Weak stability and Pareto efficiency in school choice

We propose a new notion of weak stability for two-sided matching problems. A matching is said to be weakly stable if matching any of its blocking pairs inevitably creates new blocking pairs. We then apply this concept to school choice and study its compatibility with the Pareto efficiency of students’ welfare. Our main result shows that if a matching is not Pareto dominated by any matching more stable than it, then it is weakly stable if and only if it is the efficiency-adjusted deferred acceptance outcome when its own set of blocking pairs is used as consenting constraint.