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

Abstract

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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.

How to cite

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Crown, 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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  9. 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. MR444120
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