Algorithm for Option Number Selection in Stochastic Paired Comparison Models

In this paper, paired comparison models with a stochastic background are investigated and compared from the perspective of the option numbers allowed. As two-option and three-option models are the ones most frequently used, we mainly focus on the relationships between two-option and four-option models and three-option and five-option models, and then we turn to the general s- and $(s+2)$-option models. We compare them from both theoretical and practical perspectives; the latter are based on computer simulations. We examine, when it is possible, mandatory, or advisable how to convert four-, five-, and $(s+2)$-option models into two-, three-, and s-option models, respectively. The problem also exists in reverse: when is it advisable to use four-, five-, and $(s+2)$-option models instead of two-, three-, and s-option models? As a result of these investigations, we set up an algorithm to perform the decision process.