  We characterize one-dimensional Euclidean preference profiles with a small
number of alternatives and voters. In particular, we show the following.
  1. Every preference profile with up to two voters is one-dimensional
Euclidean if and only if it is single-peaked.
  2. Every preference profile with up to five alternatives is one-dimensional
Euclidean if and only if it is single-peaked and single-crossing.
  By [12], we thus obtain that the smallest single-peaked and single-crossing
preference profiles that are not one-dimensional Euclidean consist of three
voters and six alternatives.
