The great nineteenth-century Italian economist Vilfredo Pareto (1848–1923) was the first to discover the 80/20 rule (later also known as the Pareto principle), which emphasizes the importance of few items in explaining a total. For example:
- 20% of a company's products generate 80% of its revenue.
- 20% of a company's customers generate 80% of its profit.
- 20% of people have 80% of the income.
- 20% of websites get 80% of the hits.
- 20% of computer code contains 80% of the errors.
- Around 15% of all major league baseball players create 85% of their team's wins.
- 20% of criminals commit 80% of the crimes.
- 20% of people incur 80% of health care costs.
In this chapter, we show how the concept of a power law explains the widespread presence of the Pareto principle.
Consider an unknown quantity, X, which we suppose must equal a positive integer. Examples include a person's income, number of units purchased by a customer, and number of hits on a website. Then X follows a power law if the fraction of observations (X = x) that equal x is given by
In equation (1), α >1 and C is chosen to make the sum of the probabilities equal to one. In the rest of this chapter, we will discuss the prevalence of power laws and how power laws lead to the importance of few items explaining a total. The seminal reference on power laws ...