Further results on neutral consensus functions
Crown, G. D. ; Janowitz, M.-F. ; Powers, R. C.
Mathématiques et Sciences humaines, Tome 132 (1995), p. 5-11 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 1995-01-01
@article{MSH_1995__132__5_0,
     author = {Crown, G. D. and Janowitz, M.-F. and Powers, Robert},
     title = {Further results on neutral consensus functions},
     journal = {Math\'ematiques et Sciences humaines},
     volume = {132},
     year = {1995},
     pages = {5-11},
     mrnumber = {1393629},
     zbl = {0849.90009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/MSH_1995__132__5_0}
}

Crown, G. D.; Janowitz, M.-F.; Powers, R. C. Further results on neutral consensus functions. Mathématiques et Sciences humaines, Tome 132 (1995) pp. 5-11. http://gdmltest.u-ga.fr/item/MSH_1995__132__5_0/

M.A. Aizerman, and F.T. Aleskerov (1986) Voting Operators in the Space of Choice Functions, Math. Soc. Sci. 11, 201-242. | MR 842402 | Zbl 0597.90006

K.P. Arrow (1962) Social Choice and Individual Values, 2nd edn. Wiley, New York.

J.P. Barthélemy (1982) Arrow's Theorem: Unusual Domain and Extended Codomain, Math. Soc. Sci. 3, 79-89. | MR 665572 | Zbl 0489.90012

D.J. Brown (1975) Aggregration of Preferences, Quarterly Journal of Economics, 89, 456-469.

G.D. Crown, M.F. Janowitz and R.C. Powers (1993) Neutral consensus functions, Math. Soc. Sci. 20, 231-250. | MR 1212716 | Zbl 0774.90006

G.D. Crown, M.F. Janowitz and R.C. Powers (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 1415847

B. Leclerc (1984) Efficient and Binary Consensus Functions on Transitively Valued Relations, Math. Soc. Sci. 8, 45-61. | MR 781659 | Zbl 0566.90003

B. Leclerc and B. Monjardet (1994) Latticial theory of consensus, in W. A. Bar-nett et al., eds.,Social Choice, Welfare and Ethics, Cambridge University Press, 145-160. | Zbl 0941.91029

B.G. Mirkin (1975) On the Problem of Reconciling Partitions, in Quantitative Sociology, International Perspectives on Mathematical and Statistical Modelling. New York: Academic Press, 441-449. | MR 444120

B. Monjardet (1990) Arrowian characterizations of latticial federation consensus functions, Math. Soc. Sci. 20, 51-71. | MR 1072291 | Zbl 0746.90002

B. Monjardet (1995) Ordinal Theory of Consensus, R.R. CAMS P.113, Paris, C.A.M.S.