# Stable Domination

Stable Domination

We consider a general model of indivisible goods allocation with choice-based priorities, as well as the special case of school choice. Stability is the main normative consideration for such problems. However, depending on the priority structure, it may be incompatible with Pareto-efficiency. We propose a new criterion: an allocation is stable-dominating if it weakly Pareto-improves some stable allocation.
We show that if an allocation Pareto-improves on a particular non-wasteful (and therefore stable) allocation, then it matches the same agents and matches the same number of agents to each object. This is much like the conclusion of the Rural Hospitals Theorem. In fact, we connect the existence of a stable-dominating and strategy- proof rule and the Rural Hospitals Theorem on one hand with the existence of the agent-optimal stable-dominating rule on the other.
For the school choice model, we also characterize the weak priority structures that ensure every Pareto-efficient and stable-dominating rule is stable.
Finally, for the school choice model, we show that if a rule is Pareto-efficient, stable-dominating and strategy-proof, then it is actually stable. We also show an alternative version of this result where we replace Pareto-efficiency with a mild regularity condition.