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2013 | OriginalPaper | Buchkapitel

Implications of Axiomatic Consensus Properties

verfasst von : Florent Domenach, Ali Tayari

Erschienen in: Algorithms from and for Nature and Life

Verlag: Springer International Publishing

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Abstract

Since Arrow’s celebrated impossibility theorem, axiomatic consensus theory has been extensively studied. Here we are interested in implications between axiomatic properties and consensus functions on a profile of hierarchies. Such implications are systematically investigated using Formal Concept Analysis. All possible consensus functions are automatically generated on a set of hierarchies derived from a fixed set of taxa. The list of implications is presented and discussed.

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Literatur
Zurück zum Zitat Adams, E. N., III. (1972). Consensus techniques and the comparison of taxonomic trees. Systematic Zoology, 21, 390–397.CrossRef Adams, E. N., III. (1972). Consensus techniques and the comparison of taxonomic trees. Systematic Zoology, 21, 390–397.CrossRef
Zurück zum Zitat Adams, E. N., III. (1986). N-trees as nestings: complexity, similarity, and consensus. Journal of Classification, 3, 299–317.MathSciNetMATHCrossRef Adams, E. N., III. (1986). N-trees as nestings: complexity, similarity, and consensus. Journal of Classification, 3, 299–317.MathSciNetMATHCrossRef
Zurück zum Zitat Arrow, K. J. (1951). Social choice and individual values. New York: Wiley.MATH Arrow, K. J. (1951). Social choice and individual values. New York: Wiley.MATH
Zurück zum Zitat Bandelt, H.-J., & Dress, A. (1989). Weak hierarchies associated with similarity measures: an additive clustering technique. Bulletin of Mathematical Biology, 51, 133–166.MathSciNetMATH Bandelt, H.-J., & Dress, A. (1989). Weak hierarchies associated with similarity measures: an additive clustering technique. Bulletin of Mathematical Biology, 51, 133–166.MathSciNetMATH
Zurück zum Zitat Barbut, M., & Monjardet, B. (1970). Ordres et classification: algèbre et combinatoire (tome II). Paris: Hachette. Barbut, M., & Monjardet, B. (1970). Ordres et classification: algèbre et combinatoire (tome II). Paris: Hachette.
Zurück zum Zitat Barthélemy, J.-P., McMorris, F. R., & Powers, R. C. (1992). Dictatorial consensus functions on n-trees. Mathematical Social Sciences, 25, 59–64.MathSciNetMATHCrossRef Barthélemy, J.-P., McMorris, F. R., & Powers, R. C. (1992). Dictatorial consensus functions on n-trees. Mathematical Social Sciences, 25, 59–64.MathSciNetMATHCrossRef
Zurück zum Zitat Bertrand, P., & Diday, E. (1985). A visual representation of compatibility between an order and a dissimilarity index: the pyramids. Computer Statistics Quarterly, 2, 31–44.MATH Bertrand, P., & Diday, E. (1985). A visual representation of compatibility between an order and a dissimilarity index: the pyramids. Computer Statistics Quarterly, 2, 31–44.MATH
Zurück zum Zitat Birkhoff, G. (1967). Lattice theory (3rd ed.). Providence: American Mathematical Society.MATH Birkhoff, G. (1967). Lattice theory (3rd ed.). Providence: American Mathematical Society.MATH
Zurück zum Zitat Bremer, K. (1990). Combinable component consensus. Cladistics, 6, 369–372.CrossRef Bremer, K. (1990). Combinable component consensus. Cladistics, 6, 369–372.CrossRef
Zurück zum Zitat Bryant, D. (2003). A classification of consensus methods for phylogenetics. In M. Janowitz, F. J. Lapointe, F. McMorris, B. Mirkin, & F. Roberts (Eds.), Bioconsensus, DIMACS (pp. 163–184). Providence: DIMACS-AMS. Bryant, D. (2003). A classification of consensus methods for phylogenetics. In M. Janowitz, F. J. Lapointe, F. McMorris, B. Mirkin, & F. Roberts (Eds.), Bioconsensus, DIMACS (pp. 163–184). Providence: DIMACS-AMS.
Zurück zum Zitat Colonius, H., & Schulze, H.-H. (1981). Tree structure for proximity Data. British Journal of Mathematical and Statistical Psychology, 34, 167–180.MathSciNetMATHCrossRef Colonius, H., & Schulze, H.-H. (1981). Tree structure for proximity Data. British Journal of Mathematical and Statistical Psychology, 34, 167–180.MathSciNetMATHCrossRef
Zurück zum Zitat Day, W. H. E., & McMorris, F. R. (2003). Axiomatic consensus theory in group choice and biomathematics. Philadelphia: Siam.MATHCrossRef Day, W. H. E., & McMorris, F. R. (2003). Axiomatic consensus theory in group choice and biomathematics. Philadelphia: Siam.MATHCrossRef
Zurück zum Zitat Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order (2nd ed.). Cambridge: Cambridge University Press.MATHCrossRef Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order (2nd ed.). Cambridge: Cambridge University Press.MATHCrossRef
Zurück zum Zitat Degnan, J. H., DeGiorgio, M., Bryant, D., & Rosenberg, N. A. (2009). Properties of consensus methods for inferring species trees from gene trees. Systems Biology, 58, 35–54.CrossRef Degnan, J. H., DeGiorgio, M., Bryant, D., & Rosenberg, N. A. (2009). Properties of consensus methods for inferring species trees from gene trees. Systems Biology, 58, 35–54.CrossRef
Zurück zum Zitat Dong, J., Fernández-Baca, D., McMorris, F. R., & Powers, R. C. (2011). An axiomatic study of majority-rule ( + ) and associated consensus functions on hierarchies. Discrete Applied Mathematics, 159, 2038–2044.MathSciNetMATHCrossRef Dong, J., Fernández-Baca, D., McMorris, F. R., & Powers, R. C. (2011). An axiomatic study of majority-rule ( + ) and associated consensus functions on hierarchies. Discrete Applied Mathematics, 159, 2038–2044.MathSciNetMATHCrossRef
Zurück zum Zitat Felsenstein, J. (1978). The number of evolutionary trees. Systematic Zoology, 27, 27–33.CrossRef Felsenstein, J. (1978). The number of evolutionary trees. Systematic Zoology, 27, 27–33.CrossRef
Zurück zum Zitat Ganter, B., & Wille, R. (1996). Formal concept analysis: mathematical foundations. Heidelberg: Springer.MATH Ganter, B., & Wille, R. (1996). Formal concept analysis: mathematical foundations. Heidelberg: Springer.MATH
Zurück zum Zitat Guigues, J.-L., & Duquenne, V. (1986). Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines, 95, 5–18.MathSciNet Guigues, J.-L., & Duquenne, V. (1986). Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines, 95, 5–18.MathSciNet
Zurück zum Zitat Hudry, O., & Monjardet, B. (2010). Consensus theories. An oriented survey. Mathématiques et Sciences Humaines, 190, 139–167. Hudry, O., & Monjardet, B. (2010). Consensus theories. An oriented survey. Mathématiques et Sciences Humaines, 190, 139–167.
Zurück zum Zitat Margush, T., & McMorris, F. R. (1981). Consensus n-trees. Bulletin of Mathematical Biology, 43, 239–244.MathSciNetMATH Margush, T., & McMorris, F. R. (1981). Consensus n-trees. Bulletin of Mathematical Biology, 43, 239–244.MathSciNetMATH
Zurück zum Zitat May, K. O. (1952). A set of independent necessary and sufficient conditions for simple majority decision. Econometrica, 20, 680–684.MATHCrossRef May, K. O. (1952). A set of independent necessary and sufficient conditions for simple majority decision. Econometrica, 20, 680–684.MATHCrossRef
Zurück zum Zitat Nelson, G. (1979). Cladistic analysis and synthesis: principles and definitions, with a historical note on adanson’s famille des plantes (1763–1764). Systematic Zoology, 28, 1–21.CrossRef Nelson, G. (1979). Cladistic analysis and synthesis: principles and definitions, with a historical note on adanson’s famille des plantes (1763–1764). Systematic Zoology, 28, 1–21.CrossRef
Zurück zum Zitat Page, R. D. M. (1990). Tracks and trees in the antipodes: a reply to humphries and seberg. Systematic Zoology, 39, 288–299.CrossRef Page, R. D. M. (1990). Tracks and trees in the antipodes: a reply to humphries and seberg. Systematic Zoology, 39, 288–299.CrossRef
Zurück zum Zitat Phillips, C., & Warnow, T. J. (1996). The aymmetric median tree – a new model for building consensus trees. Discrete Applied Mathematics, 71, 311–335.MathSciNetMATHCrossRef Phillips, C., & Warnow, T. J. (1996). The aymmetric median tree – a new model for building consensus trees. Discrete Applied Mathematics, 71, 311–335.MathSciNetMATHCrossRef
Zurück zum Zitat Powers, R. C., & White, J. M. (2008). Wilson’s theorem for consensus functions on hierarchies. Discrete Applied Mathematics, 156, 1321–1329.MathSciNetMATHCrossRef Powers, R. C., & White, J. M. (2008). Wilson’s theorem for consensus functions on hierarchies. Discrete Applied Mathematics, 156, 1321–1329.MathSciNetMATHCrossRef
Zurück zum Zitat Yevtushenko, S. A. (2000). System of data analysis “Concept Explorer”. In Proceedings of the 7th national conference on Artificial Intelligence KII-2000, Russia, (pp. 127–134). Yevtushenko, S. A. (2000). System of data analysis “Concept Explorer”. In Proceedings of the 7th national conference on Artificial Intelligence KII-2000, Russia, (pp. 127–134).
Metadaten
Titel
Implications of Axiomatic Consensus Properties
verfasst von
Florent Domenach
Ali Tayari
Copyright-Jahr
2013
DOI
https://doi.org/10.1007/978-3-319-00035-0_5