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With the advancement of deep learning techniques, an increasing number of methods have been proposed for optic disc and cup (OD/OC) segmentation from the fundus images. Clinically, OD/OC segmentation is often annotated by multiple clinical experts to mitigate the personal bias. However, it is hard to train the automated deep learning models on multiple labels. A common practice to tackle the issue is majority vote, e.g., taking the average of multiple labels. However such a strategy ignores the different expertness of medical experts. Motivated by the observation that OD/OC segmentation is often used for the glaucoma diagnosis clinically, in this paper, we propose a novel strategy to fuse the multi-rater OD/OC segmentation labels via the glaucoma diagnosis performance. Specifically, we assess the expertness of each rater through an attentive glaucoma diagnosis network. For each rater, its contribution for the diagnosis will be reflected as an expertness map. To ensure the expertness maps are general for different glaucoma diagnosis models, we further propose an Expertness Generator (ExpG) to eliminate the high-frequency components in the optimization process. Based on the obtained expertness maps, the multi-rater labels can be fused as a single ground-truth which we dubbed as Diagnosis First Ground-truth (DiagFirstGT). Experimental results show that by using DiagFirstGT as ground-truth, OD/OC segmentation networks will predict the masks with superior glaucoma diagnosis performance.