Pareto ratio and Pareto principle

Gennagy Alexandrovich Grachev

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Pareto ratio and Pareto principle

G. A. Grachev

2020-12-14

https://doi.org/10.24108/preprints-3112147

In the late 19th century, Vilfredo Pareto published the results of his observations of wealth inequality in Italy as a ratio in which the numerator is equal to the share of population ranked in descending order of wealth, and the denominator is the share of wealth of the population. Both the form of presentation of the concentration of inequality in the form of a visual ratio (the Pareto ratio), and an unexpectedly large inequality (80/20), which became known as the Pareto principle. In the 21st century, a new concept was introduced - the generalized Pareto principle, which is understood as any proportion in which the sum of the numerator and denominator is 100%. As a result, an extraordinary situation arose, when the empirical regularity began to be identified with the measure of its measurement. To resolve this confusion, the definition of Pareto ratio is provided in this work, based on a generally accepted concept of "wealthy" element of the system, as also an alternative explanation of the Pareto principle is proposed with the use of isoperimetric inequalities conceptually related with the principle of least action.

Ссылка для цитирования:

Grachev G. A. 2020. Pareto ratio and Pareto principle. PREPRINTS.RU. https://doi.org/10.24108/preprints-3112147

Список литературы

1. [1] V. Pareto, Cours d’Économie Politique, Vol. I. Pp. 430. I896. Vol. II. Pp. 426. I897. Lausanne: F. Rouge, Ann. Am. Acad. Pol. Soc. Sci. 9 (1897) 128–131. https://doi.org/10.1177/000271629700900314.

2. [2] G.K. Zipf, Human behavior and the principle of least effort, Cambridge, (Mass.): Addison-Wesley, 1949. https://doi.org/10.1002/1097-4679(195007)6:3<306::aid-jclp2270060331>3.0.co;2-7.

3. [3] R. Koch, The 80/20 Principle: The Secret of Achieving More with Less, Nicholas Brealey Publishing, London, 1997.

4. [4] Г.А. Грачёв, Моделирование принципа Парето, 2011.

5. [5] J.M. Juran, The Non-Pareto Principle: Repentance, Quality Progress, New York, NY: American Society for Quality Control, May 1975, 1975.

6. [6] M.O. Lorenz, Methods of Measuring the Concentration of Wealth, 1905.

7. [7] C. Gini, Measurement of Inequality of Incomes, Econ. J. 31 (1921) 124. https://doi.org/10.2307/2223319.

8. [8] L. Osberg, On the Limitations of Some Current Usages of the Gini Index, Rev. Income Wealth. 63 (2017) 574–584. https://doi.org/10.1111/roiw.12256.

9. [9] I.I. Eliazar, I.M. Sokolov, Measuring statistical evenness: A panoramic overview, Phys. A Stat. Mech. Its Appl. 391 (2012) 1323–1353.

10. [10] N. Kakwani, Income inequality and poverty : methods of estimation and policy applications, Published for the World Bank [by] Oxford University Press, 1980.

11. [11] D. Herron, Industrial engineering applications of abc curves, AIIE Trans. 8 (1976) 210–218. https://doi.org/10.1080/05695557608975069.

12. [12] Q.L. Burrell, The 80/20 rule: Library lore or statistical law?, J. Doc. 41 (1985) 24. https://doi.org/10.1108/eb026772.

13. [13] H. Kumakura, Market Structure Analysis Using Birth and Asymmetric Growth of Products Based on a Mechanism of the 80/20 Law: Why and How the 80/20 Law Emerges, 2010.

14. [14] M. Goeminne, T. Mens, Evidence for the Pareto principle in Open Source Software Activit, in: First Int. Work. Model. Softw. Migr. (MDSM 2011) Fifth Int. Work. Softw. Qual. Maintainab. (SQM 2011), 2011: pp. 74–82.

15. [15] K. Tanabe, Pareto’s 80/20 rule and the Gaussian distribution, Phys. A Stat. Mech. Its Appl. 510 (2018) 635–640. https://doi.org/10.1016/j.physa.2018.07.023.

16. [16] L. Egghe, On the 80/20 rule, Scientometrics. 10 (1986) 55–68. https://doi.org/10.1007/BF02016860.

17. [17] Y.S. Chen, P.P. Chong, M.Y. Tong, Mathematical and computer modelling of the Pareto principle, Math. Comput. Model. (1994). https://doi.org/10.1016/0895-7177(94)90041-8.

18. [18] J.C.H. Chen, P.P. Chong, Y.S. Chen, Decision criteria consolidation: A theoretical foundation of pareto principle to porter’s competitive forces, J. Organ. Comput. Electron. Commer. 11 (2001) 1–14. https://doi.org/10.1207/S15327744JOCE1101_01.

19. [19] A. Ultsch, Proof of Pareto’s 80/20 Law and Precise Limits for ABC-Analysis, 2002.

20. [20] M.E.J. Newman, Power laws, Pareto distributions and Zipf’s law, (2004). https://doi.org/10.1016/j.cities.2012.03.001.

21. [21] И.Г. Царев, О моделировании распределения доходов в обществе, Прикладная Статистика. 3 (2008) 43–51.

22. [22] S. Lipovetsky, Pareto 80/20 law: Derivation via random partitioning, Int. J. Math. Educ. Sci. Technol. 40 (2009) 271–277. https://doi.org/10.1080/00207390802213609.

23. [23] M. Hardy, Pareto’s Law, Math. Intell. 32 (2010) 38–43. https://doi.org/10.1007/s00283-010-9159-2.

24. [24] S. Banerjee, B.K. Chakrabarti, M. Mitra, S. Mutuswami, On the Kolkata index as a measure of income inequality, Phys. A Stat. Mech. Its Appl. 545 (C) (2020). https://doi.org/10.1016/j.physa.2019.123178.

25. [25] Y.L. Klimontovich, Relative ordering criteria in open systems, Physics-Uspekhi. 39 (1996) 1169–1179. https://doi.org/10.1070/PU1996v039n11ABEH000181.

26. [26] D. Acemoglu, D. Autor, Skills, tasks and technologies: implications for employment and earnings, Cambridge, MA 02138, 2010. https://doi.org/http://www.nber.org/papers/w16082.

27. [27] H. Stanley, Introduction to phase transitions and critical phenomena, Oxford University Press, New York, 1971.

28. [28] R. Gibrat, Les Inégalités Économiques: Applications, aux Inégalités des Richesses, a la Concentration des Entreprises, aux Populations des Villes, aux Statistiques des Familles, etc.: d’une Loi Nouvelle la Loi de l’Effet Proportionnel, Recueil Sirey, Paris, 1931.

29. [29] P.E. Hart, S.J. Prais, The Analysis of Business Concentration: A Statistical Approach, J. R. Stat. Soc. Ser. A. 119 (1956) 150. https://doi.org/10.2307/2342882.

30. [30] G.A. Grachev, Size Distribution of States, Counties, and Cities in the USA: New Inequality Form Information, REPRINTS.RU. (2020). https://doi.org/https://doi.org/10.24108/preprints-3112131.

31. [31] Г.А. Грачёв, Системные закономерности неравенства доходов населения, Экономические Науки. (2009) 327–331.

32. [32] Г.А. Грачёв, Модель оптимального состояния системы городского расселения, Известия Российской Академии Наук. Серия Географическая. (2010) 46–51.

33. [33] Г.А. Грачёв, К оценке политической стабильности по результатам голосования на выборах, Полис. Политические Исследования. (2011) 123–127.

34. [34] Г.А. Грачёв, К прогнозированию оптимальной структуры российской банковской системы, Проблемы Прогнозирования. 22 (2011) 103–109.

35. [35] Г.А. Грачёв, К анализу структурной эффективности государственных союзов, Экономические Науки. (2011) 212–215.

36. [36] Г.А. Грачёв, Оценка политической стабильности на прошедших выборах парламента и президента России, Полис. Политические Исследования. (2012) 30–35.

37. [37] Г.А. Грачёв, Управление структурой денежных доходов населения на основе принципа Парето, Terra Econ. 11 (2013) 57–63.

38. [38] I.W. Burr, Cumulative Frequency Functions, Ann. Math. Stat. 13 (1942) 215–232. https://doi.org/10.1214/aoms/1177731607.

39. [39] A. Ghosh, N. Chattopadhyay, B.K. Chakrabarti, Inequality in societies, academic institutions and science journals: Gini and k-indices, Phys. A Stat. Mech. Its Appl. 410 (2014) 30–34. https://doi.org/10.1016/j.physa.2014.05.026.

40. [40] A. Chatterjee, A. Ghosh, B.K. Chakrabarti, Socio-economic inequality: Relationship between Gini and Kolkata indices, Phys. A Stat. Mech. Its Appl. 465 (2017) 583–595. https://doi.org/10.1016/j.physa.2016.09.027.

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