Robust Minimal Instability of the Top Trading Cycles Mechanism

In the context of priority-based allocation objects, we formulate methods to compare assignments in terms their stability. We introduce three basic properties that a reasonable stability comparison should satisfy. show for any satisfying properties, top trading cycles mechanism is minimally unstable among efficient and strategy-proof mechanisms when objects have unit capacities. Our unifying approach covers basically all natural comparisons establishes robustness recent result by Abdulkadiro?lu et al. (2020). When nonunit capacities, characterize capacity-priority structures which our preserved. (JEL C70, C78, D61, D82)