Before revision:  Informally, our definition captures the idea that an agent should not experience a large change in their utility as long as they make " small" or " innocuous" mistakes while reporting their preferences . We study thisnotion in the context of fair and efficient allocations of indivisible goods among two agents , and show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.
After revision:  Informally, our definition captures the idea that an agent should not experience a large change in their utility as long as they make " small" or " innocuous" mistakes while reporting their preferences to experience a large change in their utility for the final outcome. To address this, we introduce a notion of algorithmic stability and study it in the context of fair and efficient allocations of indivisible goods among two agents , and show that it is impossible to achieve exact stability along with even a weak notion of fairness and even approximate efficiency.