adaptability characterizing the dynamics of complex systems might be governed by random processes irrespective of the details of each system.

Read the full article at: arxiv.org