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Algorithmic case-based decision support provides examples to help human make sense of predicted labels and aid human in decision-making tasks. Despite the promising performance of supervised learning, representations learned by supervised models may not align well with human intuitions: what models consider as similar examples can be perceived as distinct by humans. As a result, they have limited effectiveness in case-based decision support. In this work, we incorporate ideas from metric learning with supervised learning to examine the importance of alignment for effective decision support. In addition to instance-level labels, we use human-provided triplet judgments to learn human-compatible decision-focused representations. Using both synthetic data and human subject experiments in multiple classification tasks, we demonstrate that such representation is better aligned with human perception than representation solely optimized for classification. Human-compatible representations identify nearest neighbors that are perceived as more similar by humans and allow humans to make more accurate predictions, leading to substantial improvements in human decision accuracies (17.8% in butterfly vs. moth classification and 13.2% in pneumonia classification).