Inequalities and Identities

We introduce concepts and measures relating to inequality between identity groups. We define and discuss the concepts of Representational Inequality, Sequence Inequality and Group Inequality Comparison. Representational Inequality captures the extent to which an attribute is shared between members of distinct groups. Sequence Inequality captures the extent to which groups are ordered hierarchically. Group Inequality Comparison captures the extent of differences between groups-. The concepts have application in interpreting segregation, clustering and polarization in societies. There exists a mapping from familiar inequality measures to the measures we identify, making them empirically applicable.