Journal of Classification

, Volume 25, Issue 2, pp 153–158 | Cite as

A Characterization of Majority Rule for Hierarchies

  • Fred R. McMorrisEmail author
  • Robert C. Powers


The majority rule has been a popular method for producing a consensus classification from several different classifications, when the classifications are all on the same set of objects and are structured as hierarchies. In this note, a new axiomatic characterization is proved for this consensus method on hierarchies.


Hierarchy Consensus Majority rule 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AMENTA, N., CLARKE, F., and ST. JOHN, K. (2003), “A Linear-time Majority Tree Algorithm”, in Workshop on Algorithms in Bioinformatics, eds. G. Benson and R. Page, Lecture Notes in Computer Science 2812, Berlin: Springer-Verlag, 216–227.Google Scholar
  2. BARTHELEMY, J.P. and McMORRIS, F.R. (1986), “The Median Procedure for n-Trees”, Journal of Classification, 3, 329–334.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Day, W.H.E. and McMorris, F.R. (2003), Axiomatic Consensus Theory in Group Choice and Biomathematics, Philadelphia: Society for Industrial and Applied Mathematics.zbMATHGoogle Scholar
  4. MARGUSH, T. and McMORRIS, F.R. (1981), “Consensus n-Trees”, Bulletin of Mathematical Biology, 42, 239–244.MathSciNetGoogle Scholar
  5. McMorris, F.R. and Neumann, D.A. (1983), “Consensus Functions Defined on Trees”, Mathematical Social Sciences, 4, 131–135.zbMATHCrossRefMathSciNetGoogle Scholar
  6. McMORRIS, F.R. and POWERS, R.C. (2007), “Consensus Rules Based on Decisive Families of Sets”, submitted.Google Scholar
  7. MONJARDET, B. (1990), “Arrowian Characterizations of Latticial Federation Consensus Functions, Mathematical Social Sciences, 20, 51–71.zbMATHCrossRefMathSciNetGoogle Scholar
  8. SAARI, D.G. (2001), Chaotic Elections: A Mathematician Looks at Voting, Providence: American Mathematical Society.Google Scholar
  9. WAREHAM, H.T. (1985), An Efficient Algorithm for Computing M l Consensus Trees, BS Honors Thesis in Computer Science, Memorial University Newfoundland.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

Personalised recommendations