  We study one-sided matching problems where $n$ agents have preferences over
$m$ objects and each of them need to be assigned to at most one object. Most
work on such problems assume that the agents only have ordinal preferences and
usually the goal in them is to compute a matching that satisfies some notion of
economic efficiency. However, in reality, agents may have some preference
intensities or cardinal utilities that, e.g., indicate that they like an object
much more than another object, and not taking these into account can result in
a loss in welfare. While one way to potentially account for these is to
directly ask the agents for this information, such an elicitation process is
cognitively demanding. Therefore, we focus on learning more about their
cardinal preferences using simple threshold queries which ask an agent if they
value an object greater than a certain value, and use this in turn to come up
with algorithms that produce a matching that, for a particular economic notion
$X$, satisfies $X$ and also achieves a good approximation to the optimal
welfare among all matchings that satisfy $X$. We focus on several notions of
economic efficiency, and look at both adaptive and non-adaptive algorithms.
Overall, our results show how one can improve welfare by even non-adaptively
asking the agents for just one bit of extra information per object.
