  While the stable marriage problem and its variants model a vast range of
matching markets, they fail to capture complex agent relationships, such as the
affiliation of applicants and employers in an interview marketplace. To model
this problem, the existing literature on matching with externalities permits
agents to provide complete and total rankings over matchings based off of both
their own and their affiliates' matches. This complete ordering restriction is
unrealistic, and further the model may have an empty core. To address this, we
introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where
agents' preferences indicate dichotomous acceptance or rejection of another
agent in the marketplace, both for themselves and their affiliates.
  We also assume the agent's preferences over entire matchings are determined
by a general weighted valuation function of their (and their affiliates')
matches. Our results are threefold: (1) we use a human study to show that
real-world matching rankings follow our assumed valuation function; (2) we
prove that there always exists a stable solution by providing an efficient,
easily-implementable algorithm that finds such a solution; and (3) we
experimentally validate the efficiency of our algorithm versus a
linear-programming-based approach.
