Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309442 
Year of Publication: 
2024
Publisher: 
The Bichler and Nitzan Archives, Toronto
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.
Subjects: 
hierarchical index
hierarchy
measurement
hierarchical pre-order
power
JEL: 
P
P1
C02
C6
Creative Commons License: 
cc-by-nc-nd Logo
Document Type: 
Working Paper

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