# Pareto principle

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The term "Pareto principle" can also refer to Pareto efficiency.

The Pareto principle (also known as the 80–20 rule, the law of the vital few, and the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes.[1][2]

Business-management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed in 1906 that 80% of the land in Italy was owned by 20% of the population; he developed the principle by observing that 20% of the pea pods in his garden contained 80% of the peas.[2]

It is a common rule of thumb in business; e.g., "80% of your sales come from 20% of your clients". Mathematically, where something is shared among a sufficiently large set of participants, there must be a number k between 50 and 100 such that "k% is taken by (100 − k)% of the participants". The number k may vary from 50 (in the case of equal distribution, i.e. 100% of the population have equal shares) to nearly 100 (when a tiny number of participants account for almost all of the resource). There is nothing special about the number 80% mathematically, but many real systems have k somewhere around this region of intermediate imbalance in distribution.[3]

The Pareto principle is only tangentially related to Pareto efficiency, which was also introduced by the same economist. Pareto developed both concepts in the context of the distribution of income and wealth among the population.

## In economics Edit

The original observation was in connection with population and wealth. Pareto noticed that 80% of Italy's land was owned by 20% of the population.[4] He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.

Due to the scale-invariant nature of the power law relationship, the relationship applies also to subsets of the income range. Even if we take the ten wealthiest individuals in the world, we see that the top three (Warren Buffett, Carlos Slim Helú, and Bill Gates) own as much as the next seven put together.[5]

A chart that gave the inequality a very visible and comprehensible form, the so-called 'champagne glass' effect,[6] was contained in the 1992 United Nations Development Program Report, which showed the distribution of global income to be very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income.[7]

Distribution of world GDP, 1989[8]
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 has also been used to attribute the widening economic inequality in the United States to 'skill-biased technical change'—i.e. income growth accrues to those with the education and skills required to take advantage of new technology and globalization.

The distribution shows up in several different aspects relevant to entrepreneurs and business managers. For example:

• 80% of your profits come from 20% of the time you spend

Therefore, many businesses have an easy access to dramatic improvements in profitability by focusing on the most effective areas and eliminating, ignoring, automating, delegating or re-training the rest, as appropriate.

## In software Edit

In computer science and engineering control theory such as for electromechanical energy converters, the Pareto principle can be applied to optimization efforts.[10] For example, Microsoft noted that by fixing the top 20% of the most reported bugs, 80% of the errors and crashes would be eliminated.[11]

## Other applications Edit

In the systems science discipline, Epstein and 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 became emergent in their results, which suggests that the principle is a natural phenomenon.[12]

The Pareto principle has many applications in quality control.[citation needed] It is the basis for the Pareto chart, one of the key tools used in total quality control and six sigma. 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.[13]

The Pareto principle was a prominent part of the 2007 bestseller The 4-Hour Workweek by Tim Ferriss. Ferriss recommended focusing one's attention on those 20% that contribute to 80% of the income. More notably, he also recommends 'firing' – refusing to do business with – those 20% of customers who take up the majority of one's time and cause the most trouble.[14]

In human developmental biology the principle is reflected in the gestation period where the embryonic period constitutes 20% of the whole, with the fetal development taking up the rest of the time.

In health care in the United States, it has been found that 20% of patients use 80% of health care resources.[15]

Several criminology studies have found that 80% of crimes are committed by 20% of criminals.[16]

In the financial services industry, this concept is known as profit risk, where 20% or fewer of a company's customers are generating positive income while 80% or more are costing the company money.[17]

## Mathematical notes Edit

The idea has rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state that a solution to a problem "fits the 80–20 rule" just because it fits 80% of the cases; it must be implied that this solution requires only 20% of the resources needed to solve all cases. Additionally, it is a misuse of the 80–20 rule to interpret data with a small number of categories or observations.

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. 80% 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. Thus, the 80-20 rule would imply that 64% of wealth is held by 4% of the people, however, one cannot reverse this and say that 4% of the wealth is held by the poorer 64% of the people.

80–20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, 80–10 or 80–30. There is no need for the two numbers to add up to 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 very imbalanced, 80:20 is significantly imbalanced (Gini index: 60%), 70:30 is moderately imbalanced (Gini index: 40%), and 55:45 is just slightly imbalanced.

The Pareto principle is an illustration of a "power law" relationship, which also occurs in phenomena such as brush fires and earthquakes.[18] Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from 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, for example, stock movement sizes.[19]

## Equality measures Edit

### Gini coefficient and Hoover index Edit

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

$H=G=\left|2A-1 \right|=\left|1-2B \right| \,$
$A:B = \left( \tfrac{1+H}{2} \right): \left( \tfrac{1-H}{2} \right)$

### Theil index Edit

The Theil index is an entropy measure used to quantify inequalities. The measure is 0 for 50:50 distributions and reaches 1 at a Pareto distribution of 82:18. Higher inequalities yield Theil indices above 1.[20]

$T_T=T_L=T_s = 2 H \, \operatorname{arctanh} \left( H \right).\,$

## References Edit

1. Bunkley, Nick (March 3, 2008), "Joseph Juran, 103, Pioneer in Quality Control, Dies", New York Times
2. 2.0 2.1
3. Newman, MEJ Power laws, Pareto Distributions, and Zipf's law. URL accessed on 10 April 2011.
4. Pareto, Vilfredo; Page, Alfred N. (1971), 'Translation of Manuale di economia politica ("Manual of political economy"), A.M. Kelley, ISBN 9780678008812
5. Gorostiaga, Xabier (January 27, 1995), "World has become a 'champagne glass' globalisation will fill it fuller for a wealthy few", National Catholic Reporter
6. United Nations Development Program (1992), 1992 Human Development Report, New York: Oxford University Press
7. Human Development Report 1992, Chapter 3, retrieved on 2007-07-08
8. Living Life the 80/20 Way by Robert Koch
9. Gen, M.; Cheng, R. (2002), Genetic Algorithms and Engineering Optimization, New York: Wiley
10. Rooney, Paula (October 3, 2002), Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features, ChannelWeb
11. Epstein, Joshua; Axtell, Robert (1996), Growing Artificial Societies: Social Science from the Bottom-Up, MIT Press, p. 208, ISBN 0-262-55025-3
12. Rushton, Oxley & Croucher (2000), pp. 107–108.
13. Ferris, Tim (2006), The 4-Hour Workweek, Crown Publishing
14. Myrl Weinberg: In health-care reform, the 20-80 solution | Contributors | projo.com | The Providence Journal
15. Career Criminals: Who Are They and What Should Society Do About Them? | How Do I Get Off Drugs?
16. Profit Risk
17. Bak, Per (1999), How Nature Works: the science of self-organized criticality, Springer, p. 89, ISBN 0387947914
18. Taleb, Nassim (2007), The Black Swan, pp. 228–252, 274–285
19. On Line Calculator: Inequality