Best, worst, and best&worst choice probabilities for logit and reverse logit models

This paper proposes new models for analyzing best, worst, and best&worst choice probabilities for logit and reverse logit models, building on the pioneering work of Tony Marley. We assume individuals have a stochastic underlying ranking of alternatives and posit a rationality assumption relating to the random utility model. We focus on models applicable to best and worst choice scaling experiments, utilizing an inclusion-exclusion identity to propose a variety of best-worst choice probability models that can be implemented in specialized software packages. We demonstrate the versatility and utility of logit and reverse logit models in capturing the underlying ranking of alternatives. Finally, we discuss the practical implications of these models and future research directions in this field. Our models can be implemented in popular software packages such as Apollo.