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 comes 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."

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 original observation was in connection with income and wealth. Pareto noticed that 80% of Italy's wealth 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.

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

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 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.

In computer science the Pareto principle can be applied to resource optimization by observing that 80% of the resources are typically used by 20% of the operations. In software engineering, it is often a better approximation that 90% of the execution time of a computer program is spent executing 10% of the code (known as the 90/10 law in this context).

In business, dramatic improvements can often be achieved by identifying the 20% of customers, activities, products or processes that account for the 80% of contribution to profit and maximizing the attention applied to them. Similarly a vast majority of the business risk is contained in few risk scenarios. The greatest reduction in risk may therefore be focussed in this area.

An 'inverted' application of the Pareto principle is the so-called 'long tail' focus in internet marketing. Rather than focusing on the high-popularity keywords for which there is a great deal of competition, some marketers have concentrated on the much larger number of obscure phrases that each get a few searches per month. Creating web pages that are search-engine-optimized for these is a less challenging task than for the small number of popular and highly competitive key phrases.

Theil Index
The Theil index is an entropy measure used to quantify inequities. 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.

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 &minus; k)% of the participants; however, k may vary from 50 in the case of equal distribution 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").

One should not be seduced by the symmetry of the idealised case: 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, eg '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.

Note, however, that sometimes adding up to 100 is indeed meaningful. 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.

Examples

 * Megadiverse countries