  We consider the one-sided matching problem, where n agents have preferences
over n items, and these preferences are induced by underlying cardinal
valuation functions. The goal is to match every agent to a single item so as to
maximize the social welfare. Most of the related literature, however, assumes
that the values of the agents are not a priori known, and only access to the
ordinal preferences of the agents over the items is provided. Consequently,
this incomplete information leads to loss of efficiency, which is measured by
the notion of distortion. In this paper, we further assume that the agents can
answer a small number of queries, allowing us partial access to their values.
We study the interplay between elicited cardinal information (measured by the
number of queries per agent) and distortion for one-sided matching, as well as
a wide range of well-studied related problems. Qualitatively, our results show
that with a limited number of queries, it is possible to obtain significant
improvements over the classic setting, where only access to ordinal information
is given.
