  We introduce a new model for two-sided matching which allows us to borrow
popular fairness notions from the fair division literature such as
envy-freeness up to one good and maximin share guarantee. In our model, each
agent is matched to multiple agents on the other side over whom she has
additive preferences. We demand fairness for each side separately, giving rise
to notions such as double envy-freeness up to one match (DEF1) and double
maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1
cannot always be achieved, but in the special case where both sides have
identical preferences, the round-robin algorithm with a carefully designed
agent ordering achieves it. In contrast, DMMS cannot be achieved even when both
sides have identical preferences.
