Inverted rank distributions: Macroscopic statistics, universality classes, and critical exponents

Iddo Eliazar and Morrel H. Cohen

Physica A: Statistical Mechanics and its Applications, 2014, vol. 393, issue C, 450-459

Abstract: An inverted rank distribution is an infinite sequence of positive sizes ordered in a monotone increasing fashion. Interlacing together Lorenzian and oligarchic asymptotic analyses, we establish a macroscopic classification of inverted rank distributions into five “socioeconomic” universality classes: communism, socialism, criticality, feudalism, and absolute monarchy. We further establish that: (i) communism and socialism are analogous to a “disordered phase”, feudalism and absolute monarchy are analogous to an “ordered phase”, and criticality is the “phase transition” between order and disorder; (ii) the universality classes are characterized by two critical exponents, one governing the ordered phase, and the other governing the disordered phase; (iii) communism, criticality, and absolute monarchy are characterized by sharp exponent values, and are inherently deterministic; (iv) socialism is characterized by a continuous exponent range, is inherently stochastic, and is universally governed by continuous power-law statistics; (v) feudalism is characterized by a continuous exponent range, is inherently stochastic, and is universally governed by discrete exponential statistics. The results presented in this paper yield a universal macroscopic socioeconophysical perspective of inverted rank distributions.

Keywords: Rank distributions; Macroscopic statistics; Universality classes; Critical exponents; Inverse-Pareto distribution; Geometric distribution (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:393:y:2014:i:c:p:450-459

DOI: 10.1016/j.physa.2013.08.073

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