Argumentation is usually used to achieve a state in which one participant of a dialogue brings another participant to accept a belief the former presents. This idea is acceptable when it comes to disputes about (objective) facts. In the case of disputes about subjective tastes, however, the participants usually achieve a different kind of result; it often happens that they end their dialogue in a state in which they take their dispute to be resolved and, yet, retain their initial standpoints. If the disputes about tastes that end up in this state contain arguments, one may wonder what the proper use of argumentation in such disputes is. The present paper addresses this issue. The main idea consists in that the participants coordinate their positions by bringing their opponents to tolerate their respective subjective attitudes toward the items under discussion. This kind of response is framed by a contextualist semantics of predicates of personal taste.