An inequality between the weighted average and the rowwise correlation coefficient for proximity matrices

De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this note it is shown that for all three types, the absolute value of the first variant is greater than or equal to the absolute value of the second.