Pareto principle

The Pareto principle states that for many outcomes roughly 80% of consequences come from 20% of the causes (the “vital few”).[1] Other names for this principle are the 80/20 rule, the law of the vital few, or the principle of factor sparsity.[2][3]

Pareto principle applied to raising funds

Management consultant Joseph M. Juran developed the concept in the context of quality control, and improvement, naming it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896. In his first work, Cours d'économie politique, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to Pareto efficiency.

Mathematically, the 80/20 rule is roughly described by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown to exhibit such a distribution.[4] It is an axiom of business management that "80% of sales come from 20% of clients".[5]

In economicsEdit

Pareto's observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population.[6] He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.

A chart that gave the effect a very visible and comprehensible form, the so-called "champagne glass" effect,[7] was contained in the 1992 United Nations Development Program Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population generating 82.7% of the world's income.[8] Among nations, the Gini index shows that wealth distributions vary substantially around this norm.

Distribution of world GDP, 1989[9]
Quintile of population Income
Richest 20% 82.70%
Second 20% 11.75%
Third 20% 2.30%
Fourth 20% 1.85%
Poorest 20% 1.40%

The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners paid roughly 80-90% of Federal income taxes in 2000 and 2006,[10] and again in 2018.[11]

The causes of wealth owing so much to the "vital few" have been attributed to distributions of multiple talents, with the few having all the required talents and environments leading production in a meritocracy. Others have suggested that it may result from chance, Alessandro Pluchino at the Italian University of Catania suggesting that “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.[12]

The principle also holds within the tails of the distribution. The physicist Victor Yakovenko of the University of Maryland, College Park and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) also follows Pareto's principle.[13]

In computingEdit

In computer science the Pareto principle can be applied to optimization efforts.[14] For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.[15] Lowell Arthur expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!"[16] It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of COCOMO estimating for software coding.

In sportsEdit

It has been argued that the Pareto principle applies to sport, where leading players often take the majority of wins. For instance in baseball, the Pareto principle is reflected in Wins Above Replacement (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."[17] It has been suggested (but not tested) that the principle applies to training, with 20% of exercises and habits having 80% of the impact, suggesting trainees should reduce the variety of training exercises to focus on this effective set.[18]

Occupational health and safetyEdit

Occupational health and safety professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.[19]

Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.[20]

Other applicationsEdit

Engineering and quality control

The Pareto principle has many applications in quality control where it was first created.[21] It is the basis for the Pareto chart, one of the key tools used in total quality control and Six Sigma techniques. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.[22] In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.[14]

In the systems science discipline, Joshua M. Epstein and Robert Axtell created an agent-based simulation model called Sugarscape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle emerged in their results, which suggests the principle is a collective consequence of these individual rules.[23]

Health and social outcomes

In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.[24][25][26]. The Dunedin Study has found 80% of crimes are committed by 20% of criminals.[27] This statistic has been used to support both stop-and-frisk policies and broken windows policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.

Some cases of super-spreading conform to the 20/80 rule,[28] where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions.[29] In epidemics with super-spreading, the majority of individuals infect relatively few secondary contacts.

General Distribution Operations

The pareto principle is often referred to in distribution operations, normally called the 80-20 rule. In distribution operations it is common to observe that 80 percent of the production volume constitute 20 percent of the SKUs. During facility design, this rule often governs the storage area and processing area configurations.

Product Lines

Many video rental shops reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "Gone with the Wind syndrome", however, in which every store had to offer classics like Gone with the Wind, Casablanca, or The African Queen to appear to have a large inventory, even if customers very rarely rented them.[30]

Mathematical notesEdit

Valid application of the rule requires demonstrating not that one can explain most of the variance or that some small set of observations are explained by a small proportion of process variables. rather that a large proportion of process variation is associated with a small proportion of the process variables. [3]

This is a special case of the wider phenomenon of Pareto distributions. If the Pareto index α, which is one of the parameters characterizing a Pareto distribution, is chosen as α = log45 ≈ 1.16, then one has 80% of effects coming from 20% of causes.

It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.

The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.

The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 90/10 or 70/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.

Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is extremely imbalanced, 80:20 is highly imbalanced (Gini index: 76%), 70:30 is moderately imbalanced (Gini index: 28%), and 55:45 is just slightly imbalanced (Gini index 14%).

The Pareto principle is an illustration of a "power law" relationship, which also occurs in phenomena such as brush fires and earthquakes.[31] Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from Normal or Gaussian distribution phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to something like stock price movements.[32]

Equality measuresEdit

Gini coefficient and Hoover indexEdit

Using the "A : B" notation (for example, 0.8:0.2) and with A + B = 1, inequality measures like the Gini index (G) and the Hoover index (H) can be computed. In this case both are the same.

 
 

See alsoEdit

ReferencesEdit

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  2. ^ Bunkley, Nick (March 3, 2008). "Joseph Juran, 103, Pioneer in Quality Control, Dies". New York Times. Archived from the original on September 6, 2017. Retrieved 25 January 2018.
  3. ^ a b Box, George E.P.; Meyer, R. Daniel (1986). "An Analysis for Unreplicated Fractional Factorials". Technometrics. 28 (1): 11–18. doi:10.1080/00401706.1986.10488093.
  4. ^ Newman, MEJ (2005). "Power laws, Pareto Distributions, and Zipf's law" (PDF). Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004. Bibcode:2005ConPh..46..323N. doi:10.1080/00107510500052444. S2CID 202719165. Retrieved 10 April 2011.
  5. ^ Marshall, Perry (2013-10-09). "The 80/20 Rule of Sales: How to Find Your Best Customers". Entrepreneur. Retrieved 2018-01-05.
  6. ^ Pareto, Vilfredo; Page, Alfred N. (1971), Translation of Manuale di economia politica ("Manual of political economy"), A.M. Kelley, ISBN 978-0-678-00881-2
  7. ^ Gorostiaga, Xabier (January 27, 1995), "World has become a 'champagne glass' globalization will fill it fuller for a wealthy few", National Catholic Reporter
  8. ^ United Nations Development Program (1992), 1992 Human Development Report, New York: Oxford University Press
  9. ^ Human Development Report 1992, Chapter 3, retrieved 2007-07-08
  10. ^ Dubay, Curtis (May 4, 2009). "The Rich Pay More Taxes: Top 20 Percent Pay Record Share of Income Taxes". Heritage.org. Retrieved 12 April 2018.
  11. ^ Sanders, Laura (April 6, 2018). "Top 20% of Americans Will Pay 87% of Income Tax". The Wall Street Journal. Retrieved 12 April 2018.
  12. ^ Emerging Technology from the arXiv (March 1, 2018) If you’re so smart, why aren’t you rich? Turns out it’s just chance., TechnologyReview.com, accessed 1 January 2019
  13. ^ Yakovenko, Victor M.; Silva, A. Christian (2005), Chatterjee, Arnab; Yarlagadda, Sudhakar; Chakrabarti, Bikas K. (eds.), "Two-class Structure of Income Distribution in the USA: Exponential Bulk and Power-law Tail", Econophysics of Wealth Distributions: Econophys-Kolkata I, New Economic Windows, Springer Milan, pp. 15–23, doi:10.1007/88-470-0389-x_2, ISBN 978-88-470-0389-7
  14. ^ a b Gen, M.; Cheng, R. (2002), Genetic Algorithms and Engineering Optimization, New York: Wiley
  15. ^ Rooney, Paula (October 3, 2002), Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features, ChannelWeb
  16. ^ Pressman, Roger S. (2010). Software Engineering: A Practitioner's Approach (7th ed.). Boston, Mass: McGraw-Hill, 2010. ISBN 978-0-07-337597-7.
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  18. ^ Training and the 80-20 rule of Pareto's Principle, 21 November 2008
  19. ^ Woodcock, Kathryn (2010). Safety Evaluation Techniques. Toronto, ON: Ryerson University. p. 86.
  20. ^ "Introduction to Risk-based Decision-Making" (PDF). USCG Safety Program. United States Coast Guard. Retrieved 14 January 2012.
  21. ^ 50MINUTES.COM (2015-08-17). The Pareto Principle for Business Management: Expand your business with the 80/20 rule. 50 Minutes. ISBN 9782806265869.
  22. ^ Rushton, Oxley & Croucher (2000), pp. 107–108.
  23. ^ Epstein, Joshua; Axtell, Robert (1996), Growing Artificial Societies: Social Science from the Bottom-Up, MIT Press, p. 208, ISBN 0-262-55025-3
  24. ^ Myrl Weinberg: In health-care reform, the 20-80 solution | Contributors | projo.com | The Providence Journal Archived 2009-08-02 at the Wayback Machine
  25. ^ "Myrl Weinberg: In health-care reform, the 20-80 solution - Contributo…". archive.li. 2 August 2009. Archived from the original on 2 August 2009.
  26. ^ Sawyer, Bradley; Claxton, Gary. "How do health expenditures vary across the population?". Peterson-Kaiser Health System Tracker. Peterson Center on Healthcare and the Kaiser Family Foundation. Retrieved 13 March 2019.
  27. ^ Nicola, Davis (2016). "'High social cost' adults can be predicted from as young as three, says study". The Guardian.
  28. ^ Galvani, Alison P.; May, Robert M. (2005). "Epidemiology: Dimensions of superspreading". Nature. 438 (7066): 293–295. Bibcode:2005Natur.438..293G. doi:10.1038/438293a. PMC 7095140. PMID 16292292.
  29. ^ Lloyd-Smith, JO; Schreiber, SJ; Kopp, PE; Getz, WM (2005). "Superspreading and the effect of individual variation on disease emergence". Nature. 438 (7066): 355–359. Bibcode:2005Natur.438..355L. doi:10.1038/nature04153. PMC 7094981. PMID 16292310.
  30. ^ Kleinfield, N. R. (1988-05-01). "A Tight Squeeze at Video Stores". The New York Times. ISSN 0362-4331. Retrieved 2019-02-08.
  31. ^ Bak, Per (1999), How Nature Works: the science of self-organized criticality, Springer, p. 89, ISBN 0-387-94791-4
  32. ^ Taleb, Nassim (2007), The Black Swan, pp. 229–252, 274–285

Further readingEdit

External linksEdit