  A preference profile with m alternatives and n voters is 2-dimensional
Euclidean if both the alternatives and the voters can be placed into a
2-dimensional space such that for each pair of alternatives, every voter
prefers the one which has a shorter Euclidean distance to the voter. We study
how 2-dimensional Euclidean preference profiles depend on the values m and n.
We find that any profile with at most two voters or at most three alternatives
is 2-dimensional Euclidean while for three voters, we can show this property
for up to seven alternatives. The results are tight in terms of Bogomolnaia and
Laslier [2, Proposition 15(1)].
