This article discusses a procedural, minimalist approach to justice in terms of fair hearing applicable to value conflicts at impasse in politics. This approach may be summarized in the Adversary Argumentation Principle (AAP): the idea that each side in a conflict should be heard. I engage with Stuart Hampshire’s efforts to justify the AAP and argue that those efforts have failed to provide normatively cogent foundations for it. I suggest deriving such foundations from a basic idea of procedural equality (all parties in a conflict should be granted an equal chance to have a say) which all conflicting parties could be thought to endorse. But what happens once all parties have been heard if no agreement is reached? Borrowing a distinction well known to scholars of peace studies, but surprisingly neglected by justice-driven political philosophers, I claim that although the AAP might be inconclusive with regard to resolving a conflict, it is a promising principle for managing value conflicts justly. The AAP is thus considered anew through the lens of conflict management: as a principle of justice to characterize normatively the way conflicting parties should interact for their interaction to be morally justifiable to such parties with a view to changing antagonistic conflict dynamics into cooperative ones.