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The wide application of AI-based decision systems in many high-stake domains has raised concerns regarding fairness of these systems. As these systems will lead to real-life consequences to people who are subject to their decisions, understanding what these decision subjects perceive as a fair or unfair system is of vital importance. In this paper, we extend prior work in this direction by taking a perspective of repeated interactions---We ask that when decision subjects interact with an AI-based decision system repeatedly and can strategically respond to the system by determining whether to stay in the system, what factors will affect the decision subjects' fairness perceptions and retention in the system and how. To answer these questions, we conducted two randomized human-subject experiments in the context of an AI-based loan lending system. Our results suggest that in repeated interactions with the AI-based decision system, overall, decision subjects' fairness perceptions and retention in the system are significantly affected by whether the system is in favor of the group that subjects themselves belong to, rather than whether the system treats different groups in an unbiased way. However, decision subjects with different qualification levels have different reactions to the AI system's biased treatment across groups or the AI system's tendency to favor/disfavor their own group. Finally, we also find that while subjects' retention in the AI-based decision system is largely driven by their own prospects of receiving the favorable decision from the system, their fairness perceptions of the system is influenced by the system's treatment to people in other groups in a complex way.
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