Further results on neutral consensus functions
Mathématiques informatique et sciences humaines, Tome 132 (1995), pp. 5-11.

Nous abordons le problème du consensus par une voie ensembliste, en considérant un objet comme un assemblage de «briques» élémentaires. Une fonction de consensus est neutre s'il existe une famille D d'ensembles telle qu'une brique s appartient au consensus d'un profil si et seulement si l'ensemble des coordonnées des objets contenant s appartient à D. Nous donnons des conditions suffisantes pour que D soit un filtre de treillis. Dans le cas d'un treillis fini, ces conditions s'avèrent être aussi suffisantes. Notre résultat final porte sur le cas d'un sup-demi-treillis distributif fini, dans lequel nous donnons des conditions nécessaires et suffisantes pour que D soit un ultrafiltre.

We use a set theoretic approach to consensus by viewing an object as a set of smaller pieces called “bricks”. A consensus function is neutral if there exists a family D of sets such that a brick s is in the output of a profile if and only if the set of positions with objects that contain s belongs to D. We give sufficient set theoretic conditions for D to be a lattice filter and, in the case of a finite lattice, these conditions turn out to be necessary. Ourfinal result, which involves a finite distributive join semilattice, provides necessary and sufficient conditions for D to be an ultrafilter.

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Crown, G. D.; Janowitz, M.-F.; Powers, R. C. Further results on neutral consensus functions. Mathématiques informatique et sciences humaines, Tome 132 (1995), pp. 5-11. http://archive.numdam.org/item/MSH_1995__132__5_0/

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