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Precisely annotating instances with multiple labels is costly and has emerged as a significant bottleneck in the real-world multi-label learning tasks. To deal with this problem, the most straightforward strategy is partially-annotating, which aims to reduce the cost by annotating only a subset of labels. Existing works mainly includes label-level partially-annotating (LPA), where each instance is assigned a subset of positive labels, and instance-level partially-annotating (IPA), where all positive labels are assigned to an instance, but only a subset of instances are annotated. However, these methods tend to focus on improving model performance under each type of partial annotation, often neglecting a fundamental question: \textit{which method is the most cost-effective?} In this paper, we empirically evaluate which partially-annotating method achieves better model performance at the same annotation cost. To make a fair comparison, we manually annotated images in the MS-COCO dataset using two partially-annotating methods and recorded their averaging annotation time per image. This allows us to train models on two types of partial annotations with the same annotation cost and to compare their performance. Empirical results show that even when the number of examples annotated with IPA is only one-fifth that of LPA, models trained on IPA annotations significantly outperform those trained on LPA annotations, yielding that IPA is significantly more cost-effective than LPA. To explain the superiority of IPA, our causal reasoning framework shows that compared to LPA, IPA preserves complete co-occurrence relationships, enabling the model to capture correlative patterns, which is useful for improving model performance.