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This paper studies the task of comparative preference classification (CPC). Given two entities in a sentence, our goal is to classify whether the first (or the second) entity is preferred over the other or no comparison is expressed at all between the two entities. Existing works either do not learn entity-aware representations well and fail to deal with sentences involving multiple entity pairs or use sequential modeling approaches that are unable to capture long-range dependencies between the entities. Some also use traditional machine learning approaches that do not generalize well. This paper proposes a novel Entity-aware Dependency-based Deep Graph Attention Network (ED-GAT) that employs a multi-hop graph attention over a dependency graph sentence representation to leverage both the semantic information from word embeddings and the syntactic information from the dependency graph to solve the problem. Empirical evaluation shows that the proposed model achieves the state-of-the-art performance in comparative preference classification.