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Conference Papers Year : 2023

Algorithmic Recognition of 2-Euclidean Preferences

Olivier Spanjaard
Magdaléna Tydrichová


A set of voters’ preferences on a set of candidates is 2-Euclidean if candidates and voters can be mapped to the plane so that the preferences of each voter decrease with the Euclidean distance between her position and the positions of candidates. Based on geometric properties, we propose a recognition algorithm, that returns either “yes” (together with a planar positioning of candidates and voters) if the preferences are 2-Euclidean, or “no” if it is able to find a concise certificate that they are not, or “unknown” if a time limit is reached. Our algorithm outperforms a quadratically constrained programming solver achieving the same task, both in running times and the percentage of instances it is able to recognize. In the numerical tests conducted on the PrefLib library of preferences, 91.5% (resp. 4.5%) of the available sets of complete strict orders are proven not to be (resp. to be) 2-Euclidean, and the status of only 4.5% of them could not be decided. Furthermore, for instances involving 5 (resp. 6, 7) candidates, we were able to find planar representations that are compatible with 87.4% (resp. 58.1%, 60.1%) of voters’ preferences.

Dates and versions

hal-04232747 , version 1 (09-10-2023)



Bruno Escoffier, Olivier Spanjaard, Magdaléna Tydrichová. Algorithmic Recognition of 2-Euclidean Preferences. 26th European Conference on Artificial Intelligence ECAI 2023, Sep 2023, Krakow (Cracovie), Poland. pp.637-644, ⟨10.3233/FAIA230326⟩. ⟨hal-04232747⟩
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