Law of comparative judgment

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The law of comparative judgment was conceived by L. L. Thurstone. In modern-day terminology, it is more aptly described as a model that is used to obtain measurements from any process of pairwise comparison. Examples of such processes are the comparison of perceived intensity of physical stimuli, such as the weights of objects, and comparisons of the extremity of an attitude expressed within statements, such as statements about capital punishment. The measurements represent how we perceive objects, rather than being measurements of actual physical properties. This kind of measurement is the focus of psychometrics and psychophysics.

In somewhat more technical terms, the law of comparative judgment is a mathematical representation of a discriminal process, which is any process in which a comparison is made between pairs of a collection of entities with respect to magnitudes of an attribute, trait, attitude, and so on. The theoretical basis for the model is closely related to item response theory and the theory underlying the Rasch model, which are used in psychology and education to analyse data from questionnaires and tests.


Thurstone published a paper on the law of comparative judgment in 1927. In this paper he introduced the underlying concept of a psychological continuum for a particular 'project in measurement' involving the comparison between a series of stimuli, such as weights and handwriting specimens, in pairs. He soon extended the domain of application of the law of comparative judgment to things that have no obvious physical counterpart, such as attitudes and values (Thurstone, 1929). For example, in one experiment, people compared statements about capital punishment to judge which of each pair expressed a stronger positive (or negative) attitude.

The essential idea behind Thurstone's process and model is that it can be used to scale a collection of stimuli based on simple comparisons between stimuli two at a time: that is, based on a series of pairwise comparisons. For example, suppose that someone wishes to measure the perceived weights of a series of five objects of varying masses. By having people compare the weights of the objects in pairs, data can be obtained and the law of comparative judgment applied to estimate scale values of the perceived weights. This is the perceptual counterpart to the physical weight of the objects. That is, the scale represents how heavy people perceive the objects to be based on the comparisons.

Although Thurstone referred to it as a law, as stated above, in terms of modern psychometric theory the 'law' of comparative judgment is more aptly described as a measurement model. It represents a general theoretical model which, applied in a particular empirical context, constitutes a scientific hypothesis regarding the outcomes of comparisons between some collection of objects. If data agree with the model, it is possible to produce a scale from the data.

Relationships to pre-existing psychophysical theory[edit]


Weber's law essentially states that how much people perceive physical stimuli to change depends on how big a stimulus is. For example, if someone compares a light object of 1 kg with one slightly heavier, they can notice a relatively small difference, perhaps when the second object is 1.2 kg. On the other hand, if someone compares a heavy object of 30 kg with a second, the second must be quite a bit larger for a person to notice the difference, perhaps when the second object is 36 kg. People tend to perceive differences that are proportional to the size rather than always noticing a specific difference irrespective of the size. The same applies to brightness, pressure, warmth, loudness and so on.



The general form of the law of comparative judgment[edit]

The most general form of the LCJ is


in which:

  • S_i is the psychological scale value of stimuli i
  • \sigma_i is the discriminal dispersion of a stimulus R_i
  • r_{ij} is the correlation between the discriminal deviations of stimuli i and j


Case 5 of the law of comparative judgment[edit]






When a simple logistic function is employed instead of the normal density function, then the model has the structure of the Bradley-Terry-Luce model (BTL model) (Bradley & Terry, 1952; Luce, 1959). In turn, the Rasch model for dichotomous data (Rasch, 1960/1980) is identical to the BTL model after the person parameter of the Rasch model has been eliminated, as is achieved through statistical conditioning during the process of Conditional Maximum Likelihood estimation. With this in mind, the specification of uniform discriminal dispersions is equivalent to the requirement of parallel Item Characteristic Curves (ICCs) in the Rasch model. Accordingly, as shown by Andrich (1978), the Rasch model should, in principle, yield essentially the same results as those obtained from a Thurstone scale. Like the Rasch model, when applied in a given empirical context, Case 5 of the LCJ constitutes a mathematized hypothesis which embodies theoretical criteria for measurement.


One important application involving the law of comparative judgment is the widely used Analytic Hierarchy Process, a structured technique for helping people deal with complex decisions. It uses pairwise comparisons of tangible and intangible factors to construct ratio scales that are useful in making important decisions.[1][2]


  • Krus, D.J., & Kennedy, P.H. (1977) Normal scaling of dominance matrices: The domain-referenced model. Educational and Psychological Measurement, 37, 189-193 (Request reprint).

External links[edit]