Scoring rule sensitivity to weight selection

This essay examines the sensitivity of collective rankings and winners to the weights used in score vectors that are applied to sets of individual rankings to yield collectieve rankings in a typical additive manner. The paper considers probabilities of getting the same winner and the same collective ranking when different score vectors are used for three-element sets. It then discusses the propensities of score vectors to preserve the orginal winner or collective ranking when one or more elements is removed from this ranking and a lower dimensional score vector is applied to the reduced situation. The latter case is examined for three- and four-element sets. The model used for the assessments is based on equally-likely choices of rankings by individuals and applies to situations that involve large numbers of individuals. Roughly speaking, best agreements and minimum sensitivities center around linear (Borda) score vectors. The greatest discrepancies arise from the so-called plurality and reverse plurality score vectors.