Measuring Hierarchy

Measuring Hierarchy
Carbonell-Nicolau, Oriol. (2024). Department of Economics. Rutgers University. 15 October. pp. 1-42. (Article - Monograph; English).

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Alternative Locations

https://oriolcn.github.io/papers/hierarchy.pdf

Abstract or Brief Description

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.

Language

English

Publication Type

Article - Monograph

Keywords

hierarchical index hierarchy measurement hierarchical pre-order power

Subject

BN Power
BN Business Enterprise
BN Industrial Organization
BN Institutions

Depositing User

Jonathan Nitzan

Date Deposited

15 Oct 2024 19:46

Last Modified

15 Oct 2024 19:46

URL:

https://bnarchives.net/id/eprint/842

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