Cross Ranking of Cities and Regions: Population vs. Income

This paper explores the relationship between the inner economical of communities and their population distribution through a rank–rank of official data, along statistical physics ideas within two techniques. data is taken on Italian cities. The analysis is performed both at a global (national) and at a more local (regional) level in order to distinguish ‘macro’ and ‘micro’ aspects. First, the rank-size rule is found not to be a standard power law, in many other studies, but a doubly decreasing power law. Next, the Kendall τ the Spearman ρ rank correlation coefficients which measure pair concordance the correlation between fluctuations in two rankings, respectively, —as a function does in thermodynamics, are calculated for finding rank (if any) between demography and wealth. Results show non only disparities for the whole (country) set, but also (regional) disparities, when the number of cities in regions, the number of inhabitants in cities and in regions, as well as when comparing the aggregated tax income of the cities that of regions. Different outliers are pointed out and justified. Interestingly, classes of cities in the country and two classes of regions in the country found. ‘Common sense’ social, political, and economic considerations sustain findings. More importantly, the methods show that they allow to distinguish, very clearly, when specific criteria are numerically sound. A specific for the findings is presented, i. e. for the doubly decreasing power law the two phase system, based on statistics theory, e. g. urn filling. The model can be expected to hold when similar rank relationship features are observed fields. It is emphasized that the analysis makes more sense than one through Pearson Π value–value correlation analysis