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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0042377465

SN - 0040-5833

VL - 51

SP - 31

EP - 49

JO - Theory and Decision

JF - Theory and Decision

IS - 1

ER -