This note proposes a simple polynomial-time method for constructing an ex ante stable school-choice lottery satisfying equal treatment of equals (ETE). We show that the ETE reassignment of any constrained efficient stable matching is ex ante stable, satisfies ETE, and is not ordinally dominated by any other ex ante stable lottery. We further show that there exists a constrained efficient stable matching whose ETE reassignment is not ordinally dominated by any ex post stable lottery.

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