Pareto ratio and Pareto principle

In the late 19th century, Vilfredo Pareto published the results of his observations of wealth inequality in Italy as a ratio in which the numerator is equal to the share of population ranked in descending order of wealth, and the denominator is the share of wealth of the population. Both the form of presentation of the concentration of inequality in the form of a visual ratio (the Pareto ratio), and an unexpectedly large inequality (80/20), which became known as the Pareto principle. In the 21st century, a new concept was introduced - the generalized Pareto principle, which is understood as any proportion in which the sum of the numerator and denominator is 100%. As a result, an extraordinary situation arose, when the empirical regularity began to be identified with the measure of its measurement. To resolve this confusion, the definition of Pareto ratio is provided in this work, based on a generally accepted concept of "wealthy" element of the system, as also an alternative explanation of the Pareto principle is proposed with the use of isoperimetric inequalities conceptually related with the principle of least action.