Removal independence and multi-consensus functions

Mark Dwyer; Fred R. McMorris; Robert C. Powers

Mathématiques et Sciences Humaines (1999)

  • Volume: 148, page 31-40
  • ISSN: 0987-6936

Abstract

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Work of Vincke and Bouyssou showed that if aggregation procedures on weak orders are allowed to return more than one result, then it might be possible for a procedure to satisfy all the axioms of Arrow's Theorem yet not be dictatorial. This approach is extended from ordered sets to n-trees, which are set-systems used in classifications theory. Results in this context can differ from those of Vincke and Bouyssou.

How to cite

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Dwyer, Mark, McMorris, Fred R., and Powers, Robert C.. "Removal independence and multi-consensus functions." Mathématiques et Sciences Humaines 148 (1999): 31-40. <http://eudml.org/doc/94536>.

@article{Dwyer1999,
abstract = {Work of Vincke and Bouyssou showed that if aggregation procedures on weak orders are allowed to return more than one result, then it might be possible for a procedure to satisfy all the axioms of Arrow's Theorem yet not be dictatorial. This approach is extended from ordered sets to n-trees, which are set-systems used in classifications theory. Results in this context can differ from those of Vincke and Bouyssou.},
author = {Dwyer, Mark, McMorris, Fred R., Powers, Robert C.},
journal = {Mathématiques et Sciences Humaines},
keywords = {decision theory; consensus; multi-consensus function; hierarchies; Arrow's theorem},
language = {eng},
pages = {31-40},
publisher = {Ecole des hautes-études en sciences sociales},
title = {Removal independence and multi-consensus functions},
url = {http://eudml.org/doc/94536},
volume = {148},
year = {1999},
}

TY - JOUR
AU - Dwyer, Mark
AU - McMorris, Fred R.
AU - Powers, Robert C.
TI - Removal independence and multi-consensus functions
JO - Mathématiques et Sciences Humaines
PY - 1999
PB - Ecole des hautes-études en sciences sociales
VL - 148
SP - 31
EP - 40
AB - Work of Vincke and Bouyssou showed that if aggregation procedures on weak orders are allowed to return more than one result, then it might be possible for a procedure to satisfy all the axioms of Arrow's Theorem yet not be dictatorial. This approach is extended from ordered sets to n-trees, which are set-systems used in classifications theory. Results in this context can differ from those of Vincke and Bouyssou.
LA - eng
KW - decision theory; consensus; multi-consensus function; hierarchies; Arrow's theorem
UR - http://eudml.org/doc/94536
ER -

References

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  1. Adams, E.N., "Consensus techniques and the comparison of taxonomic trees", Systematic Zoology, 21 (1972), 390-397. 
  2. Arrow, K.J., Social Choice and lndividual Values. 2nd edn., New York, John Wiley (1963). 
  3. Barthélemy, J.P., Leclerc, B. and Monjardet, B., "On the use of ordered sets in problems of comparison and consensus of classifications", Journal of Classification, 3 (1986), 187-224. Zbl0647.62056MR874238
  4. Barthélemy, J.P. and McMorris, F.R., "On an independence condition for consensus n-trees", Applied Mathematics Letters, 2 (1989), 75-78. Zbl0709.90008MR989865
  5. Barthélemy, J.P., McMorris, F.R. and Powers, R.C., "Independence conditions for consensus n-trees revisited", Applied Mathematics Letters, 2 (1991), 43-46. Zbl0749.90005MR989865
  6. Barthélemy, J.P., McMorris, F.R. and Powers, R.C., "Stability conditions for consensus functions defined on n-trees", Mathematical and Computer Modelling, 22 (1995), 79-87. Zbl0833.90009MR1343655
  7. Bouyssou, D., "Democracy and efficiency: A note on 'Arrow's theorem is not a surprising result'", EuropeanJournal of Operational Research, 58 (1992), 427-430. Zbl0762.90003
  8. Colonius, H. and Schulze, H.H., "Tree structures for proximity data", The British Journal of Mathematical and Statistical Psychology, 34 (1981), 167-180. Zbl0472.62107MR649328
  9. Lapointe, F.J. and Cucumel G., "The average consensus procedure: combination of weighted trees containing identical or overlapping sets of objects", Systematic Zoology, 46 (1997), 306-312. 
  10. Leclerc, B. and Cucumel, G., "Consensus en classification: une revue bibliographique", Mathématiques Informatique et Sciences Humaines, 100 (1987),109-128. Zbl0635.62055MR941912
  11. Leclerc, B., "Consensus of classifications: the case of trees", in Advances in Data Science and Classification, A. Rizzi, M. Vicki and H.-H. Bock, Eds., Springer-Verlag, Berlin (1998), 81-90. Zbl1051.91530
  12. Vincke, P., "Arrow's Theorem is not a surprising result", European Journal of Operational Research., 10 (1982), 22-25. Zbl0483.90008MR655494

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