Abstract Let X be an n-set; we are concerned with the problem of finding a consensus order P on X that summarizes a k-tuple (profile) (Pi)1≤i≤k of orders on X. This problem is a basic one in the domain preference aggregation, but has been mainly studied in the case of linear orders. A classical approach is to consider a distance function d on the set O of all the orders on X and to search to minimize the remoteness σ1≤i≤k d(P,Pi). The fact that O is a semilattice allows us to apply some already recognized properties of consensus functions in such structures (Monjardet 1990, Leclerc 1994). Firstly, we particularize these properties to the class of lower locally distributive (LLD) semilattices, which includes O. Such semilattices are characterized by the identity of two metrics, the most extensively used ones in studies about medians in lattice structures. Then, we consider the specific case of orders, where this lattice approach allows us to extend some results about the role of majority pairs already obtained, by very different considerations, in the case of linear orders (see Charon et al. 1996). We obtain other properties of the median procedure for orders, like the Pareto property of medians with the symmetric difference metric. We compare the median procedure, for various metrics, with other consensus approaches: quota rules, Arrowian axiomatics (Brown 1975, Leclerc 1984).
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