Higher Social Choice

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URI: https://hdl.handle.net/10347/42199
ISSN: 1660-5446
DOI: 10.1007/s00009-024-02792-0

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2025-01-24

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Springer
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Abstract

The 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.

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Algebraic Topology| Algorithmic Complexity| Public Choice and Political Economy| Social Choice and Welfare| Topology| Comparative Social Policy

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Macías-Virgós, E., Pereira-Sáez, M.J. & Simón-García, I. Higher Social Choice. Mediterr. J. Math. 22, 31 (2025). https://doi.org/10.1007/s00009-024-02792-0

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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first and second authors were partially supported by MINECO and FEDER research project PID2020-MTM-114474GB-I00. The first author was partially supported by Xunta de Galicia ED431C 2019/10.

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