TY - JOUR
T1 - Inferring a linear ordering over a power set
AU - Spiegler, Ran
N1 - Funding Information:
This paper is based on a section of my Ph.D. dissertation, completed in the School of Economics at Tel-Aviv University. I am grateful to Ariel Rubinstein for his supervision. I also wish to thank Eddie Dekel, Kfir Eliaz, Gilat Levy and anonymous referees for useful comments. Partial support from the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities is gratefully acknowledged.
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
KW - Cross inferences
KW - Inference rules
KW - Prior knowledge
KW - Ranking
UR - http://www.scopus.com/inward/record.url?scp=0042377465&partnerID=8YFLogxK
U2 - 10.1023/A:1012400922478
DO - 10.1023/A:1012400922478
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AN - SCOPUS:0042377465
SN - 0040-5833
VL - 51
SP - 31
EP - 49
JO - Theory and Decision
JF - Theory and Decision
IS - 1
ER -