As data science has broadened its scope in recent years, a number of domains have applied computational methods for classification and prediction to evaluate individuals in high-stakes settings. These developments have led to an active line of recent discussion in the public sphere about the consequences of algorithmic prediction for notions of fairness and equity. In part, this discussion has involved a basic tension between competing notions of what it means for such classifications to be fair to different groups. We consider several of the key fairness conditions that lie at the heart of these debates, and in particular how these properties operate when the goal is to rank-order a set of applicants by some criterion of interest, and then to select the top-ranking applicants.
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