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An Ordered Set Approach to Neutral Consensus Functions

  • Gary D. Crown
  • Melvin F. Janowitz
  • Robert C. Powers
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Several authors have investigated consensus functions from the viewpoint of stability families. It will be shown that the stability family approach extends and enriches the ordered set approach to consensus theory. Our investigation will center on the notions of sup and inf-irreducible elements of a finite ordered set. We will see that irreducible elements give rise to natural internal stability families for a given ordered set X. We will investigate the relationship between these internal stability families and abstract stability families. Special attention will be paid to the study of different types of neutrality, thus extending earlier work of B. Monjardet. We will be particularly interested in the change in the available neutral consensus functions on an ordered set when a given internal stability family is changed.

Keywords

Consensus Function Principal Ideal Order Filter Irreducible Element Stability Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. BARTHÉLEMY, J.-P, and JANOWITZ, M. F. (1991): A formal theory of consensus. SIAM J. Discrete Math., 4, 305–322.CrossRefGoogle Scholar
  2. BARTHÉLEMY, J.-P, and MONJARDET, B. (1981): The median procedure in cluster analysis and social choice theory, Math. Social Sciences, 1, 235–268.CrossRefGoogle Scholar
  3. CROWN, G. D., JANOWITZ, M. F., and POWERS, R. C. (1993): Neutral consensus functions, Math. Social Sciences, 25, 231–250.CrossRefGoogle Scholar
  4. CROWN, G. D., JANOWITZ, M. F., and POWERS, R. C. (1994): Further results on Neutral consensus functions, to appear.Google Scholar
  5. CRITCHLEY, F. and VAN CUTSEM, B. (1993): An order-theoretic unification of certain fundamental bijections in mathematical classification, to appear.Google Scholar
  6. MONJARDET, B. (1990): Arrowian characterizations of latticial federation consensus functions, Math. Social Sciences, 20, 51–71.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Gary D. Crown
    • 1
  • Melvin F. Janowitz
    • 2
  • Robert C. Powers
    • 3
  1. 1.Department of Mathematics and StatisticsThe Wichita State UniversityWichitaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of Massachusetts at AmherstAmherstUSA
  3. 3.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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