SKM 2021 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 4: Dynamics and Scaling of Cities and Societies
SOE 4.1: Topical Talk
Donnerstag, 30. September 2021, 10:00–10:30, H3
Felix Auerbach and Zipf’s Law for Cities — •Diego Rybski1,2,3 und Antonio Ciccone4 — 1Potsdam Institute for Climate Impact Research - PIK, Member of Leibniz Association, P.O. Box 60 12 03, Potsdam 14412, Germany — 2University of California Berkeley, Department of Environmental Science, Policy and Management, 130 Mulford Hall #3114, Berkeley, CA 94720, USA — 3Complexity Science Hub Vienna, Josefstädterstrasse 39, A-1090 Vienna, Austria — 4Department of Economics, University of Mannheim, Mannheim, Germany
Power-law city size distributions are a statistical regularity researched in many countries and urban systems. In this history of science treatise we reconsider the paper by F. Auerbach published in 1913. Therefore, we review his empirical analysis and find (i) that a constant absolute concentration (AK), as introduced by him, is equivalent to a power-law distribution with exponent ≈ 1, (ii) the value of his AK relates to the size of the largest city, and (iii) the specific concentration (SpK), as also introduced by Auerbach, relates to the number of cities. We further investigate his legacy as reflected in citations and find that important follow-up work does give proper reference to his discovery – but other does not. A bibliographic analysis shows that almost all city-related works that cite Auerbach 1913 also cite Zipf 1949. However, only approximately 20 % of works citing Zipf 1949 also cite Auerbach 1913. To our best knowledge A.J. Lotka 1925 was the first to describe the power-law rank-size rule. Consequently, we suggest to use “Auerbach-Lotka-Zipf law” (or “ALZ-law”) instead of “Zipf’s law for cities”.