  We provide a problem definition of the stable marriage problem for a general
number of parties $p$ under a natural preference scheme in which each person
has simple lists for the other parties. We extend the notion of stability in a
natural way and present so called elemental and compound algorithms to generate
matchings for a problem instance. We demonstrate the stability of matchings
generated by both algorithms, as well as show that the former runs in $O(pn^2)$
time.
