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J. Chen, S. Grottke:
"Small one‑dimensional Euclidean preference profiles";
Social Choice and Welfare, 57 (2021), S. 117 - 144.

We characterize one-dimensional Euclidean preference profiles with a small number
of alternatives and voters. We show that every single-peaked preference profile
with two voters is one-dimensional Euclidean, and that every preference profile with
up to five alternatives is one-dimensional Euclidean if and only if it is both singlepeaked
and single-crossing. By the work of Chen et al. (Social Choice and Welfare
48(2):409-432, 2017), we thus obtain that the smallest single-peaked and singlecrossing
preference profiles that are not one-dimensional Euclidean consist of three
voters and six alternatives

http://dx.doi.org/10.1007/s00355-020-01301-y

https://publik.tuwien.ac.at/files/publik_300315.pdf