On uniform marginal representation of contingency tables

For a two-dimensional probability distribution represented as a contingency table, an algorithm due to Mosteller (1968) "standardizes" the table to have uniform marginals so as to obtain its "uniform marginals representation (UMR)". In this note, this algorithm is first shown to minimize the Kullback-Leibler information function between distributions with uniform marginals and the given distribution. Next, a characterization of such tables is proved, in terms of (i) their UMRs, (ii) cross-product ratios of each of their 2 x 2 subtables (iii) the ability to obtain one table from another only by adjustment of their row or column marginals.