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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.

References

Coombs, C. H. A theory of data, 1964, New York: WileyGoogle Scholar
Fishburn, P. C. Utility theory with inexact preferences and degrees of preference. Synthese, 1970, 21, 204–221CrossRefGoogle Scholar
Fishburn, P. C. Intransitive indifference with unequal indifference intervals. Journal of Mathematical Psychology, 1970, 7, 144–149CrossRefGoogle Scholar
Galanter, E. An axiomatic and experimental study of sensory order and measure. Psychological Review, 1956, 63, 16–28CrossRefGoogle ScholarPubMed
Goodman, N. The structure of appearance, 1951, Cambridge, Mass.: Harvard Univ. PressGoogle Scholar
Hodson, F. R., Kendall, D. G. and TĂutu, P. Mathematics in the archaeological and historical sciences, 1971, Edinburgh: Edinburgh Univ. PressGoogle Scholar
Luce, R. D. Semiorders and a theory of utility discrimination. Econometrica, 1956, 24, 178–191CrossRefGoogle Scholar
Luce, R. D. and Galanter, E. Discrimination. In Luce, R. D., Bush, R. R., Galanter, E. (Eds.), Handbook of mathematical psychology, 1963, New York: WileyGoogle Scholar
Luce, R. D. and Suppes, P. Preference, utility, and subjective probability. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology, 1965, New York: WileyGoogle Scholar
Scott, D. Measurement structures and linear inequalities. Journal of Mathematical Psychology, 1964, 1, 233–247CrossRefGoogle Scholar
Scott, D. and Suppes, P. Foundational aspects of theories of measurement. Journal of Symbolic Logic, 1958, 23, 113–128CrossRefGoogle Scholar
Shepard, R. N. Circularity in judgments of relative pitch. Journal of the Acoustical Society of America, 1964, 36, 2346–2353CrossRefGoogle Scholar
Siegel, S. A method for obtaining an ordered metric scale. Psychometrika, 1956, 21, 207–216CrossRefGoogle Scholar
Szpilrajn, E. Sur l'extension de l'ordre partiel. Fundamenta Mathematicae, 1930, 16, 386–389CrossRefGoogle Scholar
Tversky, A. Intransitivity of preferences. Psychological Review, 1969, 76, 31–48CrossRefGoogle Scholar