Note that each of the c i values can be tuned independently because a c i value that is optimal for predicting scores for p i essays with respect to any of the error performance measures is necessarily also the optimal c i when measuring that error on essays from all prompts.
this is not case with Pearson's correlation coefficient, as the P C value for essays from all 13 prompts cannot be simplified as a weighted sum of the P C values obtained on each individual prompt.