Macías Virgós, EnriquePereira Sáez, María JoséSimón García, Ignacio2025-06-202025-06-202025-01-24Macías-Virgós, E., Pereira-Sáez, M.J. & Simón-García, I. Higher Social Choice. Mediterr. J. Math. 22, 31 (2025). https://doi.org/10.1007/s00009-024-02792-01660-5446https://hdl.handle.net/10347/42199The problem of finding a social choice function in a given space of preferences has been dominated by Arrow’s and Chichilnisky’s Impossibility Theorems. Based on previous work by Carrasquel, Lupton and Oprea, in this paper, we use tools from Algebraic Topology to introduce a notion of higher social choice complexity that determines the minimum number of local social choices that must be aggregated to cover all possible individual preferences. We prove that this invariant is bounded between two known topological invariants, the higher topological complexity and its symmetric version. This result shifts the focus onto the topological structure of the preference space when studying social choice processes.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Algebraic TopologyAlgorithmic ComplexityPublic Choice and Political EconomySocial Choice and WelfareTopologyComparative Social Policyjournal article10.1007/s00009-024-02792-0open access