The 20/80 Rule as a Dimensional Effect in Resource Distribution

Gennady Aleksandrovich Grachev

ПРЕПРИНТ

Эта статья является препринтом и не была отрецензирована.
О результатах, изложенных в препринтах, не следует сообщать в СМИ как о проверенной информации.

The 20/80 Rule as a Dimensional Effect in Resource Distribution

G. A. Grachev

2026-03-27

https://doi.org/10.24108/preprints-3114724

This paper proposes a dimensional approach to the interpretation of empirical regularities in resource concentration within systems. The central characteristic is the concentration function, which specifies the share of the resource belonging to the upper proportion of elements ranked in descending order of contribution. For the analytical study, a simple geometric model is employed — a conical sand heap — in which, for the same carrier structure, different observable quantities may be considered: volume (mass), surface area, equivalent linear scale, and potential energy. It is shown that the corresponding concentration functions do not coincide and are determined not only by the ordering of the elements but also by the dimensionality of the effect under consideration. On this basis, the 20/80 rule is interpreted not as a universal numerical constant but as a special case within a broader class of concentration relations arising from a particular mapping of the resource onto the linear scale of its carrier. In addition, the paper discusses the relationship between symmetric parametric models and the Gini coefficient, as well as the possibility of using such models for the normative description of income and wealth distributions.

Ссылка для цитирования:

Grachev G. A. 2026. The 20/80 Rule as a Dimensional Effect in Resource Distribution. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114724

Список литературы

1. [1] V. Pareto, Cours d’Économie Politique, vols. 1 and 2, F. Rouge, Lausanne, 1896–1897.

2. [2] J.M. Juran, The Non-Pareto Principle; mea culpa, Qual. Prog. 8 (5) (1975) 8–9.

3. [3] J.M. Juran, Juran’s Quality Control, McGraw-Hill, New York, 1951.

4. [4] J.M. Juran, Universals in management planning and controlling, Manage. Rev. 43 (11) (1954) 748–761.

5. [5] G.A. Grachev, Modelling the Pareto Principle, Southern Federal University, Rostov-on-Don, 2011, 223 p.

6. [6] G.A. Grachev, Managing the Structure of Household Monetary Incomes on the Basis of the Pareto Principle, Terra Econ. 11 (1) (2013) 57–63.

7. [7] G.A. Grachev, Size distribution of states, counties, and cities in the USA: New inequality form information, Physica A 592 (2022) 126831. https://doi.org/10.1016/j.physa.2021.126831.

8. [8] G.K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, MA, 1949.

9. [9] M.E.J. Newman, Power laws, Pareto distributions and Zipf’s law, Contemp. Phys. 46 (5) (2005) 323–351.

10. [10] S.A. Krashakov, A.B. Teslyuk, L.N. Shchur, On the universality of the rank distribution of web-server popularity, Vestn. RFFI 35 (1) (2004) 46–66.

11. [11] G.A. Grachev, Pareto Principle: Predictable Resource Concentrations in Self-Organising Systems, Southern Federal University Press, Rostov-on-Don–Taganrog, 2024, 102 p.

12. [12] P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59 (4) (1987) 381–384.

13. [13] P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality, Phys. Rev. A 38 (1) (1988) 364–374.

14. [14] B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, San Francisco, 1982.

15. [15] I.W. Burr, Cumulative frequency functions, Ann. Math. Stat. 13 (2) (1942) 215–232.

16. [16] N. Kakwani, Income Inequality and Poverty: Methods of Estimation and Policy Applications, Oxford University Press, Oxford, 1980.

17. [17] V.V. Matokhin, Algebra of Control, Moscow, 1994, 12 p.

18. [18] A.V. Kryanev, V.V. Matokhin, S.G. Klimanov, Statistical Functions of Resource Distribution in Economics: 010–98, Moscow, 1998, 15 p.

19. [19] I. Antoniou, V.V. Ivanov, Yu.L. Korolev, A.V. Kryanev, V.V. Matokhin, Z. Suchanecki, Analysis of resources distribution in economics based on entropy, Physica A 304 (3) (2002) 525–534. https://doi.org/10.1016/S0378-4371(01)00575-1.

20. [20] I. Antoniou, V.V. Ivanov, A.V. Kryanev, V.V. Matokhin, M.V. Shapovalov, On the efficient resources distribution in economics based on entropy, Physica A 336 (3–4) (2004) 549–562. https://doi.org/10.1016/j.physa.2003.12.051.

21. [21] J.M. Henle, N.J. Horton, S.J. Jakus, Modelling inequality with a single parameter, in: D. Chotikapanich (Ed.), Modeling Income Distributions and Lorenz Curves, Springer, New York, 2008, pp. 255–269.

22. [22] J.M. Sarabia, V. Jordá, C. Trueba, The Lamé class of Lorenz curves, Commun. Stat. Theory Methods 46 (11) (2017) 5311–5326. https://doi.org/10.1080/03610926.2013.775306.

23. [23] B.C. Arnold, Majorization and the Lorenz Order: A Brief Introduction, Springer, New York, 1987.

24. [24] E.M. Hoover, The measurement of industrial localization, Rev. Econ. Stat. 18 (1936) 162–171.

25. [25] K. Tanabe, Pareto’s 80/20 rule and the Gaussian distribution, Physica A 510 (2018) 635–640. https://doi.org/10.1016/j.physa.2018.07.023.

26. [26] P.K. Rawlings, D. Reguera, H. Reiss, Entropic basis of the Pareto law, Physica A 343 (2004) 643–652. https://doi.org/10.1016/j.physa.2004.06.152.

27. [27] S. Banerjee, B.K. Chakrabarti, M. Mitra, S. Mutuswami, On the Kolkata index as a measure of income inequality, Physica A 545 (2020) 123178. https://doi.org/10.1016/j.physa.2019.123178.

28. [28] Special issue: Inequalities in Socio-Economic, Bio-Medical & Physical Systems: a statistical physics perspective, Physica A, 2025.

29. [29] Board of Governors of the Federal Reserve System, Distributional Financial Accounts Overview, Federal Reserve, 2026.

30. [30] M.M. Batty, J. Bricker, J.S. Briggs, E. Holmquist, S. McIntosh, K.B. Moore, E.R. Nielsen, S. Reber, M. Shatto, K. Sommer, T. Sweeney, A.H. Volz, Introducing the Distributional Financial Accounts of the United States, Finance and Economics Discussion Series 2019-017 (2019). https://doi.org/10.17016/FEDS.2019.017.

31. [31] J. Bricker, S. Goodman, K.B. Moore, A.H. Volz, Wealth and Income Concentration in the SCF: 1989–2019, FEDS Notes (2020). https://doi.org/10.17016/2380-7172.2795.

32. [32] M. Kollar, Z. Scherer, Income in the United States: 2024, Current Population Reports P60-286, U.S. Census Bureau, Washington, DC, 2025.

ПРЕПРИНТ

ИНФОРМАЦИЯ

Использование куки-файлов