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.
@article{MSH_1995__132__5_0,
author = {Crown, G. D. and Janowitz, M.-F. and Powers, R. C.},
title = {Further results on neutral consensus functions},
journal = {Math\'ematiques informatique et sciences humaines},
pages = {5--11},
publisher = {Ecole des hautes-\'etudes en sciences sociales},
volume = {132},
year = {1995},
mrnumber = {1393629},
zbl = {0849.90009},
language = {en},
url = {http://www.numdam.org/item/MSH_1995__132__5_0/}
}
TY - JOUR AU - Crown, G. D. AU - Janowitz, M.-F. AU - Powers, R. C. TI - Further results on neutral consensus functions JO - Mathématiques informatique et sciences humaines PY - 1995 SP - 5 EP - 11 VL - 132 PB - Ecole des hautes-études en sciences sociales UR - http://www.numdam.org/item/MSH_1995__132__5_0/ LA - en ID - MSH_1995__132__5_0 ER -
%0 Journal Article %A Crown, G. D. %A Janowitz, M.-F. %A Powers, R. C. %T Further results on neutral consensus functions %J Mathématiques informatique et sciences humaines %D 1995 %P 5-11 %V 132 %I Ecole des hautes-études en sciences sociales %U http://www.numdam.org/item/MSH_1995__132__5_0/ %G en %F MSH_1995__132__5_0
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://www.numdam.org/item/MSH_1995__132__5_0/
, and (1986) Voting Operators in the Space of Choice Functions, Math. Soc. Sci. 11, 201-242. | MR | Zbl
(1962) Social Choice and Individual Values, 2nd edn. Wiley, New York.
(1982) Arrow's Theorem: Unusual Domain and Extended Codomain, Math. Soc. Sci. 3, 79-89. | MR | Zbl
(1975) Aggregration of Preferences, Quarterly Journal of Economics, 89, 456-469.
, and (1993) Neutral consensus functions, Math. Soc. Sci. 20, 231-250. | MR | Zbl
, and (1994) An ordered set approach to neutral consensus functions, in E. Diday et al., New Approaches in Classification and Data Analysis, Berlin, Springer Verlag, 102-110. | MR
(1984) Efficient and Binary Consensus Functions on Transitively Valued Relations, Math. Soc. Sci. 8, 45-61. | MR | Zbl
and (1994) Latticial theory of consensus, in W. A. Bar-nett et al., eds.,Social Choice, Welfare and Ethics, Cambridge University Press, 145-160. | Zbl
(1975) On the Problem of Reconciling Partitions, in Quantitative Sociology, International Perspectives on Mathematical and Statistical Modelling. New York: Academic Press, 441-449. | MR
(1990) Arrowian characterizations of latticial federation consensus functions, Math. Soc. Sci. 20, 51-71. | MR | Zbl
(1995) Ordinal Theory of Consensus, R.R. CAMS P.113, Paris, C.A.M.S.
