The hypothesis of urban scaling: formalization, implications and challenges

TL;DR

This paper discusses the formalization and implications of the urban scaling hypothesis, which suggests that many city properties scale predictably with city size, supported by extensive empirical evidence and theoretical considerations.

Contribution

It formalizes the urban scaling hypothesis, reviews empirical evidence, and discusses methodological and theoretical challenges in understanding city properties as scale-invariant.

Findings

Cities exhibit predictable scaling laws across various properties.

Urban systems are non-extensive, affecting statistical modeling.

Methodological issues in measurement and analysis are identified.

Abstract

There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis of urban scaling, namely that certain properties of all cities change, on average, with their size in predictable scale-invariant ways. The emergence of these scaling relations depends on a few general properties of cities as social networks, co-located in space and time, that conceivably apply to a wide range of human settlements. Here, we discuss the present evidence for the hypothesis of urban scaling, some of the methodological issues dealing with proxy measurements and units of analysis and place these findings in the context of other theories of cities and urban systems. We show that a large body of evidence about the scaling properties of cities indicates, in analogy to other complex systems, that they cannot be treated as extensive systems and discuss the consequences of these results for an emerging statistical theory of cities.