### Sociological Inequality and the Second Law

#### Abstract

**Abstract. **There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power law distribution function yields an uneven distribution of particles in boxes. It is shown that the obtained distribution fits well to sociological phenomena, such as the distribution of votes in polls and the distribution of wealth and Benford's law.

**Keywords: **Maximum Entropy, Long tail distribution, 20:80 Pareto's rule, Zipf Law, Benford's law, Bell-like distribution.

**JEL. **C62.

#### Keywords

#### References

Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality, Springer-Verlag, New York.

Benford, F. (1938). The law of anomalous numbers, Proceedings of the American Mathematical Society, 78(4), 551-572.

Globes Newspaper, (2008). [Retrieved from]

Gunther, R., Levitin, L., Schapiro, B., & Wagner, P. (1996). Zipf's law and the effect of ranking on probability distributions, International Journal of Theoretical Physics, 35(2), 395-417. doi. 10.1007/BF02083823

Hill, T.P. (1986). The first digit phenomenon, American Scientist, 86(4), 358. doi. 10.1511/1998.4.358

Hill, T.P. (1996). A statistical derivation of the significant-digit law, Statistical Science, 10(4), 354-363.

Kafri, O., & Kafri, H. (2013). Entropy - God’s Dice Game. CreateSpace, pp. 154-157. [Retrieved from].

Kafri, O. (2007). The second Law as a Cause of the Evolution, Unpublished Paper, [Retrieved from].

Kafri, O. (2009). Entropy principle in direct derivation of Benford's law, Unpublished Paper, [Retrieved from].

Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson and RossStroudsburg.

Newman, M.E. (2006). Power-law, Pareto Distribution and Zipf's law, Unpublished Paper, [Retrieved from].

Planck, M. (1901). On the law of distribution of energy in the normal spectrum, Annalen der Physik, 4, 553-562.

Troll, G., & Graben, P.B. (1998). Zipf's law is not a consequence of the central limit theorem, Physical Review, 57(2), 1347-1355. doi. 10.1103/PhysRevE.57.1347

DOI: http://dx.doi.org/10.1453/jest.v3i4.1123

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