  We investigate the complexity of approximately counting stable matchings in
the $k$-attribute model, where the preference lists are determined by dot
products of "preference vectors" with "attribute vectors", or by Euclidean
distances between "preference points" and "attribute points". Irving and
Leather proved that counting the number of stable matchings in the general case
is $#P$-complete. Counting the number of stable matchings is reducible to
counting the number of downsets in a (related) partial order and is
interreducible, in an approximation-preserving sense, to a class of problems
that includes counting the number of independent sets in a bipartite graph
($#BIS$). It is conjectured that no FPRAS exists for this class of problems. We
show this approximation-preserving interreducibilty remains even in the
restricted $k$-attribute setting when $k \geq 3$ (dot products) or $k \geq 2$
(Euclidean distances). Finally, we show it is easy to count the number of
stable matchings in the 1-attribute dot-product setting.
