## Axiomatic Consensus Theory in Group Choice and BiomathematicsBioconsensus is a rapidly evolving scientific field in which consensus methods, often developed for use in social choice theory, are adapted for such areas of the biological sciences as taxonomy, systematics, and evolutionary and molecular biology. Typically, after several alternatives are produced using different data sets, methods or algorithms, one needs to find a consensus solution. The axiomatic approach of this book explores the existence or nonexistence of consensus rules that satisfy particular sets of desirable well-defined properties. The axiomatic research reviewed here focuses first on the area of group choice, then in areas of biomathematics where the objects of interest represent partitions of a set, hierarchical structures, phylogenetic trees, or molecular sequences. |

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Axiomatic Consensus Theory in Group Choice and Biomathematics William H. E. Day,F. R. McMorris Limited preview - 2003 |

Axiomatic Consensus Theory in Group Choice and Biomathematics William H. E. Day,F. R. McMorris No preview available - 2003 |

Axiomatic Consensus Theory in Group Choice and Biomathematics William H. E. Day,F. R. McMorris No preview available - 2003 |

### Common terms and phrases

abcd aggregation agreement subtree algorithm Arrovian Arrow’s theorem axiomatic axioms Barthélemy binary relation bioconsensus canonical height characterization Choice and Welfare Cladistics cladogram concepts Condorcet consensus hierarchy consensus rule covering graph decisive family decisive sets dictatorship Discrete Mathematics equivalence relations Example F. R. McMorris Figure finite graph G group choice height function impossibility results impossibility theorem Janowitz join irreducibles Journal of Classification lattice leaf labels Leclerc Lemma lower distributive majority rule McMorris McMorris and Powers median graph median rule median semilattice meet semilattice Monjardet multiconsensus rules Open Problem Pareto optimality partitions phylogenies poset Proof rule on H rules on hierarchies S-Ntr satisfies FT satisfies Ind social choice theory subsets supertree Table tree quasi-orders ultrafilter vertex VX C S Warnow weak hierarchies weak orders whence wwyz