SL-model for paired comparisons

The method of paired comparisons can be found all the way back to 1860, where Fechner made the first publication in this method, using it for his psychometric investigations [4]. Thurstone formalised the method by providing a mathematical background to it [9-11] and in 1927 the method’s birth took place with his psychometric publications, one being “a law of comparative judgment” [12-14]. The law of comparative judgment is a set of equations relating the proportion of times any stimulus k is judged greater on a given attribute than any other stimulus j to the scales and discriminal dispersions of the two stimuli on the psychological continuum. The amount of research done for discrete models of paired comparisons is not a lot. This study develops a new discrete model, the SL-model for paired comparisons. Paired comparisons data processing in which objects have an upper limit to their scores was also not yet developed, and making such a model is one of the aims of this report. The SLmodel is thus developed in this context; however, the model easily generalises to not necessarily having an upper limit on scores