When preference misreporting is Harm[less]ful?

In a school choice problem, we say that a mechanism is harmless if no student can ever misreport his preferences so that he is not hurt but someone else is. We consider two large classes of mechanisms, which include the Boston, the agent-proposing deferred acceptance, and the school-proposing deferred acceptance (sDA) mechanisms. Among all the rules in these two classes, the sDA is the unique harmless mechanism. We next provide two axiomatic characterizations of the sDA. First, the sDA is the unique stable, non-bossy, and “independent of an irrelevant student mechanism”. The last axiom requires that the outcome does not depend on the presence of a student who prefers being unassigned to any school. As harmlessness implies non-bossiness, the sDA is also the unique stable, harmless, and independent of an irrelevant student mechanism. To our knowledge, these axiomatizations as well as the well-known Gale and Shapley's (1962), which reveals that the sDA is the student-pessimal stable mechanism, are the only characterizations of the sDA.