Removal independence and multi-consensus functions
Mathématiques informatique et sciences humaines, Tome 148 (1999), pp. 31-40.

Vincke et Bouyssou ont montré que, si une procédure d'agrégation de préordres totaux peut retourner plusieurs solutions, alors elle peut satisfaire tous les axiomes du théorème d'Arrow sans être pour autant dictatoriale. Nous étendons cette approche aux hiérarchies utilisées en classification. Dans ce contexte, on obtient des résultats qui peuvent différer de ceux de Vincke et de Bouyssou.

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.

Keywords: decision theory, consensus, multi-consensus function, hierarchies, Arrow's theorem
Mots clés : théorie de la décision, consensus, multi-fonctions de consensus, hiérarchies, théorème d'Arrow 
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Dwyer, Mark; McMorris, Fred R.; Powers, Robert C. Removal independence and multi-consensus functions. Mathématiques informatique et sciences humaines, Tome 148 (1999), pp. 31-40. http://www.numdam.org/item/MSH_1999__148__31_0/

Adams, E.N., "Consensus techniques and the comparison of taxonomic trees", Systematic Zoology, 21 (1972), 390-397.

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. | MR | Zbl

Barthélemy, J.P. and Mcmorris, F.R., "On an independence condition for consensus n-trees", Applied Mathematics Letters, 2 (1989), 75-78. | MR | Zbl

Barthélemy, J.P., Mcmorris, F.R. and Powers, R.C., "Independence conditions for consensus n-trees revisited", Applied Mathematics Letters, 2 (1991), 43-46. | MR | Zbl

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. | MR | Zbl

Bouyssou, D., "Democracy and efficiency: A note on 'Arrow's theorem is not a surprising result'", European Journal of Operational Research, 58 (1992), 427-430. | Zbl

Colonius, H. and Schulze, H.H., "Tree structures for proximity data", The British Journal of Mathematical and Statistical Psychology, 34 (1981), 167-180. | MR | Zbl

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. | Numdam | MR | Zbl

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. | Zbl

Vincke, P., "Arrow's Theorem is not a surprising result", European Journal of Operational Research., 10 (1982), 22-25. | MR | Zbl