The analysis of paired comparison data in the presence of cyclicality and intransitivity

A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic patterns and potential intransitivities. Consequently, it improves upon existing methods for ranking and prediction, including enhanced performance in betting and wagering systems. Fundamental to our development is a detailed understanding and study of the parameter space that accommodates cyclicality and intransitivity. It is shown that identifying cyclicality and intransitivity reduces to a model selection problem, and a new method for model selection employing geometrical insights, unique to the problem at hand, is proposed. The large sample properties of the estimators and guarantees on the selected model are provided. Thus, it is shown that in large samples all cyclical relations and consequent intransitivities can be identified. The method is exemplified using simulations and analysis of an illustrative example.