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

Iddo Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)450-459
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Volume393
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Keywords

  • Critical exponents
  • Geometric distribution
  • Inverse-Pareto distribution
  • Macroscopic statistics
  • Rank distributions
  • Universality classes

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