Local Segregation Scores of Entropy-Based Segregation Indices

The Mutual Information segregation index M can be decomposed into a weighted average of local segregation scores. This useful property can be used to assess whether some units (say, occupations or geographic areas) contribute more to overall segregation than other units. The related segregation index H is a normalized version of the M index, such that the index is constrained to fall between 0 and 1. The question addressed in this paper is whether local segregation scores of the M index can be normalized in a similar way, to arrive at useful local segregation scores for the H index. The paper shows that it is not possible to obtain normalized local segregation scores that fall between 0 and 1 and that also aggregate to the H index. The one exception to this is the situation when all groups in the population are exactly of equal size. It is also (trivially) possible to decompose the H index into weighted local segregation scores, however, they have the same problems of interpretation as the local segregation scores of the M index.