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Inferring a linear ordering over a power set

Spiegler, R; (2001) Inferring a linear ordering over a power set. THEOR DECIS , 51 (1) 31 - 49.

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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 s be a linear ordering on 2(X). The following condition is imposed on s. For every quadruple (A,B,C,D)is an element ofY, where Y is some domain in (2(X))(4), if A boolean ORC > B boolean ORD and A boolean ORD > B boolean ORC, then A>B. The implications and interpretation of this condition for various domains Y are discussed.

Type: Article
Title: Inferring a linear ordering over a power set
Keywords: cross inferences, inference rules, prior knowledge, ranking, CHOICE, EXTENSION, FREEDOM
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: http://discovery.ucl.ac.uk/id/eprint/17304
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