Abstract
This paper treats with both the 1-q-type social matching problems and the social matching procedure problems under two-sided preference orderings. Keeping college admission institutions in mind, these problems are described as follows. The former is that “There are the set C of colleges and the set S of students. Each college has a quota q of students. Every college has a preference ordering over the set S and every student has a preference ordering over the set C, according to the willingness to match respectively. Given these preference orderings, how the colleges and the students should be matched under such the restriction that no student is matched to more than one college and no college is matched more than its quota of students?” The latter is that “The institutional arrangements by which the matching is accomplished are called the social matching procedures. What socially desirable properties they should have? Does such a procedure exist? If so, then what is it?” The purpose of this paper is to review and synthesize some literatures about these two matching problems and to discuss theoretical, practical and empirical questions which are remaining unsolved.
