The sociogeometry of inequality: Part I

•A sociogeometric framework for the measurement of socioeconomic inequality is established.•The concept of Lorenz sets is introduced and explored.•A collection of inequality indices based on Lorenz sets is analyzed.

The study of socioeconomic inequality is of prime economic and social importance, and the key quantitative gauges of socioeconomic inequality are Lorenz curves and inequality indices—the most notable of the latter being the popular Gini index. In this series of papers we present a sociogeometric framework to the study of socioeconomic inequality. In this part we shift from the notion of Lorenz curves to the notion of Lorenz sets, define inequality indices in terms of Lorenz sets, and introduce and explore a collection of distance-based and width-based inequality indices stemming from the geometry of Lorenz sets. In particular, three principle diameters of Lorenz sets are established as meaningful quantitative gauges of socioeconomic inequality—thus indeed providing a geometric quantification of socioeconomic inequality.