Further results on neutral consensus functions
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...
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| הוצא לאור ב: | URI:https://journals.openedition.org/msh, |
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| Auteurs principaux: | , , |
| פורמט: | Article ou chapitre numérique |
| שפה: | Anglais |
| יצא לאור: |
Mathématiques et sciences humaines
2006
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| גישה מקוונת: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| סיכום: | 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. Our final result, which involves a finite distributive join semilattice, provides necessary and sufficient conditions for D to be an ultrafilter. |
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