# Further results on neutral consensus functions

G. D. Crown; M.-F. Janowitz; R. C. Powers

Mathématiques et Sciences Humaines (1995)

- Volume: 132, page 5-11
- ISSN: 0987-6936

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topCrown, G. D., Janowitz, M.-F., and Powers, R. C.. "Further results on neutral consensus functions." Mathématiques et Sciences Humaines 132 (1995): 5-11. <http://eudml.org/doc/94475>.

@article{Crown1995,

abstract = {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.},

author = {Crown, G. D., Janowitz, M.-F., Powers, R. C.},

journal = {Mathématiques et Sciences Humaines},

keywords = {set theoretic approach; consensus function; brick; lattice filter; ultrafilter},

language = {eng},

pages = {5-11},

publisher = {Ecole des hautes-études en sciences sociales},

title = {Further results on neutral consensus functions},

url = {http://eudml.org/doc/94475},

volume = {132},

year = {1995},

}

TY - JOUR

AU - Crown, G. D.

AU - Janowitz, M.-F.

AU - Powers, R. C.

TI - Further results on neutral consensus functions

JO - Mathématiques et Sciences Humaines

PY - 1995

PB - Ecole des hautes-études en sciences sociales

VL - 132

SP - 5

EP - 11

AB - 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.

LA - eng

KW - set theoretic approach; consensus function; brick; lattice filter; ultrafilter

UR - http://eudml.org/doc/94475

ER -

## References

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