How the Variance-to-Mean Ratio Behaves in Relation to the Basic Principles for Inequality Measures

The phenomenon of inequality occurs when resources, opportunities, or other attributes are distributed unequally among the elements of a set. Although the literature on inequality focuses heavily on income inequality, inequality encompasses economic, social, and spatial dimensions, being relevant in different fields of society. When addressing inequality, the measure that immediately appears as a candidate for evaluating this inequality is the Gini index, however, there are several circumstances in which other measures of inequality are more appropriate, or in which the information provided by the Gini index is insufficient to adequately characterize or compare inequality. Considering that, in certain situations, the Variance-to-Mean Ratio and the Gini Index appear as viable alternatives to measure inequality, we are interested in analyzing the Variance-to-Mean Ratio regarding its compliance with the four basic criteria for inequality measures, adopting a formal and axiomatic approach. We conclude that the Variance-to-Mean Ratio does not meet all these requirements.