Inferring a linear ordering over a power set

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Abstract

An observer attempts to infer the unobserved ranking of two ideal objects, A and B, from observed rankings in which these objects are 'accompanied' by 'noise' components, C and D. In the first ranking, A is accompanied by C and B is accompanied by D, while in the second ranking, A is accompanied by D and B is accompanied by C. In both rankings, noisy-A is ranked above noisy-B. The observer infers that ideal-A is ranked above ideal-B. This commonly used inference rule is formalized for the case in which A, B, C, D are sets. Let X be a finite set and let ≻ be a linear ordering on 2X. The following condition is imposed on ≻. For every quadruple (A, B, C, D) ∈ Y, where Y is some domain in (2X)4, if A ∪ C ≻ B ∪ D and A ∪ D ≻ B ∪ C, then A ≻ B. The implications and interpretation of this condition for various domains Y are discussed.

Original languageEnglish
Pages (from-to)31-49
Number of pages19
JournalTheory and Decision
Volume51
Issue number1
DOIs
StatePublished - 2001

Keywords

  • Cross inferences
  • Inference rules
  • Prior knowledge
  • Ranking

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