Ties in ranking scores can be treated as weighted samples

Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the population or subpopulation being analyzed is exactly equal to any other member's score. It turns out to be possible to construct from the original data a weighted data set that modifies the scores, weights, and responses (dependent variables in the regression) such that the new scores are unique and (together with the new weights and responses) yield the desired cumulative statistics for the original data. This reduces the problem of analyzing data with scores that may not be unique to the problem of analyzing a weighted data set with scores that are unique by construction. Recent proposals for cumulative statistics have already detailed how to process weighted samples whose scores are unique.