Pareto principle

# Pareto principle

Discussion

Encyclopedia
The Pareto principle states that, for many events, roughly 80% of the effects come from 20% of the causes.

Joseph M. Juran
Joseph Moses Juran was a 20th century management consultant who is principally remembered as an evangelist for quality and quality management, writing several influential books on those subjects. He was the brother of Academy Award winner Nathan H...

suggested the principle and named it after Italian economist Vilfredo Pareto
Vilfredo Pareto
Vilfredo Federico Damaso Pareto , born Wilfried Fritz Pareto, was an Italian engineer, sociologist, economist, political scientist and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices....

, 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.

It is a common rule of thumb
Rule of thumb
A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...

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.

The Pareto principle is only tangentially related to Pareto efficiency
Pareto efficiency
Pareto efficiency, or Pareto optimality, is a concept in economics with applications in engineering and social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution.Given an initial allocation of...

, which was also introduced by the same economist. Pareto developed both concepts in the context of the distribution of income
Income
Income is the consumption and savings opportunity gained by an entity within a specified time frame, which is generally expressed in monetary terms. However, for households and individuals, "income is the sum of all the wages, salaries, profits, interests payments, rents and other forms of earnings...

and wealth
Wealth
Wealth is the abundance of valuable resources or material possessions. The word wealth is derived from the old English wela, which is from an Indo-European word stem...

among the population.

## In economics

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. 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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

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
Warren Buffett
Warren Edward Buffett is an American business magnate, investor, and philanthropist. He is widely regarded as one of the most successful investors in the world. Often introduced as "legendary investor, Warren Buffett", he is the primary shareholder, chairman and CEO of Berkshire Hathaway. He is...

, Carlos Slim Helú
Carlos Slim Helú
Carlos Slim Helú is a Mexican business magnate and philanthropist who as of 2011 is the richest person in the world, for the second year in a row...

, and Bill Gates
Bill Gates
William Henry "Bill" Gates III is an American business magnate, investor, philanthropist, and author. Gates is the former CEO and current chairman of Microsoft, the software company he founded with Paul Allen...

) own as much as the next seven put together.

A chart that gave the inequality a very visible and comprehensible form, the so-called 'champagne glass' effect, 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.
Distribution of world GDP, 1989
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
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

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

In computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

and engineering control theory such as for electromechanical energy converters, the Pareto principle can be applied to optimization
Optimization (computer science)
In computer science, program optimization or software optimization is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources...

efforts. For example, Microsoft
Microsoft
Microsoft Corporation is an American public multinational corporation headquartered in Redmond, Washington, USA that develops, manufactures, licenses, and supports a wide range of products and services predominantly related to computing through its various product divisions...

noted that by fixing the top 20% of the most reported bugs, 80% of the errors and crashes would be eliminated.

## Other applications

In the systems science discipline, Epstein
Joshua M. Epstein
Joshua M. Epstein is Professor of Emergency Medicine at Johns Hopkins University, and a member of the External Faculty of the Santa Fe Institute.- Early life and Education:Epstein was born in New York City and grew up in Amherst....

and Axtell
Robert Axtell
- References :...

created an agent-based simulation
Agent-based social simulation
Agent-based social simulation consists in social simulations that are based on Agent-based modeling, and implemented using artificial agent technologies....

model called SugarScape
Sugarscape
Sugarscape is a model artificially intelligent agent-based social simulation following some or all rules presented by Joshua M. Epstein & Robert Axtell in their book Growing Artificial Societies.-Origin:...

, from a decentralized modeling
Decentralised system
Decentralised systems in systems theory are naturally occurring, usually self-regulating systems found which function without an organized center or authority...

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.

The Pareto principle has many applications in quality control. It is the basis for the Pareto chart, one of the key tools used in total quality control
Total Quality Management
Total quality management or TQM is an integrative philosophy of management for continuously improving the quality of products and processes....

and six sigma
Six Sigma
Six Sigma is a business management strategy originally developed by Motorola, USA in 1986. , it is widely used in many sectors of industry.Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects and minimizing variability in manufacturing and...

. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics
Logistics
Logistics is the management of the flow of goods between the point of origin and the point of destination in order to meet the requirements of customers or corporations. Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging, and...

and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.

The Pareto principle was a prominent part of the 2007 bestseller
Bestseller
A bestseller is a book that is identified as extremely popular by its inclusion on lists of currently top selling titles that are based on publishing industry and book trade figures and published by newspapers, magazines, or bookstore chains. Some lists are broken down into classifications and...

The 4-Hour Workweek
The 4-Hour Workweek
The 4-Hour Workweek: Escape 9-5, Live Anywhere, and Join the New Rich is a semi-autobiographical self-help book written by Timothy Ferriss, an American writer, educational activist, and entrepreneur....

by Tim Ferriss
Timothy Ferriss
Timothy Ferriss is an American author, entrepreneur, and public speaker. In 2007, he published The 4-Hour Workweek: Escape 9-5, Live Anywhere, and Join the New Rich, which was a New York Times and USA Today bestseller. In 2010, he followed up with The 4-Hour Body...

. 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.

In human developmental biology the principle is reflected in the gestation period
Gestation period
For mammals the gestation period is the time in which a fetus develops, beginning with fertilization and ending at birth. The duration of this period varies between species.-Duration:...

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.

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

In the financial services industry, this concept is known as profit risk
Profit risk
Profit risk is a risk management tool that focuses on understanding concentrations within the income statement and assessing the risk associated with those concentrations from a net income perspective.-Alternate definitions:...

, where 20% or fewer of a company's customers are generating positive income while 80% or more are costing the company money.

## 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. 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
Pareto index
In economics the Pareto index, named after the Italian economist and sociologist Vilfredo Pareto, is a measure of the breadth of income or wealth distribution. It is one of the parameters specifying a Pareto distribution and embodies the Pareto principle...

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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

" relationship, which also occurs in phenomena such as brush fires and earthquakes.
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.

### Gini coefficient and Hoover index

Using the "A : B" notation (for example, 0.8:0.2) and with A + B = 1, inequality measures
Income inequality metrics
The concept of inequality is distinct from that of poverty and fairness. Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income, and economic inequality among the participants in a particular economy, such as that of a specific...

like the Gini index and the Hoover index can be computed. In this case both are the same.

### Theil index

The Theil index
Theil index
The Theil index is a statistic used to measure economic inequality. It has also been used to measure the lack of racial diversity. The basic Theil index TT is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. It is a special...

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.

• 1% rule (Internet culture)
• 10/90 gap
10/90 gap
The 10/90 gap refers to the statistical finding of the Global Forum for Health Research that only 10% of worldwide expenditure on health research and development is devoted to the problems that primarily affect the poorest 90% of the world's population....

• Benford's law
Benford's law
Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way...

• Elephant flow
Elephant Flow
In computer networking, an elephant flow is an extremely large continuous flow set up by a TCP flow measured over a network link. Elephant flows, though not numerous, can occupy a disproportionate share of the total bandwidth over a period of time...

• Mathematical economics
Mathematical economics
Mathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...

The megadiverse countries are a group of countries that harbor the majority of the Earth's species and are therefore considered extremely biodiverse...

• Ninety-ninety rule
Ninety-ninety rule
In computer programming and software engineering, the ninety-ninety rule is a humorous aphorism that states:That the total development time sums to 180% is a wry allusion to the notorious tendency of software development projects to significantly overrun their original schedules...

• Pareto distribution
• Pareto priority index
Pareto Priority Index
The Pareto priority index , so named because of its connection with the Pareto principle, which is in turn named after the economist Vilfredo Pareto, can be used to prioritize several projects. It is especially used in the surroundings of six sigma projects...

• Parkinson's law
Parkinson's law
Parkinson's law is the adage first articulated by Cyril Northcote Parkinson as the first sentence of a humorous essay published in The Economist in 1955:...

• Principle of least effort
Principle of least effort
The principle of least effort is a broad theory that covers diverse fields from evolutionary biology to webpage design. It postulates that animals, people, even well designed machines will naturally choose the path of least resistance or "effort". It is closely related to many other similar...

• Profit risk
Profit risk
Profit risk is a risk management tool that focuses on understanding concentrations within the income statement and assessing the risk associated with those concentrations from a net income perspective.-Alternate definitions:...

• Sturgeon's law
Sturgeon's Law
Sturgeon's revelation, commonly referred to as Sturgeon's law, is an adage derived from quotations by Theodore Sturgeon, an American science fiction author. While Sturgeon coined another adage that he termed "Sturgeon's law", it is his "revelation" that is usually referred to by that term...

• The Long Tail
The Long Tail
The Long Tail or long tail refers to the statistical property that a larger share of population rests within the tail of a probability distribution than observed under a 'normal' or Gaussian distribution...

• Vitality curve
Vitality curve
A vitality curve is a leadership construct whereby a workforce is graded in accordance with the productivity of its members.For example, there is an often cited "80-20 rule" - also known as the "Pareto principle" or the "Law of the Vital Few" - whereby 80% of crimes are committed by 20% of...

• Wealth condensation
• Zipf's law