A biproportional measure of multidimensional inequality

Bradburd and Ross have proposed a measure of multidimensional inequality based on a quadratic-loss criterion: one matrix is compared to another even if they have not the same margins. This is reconsidered. One removes the effect of size variation between the analyzed distribution and the reference distribution by giving to the two matrices the same margins with a biproportional operator. The size differences inside the analyzed structure are removed by a bimarkovian biproportional operator. As homogeneity does not signify equality, the homogeneous reference structure is replaced by a uniform matrix to be compared to the first matrix.