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On the Construction of Weak Orders from Fragmentary Information

Published online by Cambridge University Press:  01 January 2025

Peter C. Fishburn
Peter C. Fishburn*
Affiliation:
The Pennsylvania State University
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Abstract

An iterative method is proposed for constructing a weak order from a partial order on a set of stimuli that is based on individual pairwise comparison data. The method generalizes Duncan Luce's construction of the weak order induced by a semiorder. Various aspects of the iterative procedure are discussed, including its rationale, the number of iterations required to obtain a weak order, and the extent to which the data support additions to the initial partial order as a function of the number of iterations performed before the additions occur.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 4 , December 1973 , pp. 459 - 472
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

This work was supported in part by a grant from the Alfred P. Sloan Foundation to The Institute for Advanced Study.

†

The computer simulation programs for this study were written and run by William Gehrlein. I am grateful to him for his assistance.

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