Localizing Preference Aggregation Conflicts: A Graph-Theoretic Approach Using Sheaves

Karen Sargsyan

Papers from arXiv.org

Abstract: We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation and, more broadly, in the fusion of partial rankings supplied by many overlapping sources. Unlike linearization methods such as HodgeRank, which embed comparisons into a numerical flow, this approach stays purely ordinal and locates conflict in the interaction structure via the Obstruction Locus, identifying which voter pairs fail to cohere. We formalize the Incompatibility Index to quantify these local conflicts and examine their behavior under stochastic variations using the Mallows model. We further develop a sheaf-theoretic pushforward operation to model voter merging, implemented via a polynomial-time constraint digraph algorithm. We demonstrate that graph quotients transform distributed edge conflicts into local impossibilities (empty stalks), showing topologically how aggregation paradoxes can persist across scales.

Date: 2025-12, Revised 2026-07
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2512.02416 Latest version (application/pdf)

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:arx:papers:2512.02416

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().