House allocation when availability of houses may change unexpectedly

We study the problem of allocating a set of objects, e.g. houses, tasks, offices to a group of people having preferences over these objects. For various reasons, there may be more or fewer objects than initially planned and allocated. How should such unexpected changes be handled? One way is to declare the initial decision irrelevant and reallocate all available objects. Alternatively, one can use the initial decision as starting point in allocating the new objects. Since both perspectives seem equally reasonable, a natural robustness principle on the rule is that it should produce the same outcome no matter which one is taken. We define two robustness properties based on this idea, pertaining to more objects and fewer objects, respectively.