Scoring Rule Sensitivity to Weight Selection

In: Public choice, Volume 40, Issue 3, p. 249-261

Abstract

An examination of the sensitivity of collective rankings & winners to the weights used in score vectors that are applied to sets of individual rankings to yield collective rankings in a typical additive manner. Probabilities of getting the same winner & the same collective ranking when different score vectors are used for three-element sets are considered. The propensities of score vectors to preserve the original winner or collective ranking when one element or more is removed from this ranking & a lower dimensional score vector is applied to the reduced situation are discussed. The latter case is examined for three- & four-element sets. The model used for the assessments is based on equally-likely choices of rankings by individuals & applies to situations that involve large numbers of individuals. Roughly speaking, best agreements & minimum sensitivities center around linear (Borda) score vectors. The greatest discrepancies arise from the so-called plurality & reverse plurality score vectors. 5 Tables, 10 References. HA.