Application of arrangement theory to unfolding models

TL;DR

This paper explores how arrangement theory can be applied to analyze unfolding models, providing methods to count admissible rankings and ranking patterns, including new bounds for the unidimensional case.

Contribution

It introduces the application of arrangement theory to unfolding models and presents new bounds for the number of ranking patterns in one-dimensional scenarios.

Findings

Derived simple upper and lower bounds for ranking patterns in unidimensional unfolding models

Demonstrated the usefulness of arrangement theory in counting admissible rankings

Provided an expository overview linking arrangement theory and unfolding models

Abstract

Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible rankings in an unfolding model and (ii) the number of ranking patterns generated by unfolding models. The paper is mostly expository but also contains some new results such as simple upper and lower bounds for the number of ranking patterns in the unidimensional case.