Single or Multiple Consensus for Linear Orders

Abstract

To establish a consensus order, summarizing a profile of linear orders on the same item set is a common problem. It appears in Social Choice Theory, when voters rank candidates in an elective process or in Preference Aggregation, when individuals or criteria put several orders on the items. Often the consensus order is a median order for Kendall’s distance, but other definitions, more easily computable, can be used. In the following, we tackle the question of the quality of this summary by a single consensus order. We study the possibility to represent a given profile by several linear orders making a Multiple Consensus. We introduce an original criterion to measure the quality of the single or multiple consensus, and so to decide if it is preferable to retain one linear order or to adopt several orders making a better representation. Two applications are described; the first one in Agronomy to select varieties according to yield estimations in several trials and the second one is about the event orders along Jesus, life according to the three Gospels of Mark, Luke, and Matthew.