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

top
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

top

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

top
  1. M.A. Aizerman, and F.T. Aleskerov (1986) Voting Operators in the Space of Choice Functions, Math. Soc. Sci.11, 201-242. Zbl0597.90006MR842402
  2. K.P. Arrow (1962) Social Choice and Individual Values, 2nd edn. Wiley, New York. 
  3. J.P. Barthélemy (1982) Arrow's Theorem: Unusual Domain and Extended Codomain, Math. Soc. Sci.3, 79-89. Zbl0489.90012MR665572
  4. D.J. Brown (1975) Aggregration of Preferences, Quarterly Journal of Economics, 89, 456-469. 
  5. G.D. Crown, M.F. Janowitz and R.C. Powers (1993) Neutral consensus functions, Math. Soc. Sci.20, 231-250. Zbl0774.90006MR1212716
  6. 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. MR1415847
  7. B. Leclerc (1984) Efficient and Binary Consensus Functions on Transitively Valued Relations, Math. Soc. Sci.8, 45-61. Zbl0566.90003MR781659
  8. 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. Zbl0941.91029
  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
  10. B. Monjardet (1990) Arrowian characterizations of latticial federation consensus functions, Math. Soc. Sci.20, 51-71. Zbl0746.90002MR1072291
  11. B. Monjardet (1995) Ordinal Theory of Consensus, R.R. CAMS P.113, Paris, C.A.M.S. Zbl0941.91029

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.