  We consider an assignment problem that has aspects of fair division as well
as social choice. In particular, we investigate the problem of assigning a
small subset from a set of indivisible items to multiple players so that the
chosen subset is \emph{agreeable} to all players, i.e., every player weakly
prefers the chosen subset to any subset of its complement. For an arbitrary
number of players, we derive tight upper bounds on the size for which a subset
of that size that is agreeable to all players always exists when preferences
are monotonic. We then present polynomial-time algorithms that find an
agreeable subset of approximately half of the items when there are two or three
players and preferences are responsive. Our results translate to a
2-approximation on the individual welfare of every player when preferences are
subadditive.
