# Pareto principle

Pareto principle

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, 80% of the effects come from 20% of the causes. Business management thinker Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed that 80% of income in Italy went to 20% of the population. It is a common rule of thumb in business; e.g., "80% of your sales comes from 20% of your clients."

It is worthy of note that some applications of the Pareto principle appeal to a pseudo-scientific "law of nature" to bolster non-quantifiable or non-verifiable assertions that are "painted with a broad brush".Fact|date=January 2008 The fact that hedges such as the 90/10, 70/30, and 95/5 "rules" exist is sufficient evidence of the non-exactness of the Pareto principle. On the other hand, there is adequate evidence that "clumping" of factors does occur in most phenomena.Fact|date=January 2008

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

Practical applications

The observation was in connection with income and wealth. Pareto noticed that 80% of Italy's wealth was owned by 20% of the population.Fact|date=January 2008 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 inequality a very visible and comprehensible form, the so-called 'champagne glass' effect, [44] 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. [45]

+ Distribution of world GDP, 1989 Quintile of Population Income Richest 20% 82.7% Second 20% 11.7% Third 20% 2.3% Fourth 20% 1.4% Poorest 20% 1.2%

SOURCE: United Nations Development Program. 1992 Human Development Report [46]

It also applies to a variety of more mundane matters: one might guess approximately that we wear our 20% most favoured clothes about 80% of the time, perhaps we spend 80% of the time with 20% of our acquaintances, etc.

The Pareto principle has many applications in quality control.Fact|date=January 2008 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 (Rushton "et al". 2000, pp. 107-108).

In computer science and engineering control theory such as for electromechanical energy converters, the Pareto principle can be applied to optimization efforts. (M. Gen & R. Cheng, Generic Algorithms and Engineering Optimisation. New York, Wiley, 2002)

The Pareto principle was a prominent part of the 2007 bestseller "The 4-Hour Workweek" by Tim Ferriss. Ferriss recommended focusing ones' activities to those 20% that contribute to 80% of the income. More notably, he also recommends firing the 20% customers who take up the majority of one's time and cause most trouble. [Ferris, Tim (2006.) "The 4-Hour Workweek". Crown Publishing]

Microsoft also noted that by fixing the top 20% of the most reported bugs, 80% of the users would not encounter any bugs. [ [http://www.crn.com/security/18821726 Microsoft's CEO: 80-20 Rule Applies To Bugs, Not Just Features] ]

Mathematical notes

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.

Mathematically, where something is shared among a sufficiently large set of participants, there will always be a number "k" between 50 and 100 such that "k"% is taken by (100 − "k")% of the participants; however, "k" may vary from 50 in the case of equal distribution (e.g. exactly 50% of the people take 50% of the resources) to nearly 100 in the case of a tiny number of participants taking almost all of the resources. There is nothing special about the number 80, but many systems will have "k" somewhere around this region of intermediate imbalance in distribution.

This is a special case of the wider phenomenon of Pareto distributions. If the parameters in the Pareto distribution are suitably chosen, then one would have not only 80% of effects coming from 20% of causes, but also 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").

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'). The classic 80-20 distribution occurs when the gradient of the line is -1 when plotted on log-log axes of equal scaling. Pareto rules are not mutually exclusive. Indeed, the 0-0 and 100-100 rules always hold.

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.

Inequality measures

Gini coefficient and Hoover index

Using the “$A:B$” notation, (example : $0,8:0,2$) and with $A+B=1$ inequality measures like the Gini index "and" the Hoover index (Robin Hood index) can be computed. In this case both are the same.: $left\left(A+B ight\right)=1$: $2left\left(A+B ight\right)=2$: $left\left(2A-1 ight\right)=left\left(1-2B ight\right)$

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

Theil index

The Theil index is an entropy measure used to quantify inequities and can be computed from the Hoover Index. The measure is 0 for 50:50 distributions and reaches 1 at a Pareto distribution of 82:18. Higher inequities yield Theil indices above 1. [ [http://www.poorcity.richcity.org/calculator/?quantiles=82.4,17.6|17.6,82.4 On Line Calculator: Inequality ] ] : $T_T=T_L=T_s = 2 H , operatorname\left\{arctanh\right\} left\left( H ight\right).,$

ee also

* 10-90 gap
* Benford's law
* Mathematical economics
* Sturgeon's law
* The Long Tail
* Vitality curve
* Wealth condensation
* Zipf's law
* Principle of least effort
* Richard Koch
* Ninety-ninety rule

Examples

Notes

References

* Bookstein, Abraham. 1990. "Informetric distributions, part I: Unified overview". "Journal of the American Society for Information Science" 41: 368–75.
* Klass, O. S., Biham, O., Levy, M., Malcai, O., & Soloman, S. 2006. "The Forbes 400 and the Pareto wealth distribution". "Economics Letters", 90, 290-295.
* Reed, W. J. (2001). "The Pareto, Zipf and other power laws". "Economics Letters", 74, 15-19.
* Rosen, K. T., & Resnick, M. (1980). "The size distribution of cities: an examination of the Pareto law and primacy". "Journal of Urban Economics", 8, 165-186.
* Rushton, A., Oxley, J. and Croucher, P. 2000. "The handbook of logistics and distribution management". 2nd ed. London: Kogan Page. ISBN 978-0-7494-3365-9.

* [http://www.flatstats.co.uk/articles/turf/80_20_rule_applied_to_horse_racing.html 80-20 in horseracing]
* [http://www.ma.hw.ac.uk/~des/HWM00-26.pdf Wealth Condensation in Pareto Macro-Economies]

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