Comparing Multidimensional Ordinal Distributions under Partial Orderings

Sahar F. Yousef and Mohammad Abu-Zaineh
Additional contact information
Sahar F. Yousef: Doha Institute for Graduate Studies
Mohammad Abu-Zaineh: Aix Marseille Univ, CNRS, AMSE, Marseille, France

No 2619, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: This paper studies the comparison of multidimensional ordinal distributions when outcome profiles are only partially ordered. Such settings arise naturally in inequality analysis whenever well-being is described by several ordinal attributes and some profile comparisons cannot be resolved without introducing additional value judgments about the relative importance of dimensions. To address this problem, the paper introduces a rank-membership representation based on the admissible linear extensions of the underlying partial order. Each profile is thereby associated with a probability distribution over ranks, which in turn yields completion-averaged rank frequencies and multidimensional Hammond coordinates. The paper shows that these coordinates coincide with the uniform average of the corresponding one-dimensional Hammond coordinates across admissible completions. We define a coordinate-wise multidimensional Hammond dominance criterion and establish its relation to unanimous completion-wise Hammond dominance. We also introduce a graded refinement based on the proportion of coordinates at which one distribution weakly dominates another and derives its basic transitivity structure. The proposed framework provides a way to extend rank-sensitive inequality comparisons to multidimensional ordinal settings with incomplete comparability, while making explicit the informational trade-off implied by averaging across admissible completions.

Keywords: Ordinal Data; Partial Orderings; Dominance Criteria; Rank-Sensitive Comparisons; Multidimensional Inequality (search for similar items in EconPapers)
JEL-codes: C43 D3 D63 D71 (search for similar items in EconPapers)
Date: 2026-05-01
Note: Working paper AMSE 2026-19
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05677394/document (application/pdf)
no

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:2619

Access Statistics for this paper

More papers in AMSE Working Papers from Aix-Marseille School of Economics, France AMU-AMSE - 5-9 Boulevard Maurice Bourdet, CS 50498 - 13205 Marseille Cedex 1. Contact information at EDIRC.
Bibliographic data for series maintained by Gregory Cornu ().