Measuring Hierarchy

Carbonell-Nicolau, Oriol

Measuring Hierarchy

dc.contributor.author	Carbonell-Nicolau, Oriol
dc.date.accessioned	2025-03-07T01:06:16Z
dc.date.available	2025-03-07T01:06:16Z
dc.date.issued	2024
dc.description.abstract	This paper presents a novel axiomatic approach to measuring and comparing hierarchical structures. Hierarchies are fundamental across a range of disciplines – from ecology to organizational science – yet existing measures of hierarchical degree often lack systematic criteria for comparison. We introduce a mathematically rigorous framework based on a simple partial pre-order over hierarchies, denoted as ≽H, and demonstrate its equivalence to intuitively appealing axioms for hierarchy comparisons. Our analysis yields three key results. First, we establish that for fixed-size hierarchies, one hierarchy is strictly more hierarchical than another according to ≽H if the latter can be derived from the former through a series of subordination removals. Second, we fully characterize the hierarchical pre-orders that align with ≽H using two fundamental axioms: Anonymity and Subordination Removal. Finally, we extend our framework to varying-size hierarchies through the introduction of a Replication Principle, which enables consistent comparisons across different scales.
dc.identifier.citation	Measuring Hierarchy. Carbonell-Nicolau, Oriol. (2024). Department of Economics. Rutgers University. 15 October. pp. 1-42. (Article - Monograph; English).
dc.identifier.uri	https://hdl.handle.net/10315/42661
dc.language.iso	en
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 International	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject	hierarchical index
dc.subject	hierarchy measurement
dc.subject	hierarchical pre-order
dc.subject	power
dc.title	Measuring Hierarchy
dc.type	Article