# American Institute of Mathematical Sciences

June  2016, 21(4): 1149-1166. doi: 10.3934/dcdsb.2016.21.1149

## The 20-60-20 rule

 1 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland 2 Institute of Mathematics, Jagiellonian University, S. Łojasiewicza 6, 30-348 Kraków, Poland

Received  June 2015 Published  March 2016

In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio often implies some sort of balance. From practical point of view, this feature leads to efficient management or control. We provide a mathematical illustration, justifying the occurrence of this rule in many real world situations. We show that for any population, which could be described using multivariate normal vector, this fixed ratio leads to a global equilibrium state, when dispersion and linear dependance measurement is considered.
Citation: Piotr Jaworski, Marcin Pitera. The 20-60-20 rule. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1149-1166. doi: 10.3934/dcdsb.2016.21.1149
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##### References:
 [1] S. Annunzio, E-leadership - proven techniques for creating an environment of speed and flexibility in the digital economy, Human Resource Management, 40 (2001), 381-383. [2] D. Bach, Start Late, Finish Rich: A No-fail Plan for Achieving Financial Freedom at Any Age, Crown Business, 2005. [3] B. Bolger, Ten steps to designing an effective incentive program, Employment Relations Today, 31 (2004), 25-33. doi: 10.1002/ert.20003. [4] J. Creelman, An act of faith, The TQM Magazine, 5 (1993). doi: 10.1108/EUM0000000003073. [5] D. Dupper, School Social Work: Skills and Interventions for Effective Practice, John Wiley & Sons, 2002. [6] E. Gómez, M. A. Gómez-Villegas and J. M. Marín, A survey on continuous elliptical vector distributions, Revista matemática complutense, 16 (2003), 345-361. doi: 10.5209/rev_REMA.2003.v16.n1.16889. [7] M. A. Grey and A. C. Woodrick, Latinos have revitalized our community: Mexican migration and Anglo responses in Marshalltown, Iowa, in New destinations: Mexican immigration in the United States, (2005), 133-154. [8] L. M. Hinman, The impact of the internet on our moral lives in academia, Ethics and information technology, 4 (2002), 31-35. [9] P. Jaworski and M. Pitera, On spatial contagion and multivariate GARCH models, Applied Stochastic Models in Business and Industry, 30 (2014), 303-327. doi: 10.1002/asmb.1977. [10] N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, John Wiley & Sons, 1994. [11] A. Kamiya, F. Makino, and S. Kobayashi, Worker ants' rule-based genetic algorithms dealing with changing environments, in Proceedings of IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications (SMCia/05), 2005, 117-121. doi: 10.1109/SMCIA.2005.1466958. [12] R. B. Nelsen, An Introduction to Copulas, Springer, 2006. [13] L. Robinson, A summary of diffusion of innovations - Enabling Change., 2009. Available from: , (). [14] J. Slagell and J. Holtermann, Climbing peaks and navigating valleys: Managing personnel from high altitude, The Serials Librarian, 52 (2007), 271-275. doi: 10.1300/J123v52n03_04. [15] S. A. Tynan, Best behaviors, Management Review, 88 (1999), 58-61.
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