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We show that every single-peaked preference profile with<jats:italic>two<\/jats:italic>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 single-peaked and single-crossing. By the work of Chen et al. \u00a0(Social Choice and Welfare 48(2):409\u2013432, 2017), we thus obtain that the smallest single-peaked and single-crossing preference profiles that are<jats:italic>not<\/jats:italic>one-dimensional Euclidean consist of three voters and six alternatives.<\/jats:p>","DOI":"10.1007\/s00355-020-01301-y","type":"journal-article","created":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T08:47:56Z","timestamp":1613033276000},"page":"117-144","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Small one-dimensional Euclidean preference profiles"],"prefix":"10.1007","volume":"57","author":[{"given":"Jiehua","family":"Chen","sequence":"first","affiliation":[]},{"given":"Sven","family":"Grottke","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,10]]},"reference":[{"issue":"2","key":"1301_CR1","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s00355-010-0476-3","volume":"36","author":"M\u00c1 Ballester","year":"2011","unstructured":"Ballester M\u00c1, Haeringer G (2011) A characterization of the single-peaked domain. 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