Publication: An optimization-based approach to ranking aggregation with weak order outputs
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Date
2026
Authors
Aledo, Juan A. ; Landete, Mercedes ; Domínguez Sánchez, Concepción ; Jaime Alcántara, Juan de Dios
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Facultades de la UMU::Facultad de Matemáticas
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info:eu-repo/semantics/preprint
Description
Abstract
Rank aggregation problems combine individual orderings of a common set of items into a consensus ranking reflecting collective preferences. This paper introduces a general Integer Linear Programming (ILP) framework to model and solve aggregation problems whose solutions are weak orders (bucket orders). The framework provides a flexible and tractable architecture that incorporates structural and normative constraints required in practice.
Within this setting, we develop several ILP formulations embedding additional structural requirements on the consensus bucket order, including a fixed number of buckets, predefined bucket sizes, top-$k$ constraints, and group-based fairness conditions. The formulations are modular and adaptable to different aggregation contexts.
A particularly relevant case is the Optimal Bucket Order Problem (OBOP), for which we present the first exact mixed-integer linear programming formulation. We evaluate the models through computational experiments, comparing optimal solutions with the heuristics of Aledo et al.\ (2018) and assessing scalability on benchmark instances from the PrefLib library. Finally, we present a real-world case study on Spanish universities, where the proposed models aggregate competing rankings under structural and fairness constraints.
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Este ítem está sujeto a una licencia Creative Commons. http://creativecommons.org/licenses/by-nc-nd/4.0/