As algorithms increasingly take managerial and governance roles, it is ever more important to build them to be perceived as fair and adopted by people. With this goal, we propose a procedural justice framework in algorithmic decision-making drawing from procedural justice theory, which lays out elements that promote a sense of fairness among users. As a case study, we built an interface that leveraged two key elements of the framework---transparency and outcome control---and evaluated it in the context of goods division. Our interface explained the algorithm's allocative fairness properties (standards clarity) and outcomes through an input-output matrix (outcome explanation), then allowed people to interactively adjust the algorithmic allocations as a group (outcome control). The findings from our within-subjects laboratory study suggest that standards clarity alone did not increase perceived fairness; outcome explanation had mixed effects, increasing or decreasing perceived fairness and reducing algorithmic accountability; and outcome control universally improved perceived fairness by allowing people to realize the inherent limitations of decisions and redistribute the goods to better fit their contexts, and by bringing human elements into final decision-making.
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