# 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

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topDwyer, 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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- Arrow, K.J., Social Choice and lndividual Values. 2nd edn., New York, John Wiley (1963).
- 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
- Barthélemy, J.P. and McMorris, F.R., "On an independence condition for consensus n-trees", Applied Mathematics Letters, 2 (1989), 75-78. Zbl0709.90008MR989865
- 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
- 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
- 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
- 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
- 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.
- Leclerc, B. and Cucumel, G., "Consensus en classification: une revue bibliographique", Mathématiques Informatique et Sciences Humaines, 100 (1987),109-128. Zbl0635.62055MR941912
- 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
- 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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