## 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 language | English (US) |
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Pages (from-to) | 450-459 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 393 |

DOIs | |

State | Published - 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