A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for nonmetric scaling, multidimensional unfolding, conjoint measurement, factor analysis, subjective expected utility, and the Bradley-Terry-Luce choice problem are presented. (Author)