Strategy-proof size improvement: is it possible?

In unit-demand and multi-copy object allocation problems, we say that a mechanism size-wise dominates another mechanism if the latter never allocates more objects than the former does, while the converse is true for some problem. Our main result shows that no individually rational and strategy-proof mechanism size-wise dominates a non-wasteful, truncation-invariant, and extension-responding mechanism. As a corollary of this, the wellknown deferred-acceptance, serial dictatorship, and Boston mechanisms are not size-wise dominated by an individually rational and strategy-proof mechanism. We also show that whenever the number of agents does not exceed the total number of object copies, no group strategy-proof and ecient mechanism, such as top trading cycles mechanism, is size-wise dominated by an individually rational, weakly population-monotonic, and strategy-proof mechanism.