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	Urban Scaling Laws	Rank-Size Rule
分野	Urban Studies	Human Geography
系統	Regression model	Process / pipeline
提唱年	2007	1949
提唱者	Luís Bettencourt & Geoffrey West	George Kingsley Zipf
種類	Power-law regression of urban indicators against population size	Empirical regularity and diagnostic for the size distribution of cities
原典	Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C., & West, G. B. (2007). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences, 104(17), 7301–7306.	Zipf, G. K. (1949). Human Behavior and the Principle of Least Effort. Addison-Wesley, Cambridge, MA. ISBN: 9781614273790
別名	Urban Scaling, Settlement Scaling Theory, Power-Law Urban Scaling, Superlinear and Sublinear Urban Scaling	Zipf's Law for Cities, Rank-Size Distribution, City-Size Rank-Size Relationship, Rank-Size Regularity
関連	4	4
概要	Urban scaling laws describe how the aggregate properties of cities — wealth, innovation, infrastructure, crime — change systematically with population size, following power laws rather than growing in simple proportion. Building on the 2007 work of Luís Bettencourt, Geoffrey West and colleagues, the framework shows that socioeconomic outputs typically scale superlinearly (a doubling of population more than doubles GDP and patents) while infrastructure scales sublinearly (larger cities need proportionally fewer roads and cables per person), with a single exponent β capturing the regularity across an entire urban system.	The rank-size rule is an empirical regularity describing the size distribution of cities within a country or region. In its simplest form, popularized by George Kingsley Zipf in 1949, the population of a city is inversely proportional to its rank, so the second-largest city is about half the size of the largest, the third about a third, and so on. Generalized to a power law with an exponent q, it provides a compact way to summarize how evenly or unevenly population is spread across a settlement system and to diagnose urban primacy.