Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings

Abstract Preference data are a particular type of ranking where some subjects (voters, judges,...) express their preferences over set alternatives (items). In most real life cases, items receive the same preference by judge, thus giving rise to with ties. An important issue involving rankings concerns aggregation into “consensus”. The purpose this paper is investigate consensus between ties, taking account importance swapping elements belonging top (or bottom) ordering (position weights). By combining structure $$\tau _x$$ τ x proposed Emond and Mason (J Multi-Criteria Decis Anal 11(1):17–28, 2002) class weighted Kemeny-Snell distances, position rank correlation coefficient for comparing one-to-one correspondence distance proved, analytically speaking, using both equal decreasing weights.