We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the Student Exchange under Partial Fairness (SEPF)....

Even though kidney exchange became an important source of kidney transplants over the last decade with the introduction of market design techniques to organ transplantation, the shortage of kidneys for transplantation is greater than ever. Due to biological disadvantages, patient populations of...