Vilfredo Pareto was an Italian economist in the 19th and 20th centuries. Pareto has several contributions to the field of microeconomics, but his most famous one was based on an observation of wealth distribution in 1890s Italy. Specifically, the distribution of wealth followed a power law, where the output of a function follows a trend line based on the ratio of a minimum unit of scale to the input variable, raised to an exponent. The exponent, known as the Pareto Index, is always in the form of α = logₓ₋₁x for distiributions adding up to 100%. Pareto showed that the distribution of Italian incomes had the form of x = 5, or in other words, α = log₄5. This defines a distribution where 80 percent of the wealth was held by 20 percent of income earners, while the other 20 percent was held by the other 80 percent.
This is the Pareto principle in its strictest form: wealth follows a power law distribution, and that power (α) is usually log₄5. That said, a number of other investigations into power law distributions — especially in business — frequently find the same value for α, e.g. sales to products, sales to customers, problems to causes, and bug reports to actual bugs.
Dr. Joseph Juran later applied this distribution to the problem of quality control in electrical engineering, and named it after Pareto.
What is notable is that there is an α for *any* Pareto distribution. In other words, there is always a proportion n such that 1-n of the inputs yield n of the outputs (and n/(1-n) is called the “joint ratio”). Finding n and α tells you how concentrated the distribution is at the top: the greater α, the lesser the distance between n and 1-n.