Discrimination in selection problems such as hiring or college admission is often explained by implicit bias from the decision maker against disadvantaged demographic groups. In this paper, we consider a model where the decision maker receives a noisy estimate of each candidate's quality, whose variance depends on the candidate's group—we argue that such differential variance is a key feature of many selection problems. We analyze two notable settings: in the first, the noise variances are unknown to the decision maker who simply picks the candidates with the highest estimated quality independently of their group; in the second, the variances are known and the decision maker picks candidates having the highest expected quality given the noisy estimate. We show that both baseline decision makers yield discrimination, although in opposite directions: the first leads to underrepresentation of the low-variance group while the second leads to underrepresentation of the high-variance group. We study the effect on the selection utility of imposing a fairness mechanism that we term the γ-rule (it is an extension of the classical four-fifths rule and it also includes demographic parity). In the first setting (with unknown variances), we prove that under mild conditions, imposing the γ-rule increases the selection utility—here there is no trade-off between fairness and utility. In the second setting (with known variances), imposing the γ-rule decreases the utility but we prove a bound on the utility loss due to the fairness mechanism.

招聘或大学录取等选择问题中的歧视通常是由决策者对弱势人口群体的隐性偏见来解释的。在本文中，我们考虑一个模型，其中决策者收到每个候选人质量的噪声估计，其方差取决于候选人所在的组——我们认为这种差异方差是许多选择问题的一个关键特征。我们分析了两个值得注意的设置：第一个，决策者不知道噪声方差，他们只是独立于其组挑选具有最高估计质量的候选者；在第二种情况下，方差是已知的，决策者会根据噪声估计选择具有最高预期质量的候选者。我们表明，两个基线决策者都会产生歧视，尽管方向相反：第一个导致低方差组的代表性不足，而第二个导致高方差组的代表性不足。我们研究了施加公平机制对选择效用的影响，我们称之为γ- 规则（它是经典五分之四规则的扩展，还包括人口均等）。在第一个设置中（方差未知），我们证明在温和条件下，施加γ 规则会增加选择效用——这里在公平性和效用之间没有权衡。在第二个设置中（具有已知的方差），施加γ 规则会降低效用，但我们证明了由于公平机制导致的效用损失的界限。