Axioms for consensus functions based on lower bounds in posets

  • Day W
  • McMorris F
  • Meronk D
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Abstract

Let (X, ≤) be a finite partially ordered set with a unique minimal element, and consider the problem of associating with each subset of X a corresponding set of consensus objects. When based on lower bound operators, such consensus functions are interesting because their consensus objects can be interpreted as conservative representations of structure inherent in the objects being studied. We extend early results of Pfaltz to obtain an axiomatic characterization of a consensus function based on an iterated maximal lower bound operator, and we relate this function to a recent consensus proposal of Bonacich. © 1986.

Author-supplied keywords

  • Axiomatic characterization
  • consensus method
  • iterated maximal lower bound operator
  • partially ordered set

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