# 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 & Continuous Dynamical Systems - B, 2016, 21 (4) : 1149-1166. doi: 10.3934/dcdsb.2016.21.1149
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##### References:
 [1] Carlo Cercignani. The Boltzmann equation in the 20th century. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 83-94. doi: 10.3934/dcds.2009.24.83 [2] Abraão D. C. Nascimento, Leandro C. Rêgo, Raphaela L. B. A. Nascimento. Compound truncated Poisson normal distribution: Mathematical properties and Moment estimation. Inverse Problems & Imaging, 2019, 13 (4) : 787-803. doi: 10.3934/ipi.2019036 [3] Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6581-6597. doi: 10.3934/dcds.2016085 [4] Zheng Yin, Ercai Chen. The conditional variational principle for maps with the pseudo-orbit tracing property. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 463-481. doi: 10.3934/dcds.2019019 [5] Josef Hofbauer, Rida Laraki, Jérôme Renault. Preface: Special Issue in Honor of the 60th Birthday of Sylvain Sorin. Journal of Dynamics & Games, 2014, 1 (3) : i-iv. doi: 10.3934/jdg.2014.1.3i [6] Luis Alberto Fernández, Mariano Mateos, Cecilia Pola, Fredi Tröltzsch, Enrique Zuazua. Preface: A tribute to professor Eduardo Casas on his 60th birthday. Mathematical Control & Related Fields, 2018, 8 (1) : i-ii. doi: 10.3934/mcrf.201801i [7] Hongwei Lou, Qi Lü, Gengsheng Wang, Xu Zhang. Preface: A tribute to professor Jiongmin Yong on his 60th birthday. Mathematical Control & Related Fields, 2018, 8 (3&4) : ⅰ-ⅰ. doi: 10.3934/mcrf.201803i [8] Wenqing Hu, Chris Junchi Li. A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 4951-4977. doi: 10.3934/dcds.2018216 [9] H. O. Fattorini. The maximum principle in infinite dimension. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557 [10] Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367 [11] Chiun-Chuan Chen, Li-Chang Hung, Hsiao-Feng Liu. N-barrier maximum principle for degenerate elliptic systems and its application. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 791-821. doi: 10.3934/dcds.2018034 [12] Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897 [13] Hal L. Smith. Tribute to Horst R. Thieme on the occasion of his 60th birthday. Mathematical Biosciences & Engineering, 2010, 7 (1) : i-iii. doi: 10.3934/mbe.2010.7.1i [14] Goro Akagi, Jun Kobayashi, Mitsuharu Ôtani. Principle of symmetric criticality and evolution equations. Conference Publications, 2003, 2003 (Special) : 1-10. doi: 10.3934/proc.2003.2003.1 [15] Peng Gao, Yong Li. Averaging principle for the Schrödinger equations†. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2147-2168. doi: 10.3934/dcdsb.2017089 [16] Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 735-742. doi: 10.3934/cpaa.2005.4.735 [17] Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5499-5519. doi: 10.3934/dcds.2015.35.5499 [18] Baojun Bian, Pengfei Guan. A structural condition for microscopic convexity principle. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 789-807. doi: 10.3934/dcds.2010.28.789 [19] Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309 [20] Robert Stephen Cantrell, Suzanne Lenhart, Yuan Lou, Shigui Ruan. Preface on the special issue of Discrete and Continuous Dynamical Systems- Series B in honor of Chris Cosner on the occasion of his 60th birthday. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : i-ii. doi: 10.3934/dcdsb.2014.19.1i

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