  Motivated by the common academic problem of allocating papers to referees for
conference reviewing we propose a novel mechanism for solving the assignment
problem when we have a two sided matching problem with preferences from one
side (the agents/reviewers) over the other side (the objects/papers) and both
sides have capacity constraints. The assignment problem is a fundamental
problem in both computer science and economics with application in many areas
including task and resource allocation. We draw inspiration from multi-criteria
decision making and voting and use order weighted averages (OWAs) to propose a
novel and flexible class of algorithms for the assignment problem. We show an
algorithm for finding a $\Sigma$-OWA assignment in polynomial time, in contrast
to the NP-hardness of finding an egalitarian assignment. Inspired by this
setting we observe an interesting connection between our model and the classic
proportional multi-winner election problem in social choice.
