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Entropy 2013, 15(6), 1985-1998; doi:10.3390/e15061985

Inequality of Chances as a Symmetry Phase Transition

Institut National de Sciences Appliquées, 20 Avenue des Buttes de Coësmes F-35708 Rennes Cedex 7, France
Received: 7 February 2013 / Revised: 27 April 2013 / Accepted: 15 May 2013 / Published: 23 May 2013
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We propose a model for Lorenz curves. It provides two-parameter fits to data on incomes, electric consumption, life expectation and rate of survival after cancer. Graphs result from the condition of maximum entropy and from the symmetry of statistical distributions. Differences in populations composing a binary system (poor and rich, young and old, etc.) bring about chance inequality. Symmetrical distributions insure equality of chances, generate Gini coefficients Gi £ ⅓, and imply that nobody gets more than twice the per capita benefit. Graphs generated by different symmetric distributions, but having the same Gini coefficient, intersect an even number of times. The change toward asymmetric distributions follows the pattern set by second-order phase transitions in physics, in particular universality: Lorenz plots reduce to a single universal curve after normalisation and scaling. The order parameter is the difference between cumulated benefit fractions for equal and unequal chances. The model also introduces new parameters: a cohesion range describing the extent of apparent equality in an unequal society, a poor-rich asymmetry parameter, and a new Gini-like indicator that measures unequal-chance inequality and admits a theoretical expression in closed form.
Keywords: Lorenz plots; inequality of chances; symmetry; phase transition; maximum entropy; Gini coefficient Lorenz plots; inequality of chances; symmetry; phase transition; maximum entropy; Gini coefficient

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Rosenblatt, J. Inequality of Chances as a Symmetry Phase Transition. Entropy 2013, 15, 1985-1998.

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