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

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  • Karen Sargsyan

Abstract

We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation. Unlike traditional linearization methods (e.g., HodgeRank), this approach preserves the discrete structure of ordinal preferences, identifying which specific voter interactions cause aggregation failure -- information that global methods cannot provide -- via the Obstruction Locus. We formalize the Incompatibility Index to quantify these local conflicts and examine their behavior under stochastic variations using the Mallows model. Additionally, we develop a rigorous sheaf-theoretic pushforward operation to model voter merging, implemented via a polynomial-time constraint DAG algorithm. We demonstrate that graph quotients transform distributed edge conflicts into local impossibilities (empty stalks), providing a topological characterization of how aggregation paradoxes persist across scales.

Suggested Citation

  • Karen Sargsyan, 2025. "Localizing Preference Aggregation Conflicts: A Graph-Theoretic Approach Using Sheaves," Papers 2512.02416, arXiv.org.
    • Handle: RePEc:arx:papers:2512.02416
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    References listed on IDEAS

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    6. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
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