Due to the importance of artificial intelligence (AI) in a variety of high-stakes decisions, such as loan approval, job hiring, and criminal bail, researchers in Explainable AI (XAI) have developed algorithms to provide users with recourse for an unfavorable outcome. We analyze the incentives for a decision-maker to offer recourse to a set of applicants. Does the decision-maker have the incentive to offer recourse to all rejected applicants? We show that the decision-maker only offers recourse to all applicants in extreme cases, such as when the recourse process is impossible to manipulate. Some applicants may be worse off when the decision-maker can offer recourse.
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