![]() ![]() While mechanisms of proportional growth 38, cumulative advantage 39, and preferential attachment 40 are often used to explain the heavy-tailed distributions of ranking lists at single points of time 41, 42, they fail to reproduce the way elements actually move in rank 43, such as the sudden changes in city size throughout history 44, 45. The similarity of score-rank distributions across systems raises the question of the existence of simple generative mechanisms behind them. Recently, studies of language use 17, 35, sports performance 36, and many biological and socioeconomic rankings 37 have strengthened the notion of universality suggested by Zipf’s law: despite microscopic differences in elements, scores, and types of interaction, the aggregate, macroscopic properties of ranking lists are remarkably similar throughout nature and society. Rankings have also proven useful when analyzing productivity and impact in science and the arts 7, 26, 27, 28, 29, in human urban mobility 30, 31, 32, epidemic spreading by influentials 33, and the development pathways of entire countries 34. Zipf’s law appears even in the score-rank distributions of natural systems, such as earthquakes 22, 23, DNA sequences 24, and metabolic networks 25. A heavy-tailed decay of score with rank, commonly known as Zipf’s law 8, 9, has been systematically observed in the ranking of cities by population 10, 11, words and phrases by frequency of use 12, 13, 14, 15, 16, 17, companies by size 18, 19, 20, and many features of the Internet 21. The statistical properties of ranking lists have caught the attention of natural and social scientists for more than a century. ![]() Since rankings often determine who gets access to resources (education, jobs, and funds), they play a role in the formation of social hierarchies 5, 6 and the potential rise of systematic inequality 7. Rankings are being used to identify the most accomplished individuals or institutions, and to find the essential pieces of knowledge or infrastructure in society 1. Rankings are, in this sense, a proxy of relevance or fitness to perform a function in the system. The ubiquity of rankings stems from the generality of their definition: reducing the (often high-dimensional) complexity of a system to a few or even a single measurable quantity of interest 3, 4, dubbed score, leads to an ordered list where elements are ranked, typically from highest to lowest score. From country development indices, academic indicators, and candidate poll numbers to music charts and sports scoreboards, rankings are key to how humans measure and make sense of the world 1, 2. Our results indicate that the balance between robustness and adaptability in ranked systems might be governed by simple random processes irrespective of system details. The model uncovers two regimes of behavior fast and large rank changes, or slow diffusion. We show that two basic mechanisms - displacement and replacement of elements - capture empirical ranking dynamics. 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. 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. Far less is known, however, about how rankings change in time. A century of research has found regularities when temporal rank data is aggregated. 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. ![]() Virtually anything can be and is ranked people, institutions, countries, words, genes. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |