Simultaneous conjoint measurement: A new type of fundamental measurement

https://doi.org/10.1016/0022-2496(64)90015-XGet rights and content

Abstract

The essential character of what is classically considered, e.g., by N. R. Campbell, the fundamental measurement of extensive quantities is described by an axiomatization for the comparision of effects of (or responses to) arbitrary combinations of “quantities” of a single specified kind. For example, the effect of placing one arbitrary combination of masses on a pan of a beam balance is compared with another arbitrary combination on the other pan. Measurement on a ratio scale follows from such axioms. In this paper, the essential character of simultaneous conjoint measurement is described by an axiomatization for the comparision of effects of (or responses to) pairs formed from two specified kinds of “quantities”. The axioms apply when, for example, the effect of a pair consisting of one mass and one difference in gravitational potential on a device that responds to momentum is compared with the effect of another such pair. Measurement on interval scales which have a common unit follows from these axioms; usually these scales can be converted in a natural way into ratio scales.

A close relation exists between conjoint measurement and the establishment of response measures in a two-way table, or other analysis-of-variance situations, for which the “effects of columns” and the “effects of rows” are additive. Indeed, the discovery of such measures, which are well known to have important practical advantages, may be viewed as the discovery, via conjoint measurement, of fundamental measures of the row and column variables. From this point of view it is natural to regard conjoint measurement as factorial measurement.

References (16)

  • D. Davidson et al.

    A finitistic axiomatization of subjective probability and utility

    Econometrica

    (1956)
  • E. Adams et al.

    A model of riskless choice

    Behav. Sci

    (1959)
  • N.R. Campbell

    Foundations of science: The philosophy of theory and experiment

    (1957)
  • N.R. Campbell

    An account of the principles of measurement and calculation

    (1928)
  • R.B. Cattell

    The relational simplex theory of equal interval and absolute scaling

    Acta Psychol

    (1962)
  • D. Davidson et al.

    Decision-making: An experimental approach

    (1957)
  • G. Debreu

    Cardinal utility for even-chance mixtures of pairs of sure prospects

    Rev. Econ. Stud

    (1959)
  • G. Debreu

    Topological methods in cardinal utility theory

There are more references available in the full text version of this article.

Cited by (1221)

View all citing articles on Scopus
1

The hospitality of the Center for Advanced Study in the Behavioral Sciences and of Stanford University is gratefully acknowledged. We wish to thank Francis W. Irwin and Richard Robinson for careful readings of an earlier version which have led to corrections and clarifications of the argument.

2

Research supported in part by the National Science Foundation grant NSF G-17637 to the University of Pennsylvania.

3

Research in part at Princeton University under the sponsorship of the Army Research Office (Durham).

View full text