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. Business management thinker 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. 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.
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.
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.
Because of 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.
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.
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 a similarly implies a "51.2-0.8" 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'). 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 to 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. 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 like the Gini index and the Hoover index can be computed. In this case both are the same.
