An alternative to multiple regression that is appropriate when the dependent variable is ordinal is suggested. The goal of the system is to predict correctly as many as possible of the binary ordinal relations on the dependent variable. This can be done by treating the problem as one in discriminant analysis by discriminating the pairs of subjects whose ordinal relations are in one direction from those with relations in the other. The bases of prediction can be raw score differences on predictors, their rank differences, or their directions of difference. For each, it is possible to find a system of weights that approximately maximizes discrimination. These turn out to depend on the variables' co-variances, on their rank correlations, and on their tau correlations, respectively. It is also possible to estimate the odds that any given relation is in a particular direction. A solution for the weights that exactly maximizes probability of correct ordinal prediction is available in the case of predicting from directions of difference. An example is given.