Hostname: page-component-6766d58669-kl59c Total loading time: 0 Render date: 2026-05-21T06:44:51.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Alternative Methods of Constructing Strict Weak Orders from Interval Orders

Published online by Cambridge University Press:  01 January 2025

Peter C. Fishburn  and
William V. Gehrlein
Peter C. Fishburn
Affiliation:
The Pennsylvania State University
William V. Gehrlein
Affiliation:
The Pennsylvania State University
Get access Rights & Permissions [Opens in a new window]

Abstract

Let n stimuli be linearly ordered by a physical attribute. Consider an individual's “more than” relation based on perceived attribute values. Assuming that the individual's relation agrees with the linear order and is an interval order, the paper examines the extent to which ordered pairs in the linear order but not in the interval order (due to nondetection of “small” differences) can be correctly identified on the basis of the interval order alone. Different methods of constructing strict weak orders from interval orders are compared by the degree of agreement with the underlying linear order.

Information

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 4 , December 1974 , pp. 501 - 516
Copyright
Copyright © 1974 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bogart, K. P. Preference structures I: distances between transitive preference relations. Journal of Mathematical Sociology, 1973, 3, 49–67.CrossRefGoogle Scholar
Draper, N. R. and Smith, H. Applied regression analysis. New York: Wiley. 1966, 22–22.Google Scholar
Fishburn, P. C. Intransitive indifference with unequal indifference intervals. Journal of Mathematical Psychology, 1970, 7, 144–149.CrossRefGoogle Scholar
Fishburn, P. C. On the construction of weak orders from fragmentary information. Psychometrika, 1973, 38, 459–472.CrossRefGoogle Scholar
Fishburn, P. C. Interval representations for interval orders and semiorders. Journal of Mathematical Psychology, 1973, 10, 91–105.CrossRefGoogle Scholar
Fishburn, P. C. and Gehrlein, W. V. A comparative analysis of methods for constructing weak orders from partial orders. Journal of Mathematical Sociology, (In Press).Google Scholar
Gröbner, W. and Hofreiter, N. Unbestimmte integraltafel, Vol. 1, 1965, Wein: Springer-Verlag.CrossRefGoogle Scholar
Gröbner, W.and Hofreiter, N. Bestimmte integraltafel, Vol. 2, 1966, Wein: Springer-Verlag.Google Scholar
Hodgman, C. Handbook of chemistry and physics. Cleveland: Chemical Rubber Publishing Co.. 1962, 219–219.Google Scholar
Hogg, R. V. and Craig, A. T. Introduction to mathematical statistics. New York: Macmillan. 1965, 173–173.Google Scholar
Kemeny, J. G. Mathematics without numbers. Daedalus, 1959, 88, 577–591.Google Scholar
Kemeny, J. G. and Snell, J. L. Mathematical models in the social sciences. Boston: Ginn and Company. 1962, 11–19.Google Scholar
Krantz, D. H., Luce, R. D., Suppes, P. and Tversky, A. Foundations of measurement, Vol. II. New York: Academic Press (In Press).Google Scholar
Luce, R. D. Semiorders and a theory of utility discrimination. Econometrica, 1956, 24, 178–191.CrossRefGoogle Scholar
Scott, D. and Suppes, P. Foundational aspects of theories of measurement. Journal of Symbolic Logic, 1958, 23, 113–128.CrossRefGoogle Scholar