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Artificial Intelligence and algorithms are increasingly able to replace human workers in cognitively sophisticated tasks, including ones related to justice. Many governments and international organizations are discussing policies related to the application of algorithmic judges in courts. In this paper, we investigate the public perceptions of algorithmic judges. Across two experiments (N = 1,822), and an internal meta-analysis (N = 3,039), our results show that even though court users acknowledge several advantages of algorithms (i.e., cost and speed), they trust human judges more and have greater intentions to go to the court when a human (vs. an algorithmic) judge adjudicates. Additionally, we demonstrate that the extent that individuals trust algorithmic and human judges depends on the nature of the case: trust for algorithmic judges is especially low when legal cases involve emotional complexities (vs. technically complex or uncomplicated cases).