An algebraic setting for near-unanimity consensus

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Erscheinungsjahr:
1990
Medientyp:
Text
Schlagworte:
  • AMS subject classification (1980): 06A12
  • Majority rule
  • median algebra
  • median semilattice
  • n-ary near-unanimity algebra
  • near-unanimity rule
  • weak hierarchy
Beschreibung:
  • Some sets of taxonomic models can be structured as meet-semilattices having the properties that (i) every principal ideal is a distributive lattice and (ii) each finite subset has an upper bound whenever each of its (n-1)-subsets is bounded above, where n≥3 is a fixed number. Every such semilattice is endowed with an n-ary near-unanimity operation. We show that for n≥4 one can define these semilattices solely in terms of this n-ary operation. The resulting algebras are subdirect powers of two-element algebras, and of course, generalize median algebras. © 1990 Kluwer Academic Publishers.
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oai:www.edit.fis.uni-hamburg.de:publications/9cdc7e6b-7f22-4238-861d-4c2c65e11f56