Robustness of positional scoring over subsets of alternatives

摘要

Positional score vectorsw=(w1,⋯,wm) for anm-element setA, andv=(v1,⋯,vk) for ak-element proper subsetBofA, agreeat a profilesof linear orders onAwhen the restriction toBof the ranking overAproduced bywoperating onsequals the ranking overBproduced byvoperating on the restriction ofstoB.Givenw1>wmandv1>vk, this paper examines the extent to which pairs of nonincreasing score vectors agree over sets of profiles. It focuses on agreement ratios as the number of terms in the profiles becomes infinite. The limiting agreement ratios that are considered for (m, k) in {(3,2),(4,2),(4,3)} are uniquely maximized by pairs of Borda (linear, equally-spaced) score vectors and are minimized when (w,v) is either ((1,0,⋯,0),(1,⋯,1,0)) or ((1,,⋯,1,0),(