×

Axioms for consensus functions on undirected phylogenetic trees. (English) Zbl 0569.92001

A version of Arrow’s impossibility theorem is established for consensus functions on undirected phylogenetic trees.

MSC:

92B05 General biology and biomathematics
05C05 Trees
92F05 Other natural sciences (mathematical treatment)
92D10 Genetics and epigenetics
91D99 Mathematical sociology (including anthropology)
91B14 Social choice
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adams, E. N., Consensus techniques and the comparison of taxonomic trees, Syst. Zool., 21, 390-397 (1972)
[2] Arrow, K. J., Social Choice and Individual Values (1963), Wiley: Wiley New York · Zbl 0984.91513
[3] Colonius, H.; Schulze, H. H., Tree structures for proximity data, British J. Math. Statist. Psych., 34, 167-180 (1981) · Zbl 0472.62107
[4] Harary, F., Graph Theory (1969), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0797.05064
[5] Leclerc, B., Description, evaluation et comparison des hierarchies de parties (1982), Centre d’Analyze et Mathématique Sociale: Centre d’Analyze et Mathématique Sociale Paris, manuscript
[6] Margush, T.; McMorris, F. R., Consensus \(n\)-trees, Bull. Math. Biol., 43, 239-244 (1981) · Zbl 0455.92019
[7] McGuire, J. B., On the consensus construction of an evolutionary tree, J. Social Biol. Struct., 2, 107-118 (1979)
[8] McMorris, F. R.; Neumann, D., Consensus functions defined on trees, Math. Social Sci., 4, 131-136 (1983) · Zbl 0511.90010
[9] Neumann, D., Faithful consensus methods for \(n\)-trees, Math. Biosci., 63, 271-287 (1983) · Zbl 0539.62073
[10] Norton, V., Hierarchical consensus methods (1983), Bowling Green State Univ, manuscript
[11] R. Stinebricker, An extension of intersection methods from trees to dendrograms, Syst. Zool., to appear.; R. Stinebricker, An extension of intersection methods from trees to dendrograms, Syst. Zool., to appear.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.