  We propose a class of semimetrics for preference relations any one of which
is an alternative to the classical Kemeny-Snell-Bogart metric. (We take a
fairly general viewpoint about what constitutes a preference relation, allowing
for any acyclic order to act as one.) These semimetrics are based solely on the
implications of preferences for choice behavior, and thus appear more suitable
in economic contexts and choice experiments. In our main result, we obtain a
fairly simple axiomatic characterization for the class we propose. The
apparently most important member of this class (at least in the case of finite
alternative spaces), which we dub the top-difference semimetric, is
characterized separately. We also obtain alternative formulae for it, and
relative to this metric, compute the diameter of the space of complete
preferences, as well as the best transitive extension of a given acyclic
preference relation. Finally, we prove that our preference metric spaces cannot
be isometically embedded in a Euclidean space.
