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

TL;DR

This paper introduces a new methodology for analyzing paired comparison data that accounts for cyclicality and intransitivity, improving ranking accuracy and model selection through geometric insights and large sample guarantees.

Contribution

It develops a principled approach to detect and model cyclicality and intransitivity in paired comparison data, enhancing existing ranking and prediction methods.

Findings

Method accurately identifies cyclicality and intransitivity in large samples.

Proposed model selection approach uses geometrical insights for better accuracy.

Simulations and examples demonstrate improved ranking performance.

Abstract

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.