  A permutation representation of a Coxeter group $W$ naturally defines an
absolute order. This family of partial orders (which includes the absolute
order on $W$) is introduced and studied in this paper. Conditions under which
the associated rank generating polynomial divides the rank generating
polynomial of the absolute order on $W$ are investigated when $W$ is finite.
Several examples, including a symmetric group action on perfect matchings, are
discussed. As an application, a well-behaved absolute order on the alternating
subgroup of $W$ is defined.
