The Use of Limit Theorems in Paired Comparison Model Building

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Abstract
The Thurstone and the Bradley-Terry models, both initially advanced on intuitive grounds, have proved useful in the analysis of paired comparisons. The psychological meaning of these models and their relation to one another is unclear, but they fit data. Stevens has observed that there may be two basic mechanisms of discrimination 1) additive and 2) substitutive. We advance two corresponding mathematical models: that experienced sensation is 1) the sum of a large number of independent signals and 2) the maximum of a large number of independent signals. These assumptions yield 1) Thurstone's model and 2) the model of Bradley-Terry. Psychological interpretations of the various parameters, in terms of sensation, present themselves in a natural manner. Thus this paper presents a theory which unifies and interprets two paired comparison models that have proved useful in fitting experimental data.

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