2006/02/23 by Pavel Chebotarev, Elena Shamis · 1 citation
Computer Science · Mathematics · #cs.MA #math.FA #math.OC #msc:91B08 #msc:91B10 #msc:91B12 #msc:91B16
published as Annals of Operations Research, 1998. V. 80. P.299-332 · 33 pages; with tables and figures
arxiv created 2006/02/23 · arxiv updated 2009/12/01
The paper surveys more than forty characterizations of scoring methods for preference aggregation and contains one new result. A general scoring operator is \it self-consistent if alternative i is assigned a greater score than j whenever i gets no worse (better) results of comparisons and its `opponents' are assigned respectively greater (no smaller) scores than those of j. We prove that self-consistency is satisfied if and only if the application of a scoring operator reduces to the solution of a homogeneous system of algebraic equations with a monotone function on the left-hand side.