To better understand discriminations and the effect of affirmative actions in selection problems (e.g., college admission or hiring), a recent line of research proposed a model based on differential variance. This model assumes that the decision-maker has a noisy estimate of each candidate's quality and puts forward the difference in the noise variances between different demographic groups as a key factor to explain discrimination. The literature on differential variance, however, does not consider the strategic behavior of candidates who can react to the selection procedure to improve their outcome, which is well-known to happen in many domains. In this paper, we study how the strategic aspect affects fairness in selection problems. We propose to model selection problems with strategic candidates as a contest game: A population of rational candidates compete by choosing an effort level to increase their quality. They incur a cost-of-effort but get a (random) quality whose expectation equals the chosen effort. A Bayesian decision-maker observes a noisy estimate of the quality of each candidate (with differential variance) and selects the fraction $\alpha$ of best candidates based on their posterior expected quality; each selected candidate receives a reward $S$. We characterize the (unique) equilibrium of this game in the different parameters' regimes, both when the decision-maker is unconstrained and when they are constrained to respect the fairness notion of demographic parity. Our results reveal important impacts of the strategic behavior on the discrimination observed at equilibrium and allow us to understand the effect of imposing demographic parity in this context. In particular, we find that, in many cases, the results contrast with the non-strategic setting.
翻译:为了更好地理解甄选问题(如大学录取或雇用)中的歧视和平等权利行动的影响,最近一行研究提出了基于差异差异的模式。这一模式假定决策者对每个候选人的质量作出粗略的估计,并提出了不同人口群体之间噪音差异的差异,以此作为解释歧视的关键因素。关于差异的文献没有考虑到候选人对甄选程序作出反应以改善其结果的战略行为,这在许多领域都是众所周知的。在本文件中,我们研究战略方面如何影响甄选问题的公平性。我们提议将战略候选人的甄选问题作为非竞争游戏来模拟:理性候选人群体通过选择提高质量的努力水平进行竞争。他们需要付出成本,但获得与所选择的努力相等的(随机)质量。关于差异的文献没有考虑到候选人对甄选程序作出响应以改善其结果的战略行为。在本文中,我们研究战略方面的最佳候选人如何影响如何影响公平性;每个选定的候选人都作为非竞争游戏:通过选择提高质量的努力水平来进行竞争:一个理性候选人群体群体群体;他们需要付出成本,但获得与所选择的(随机)质量的差异性质量。当我们把这种战略表现的判断结果与我们所了解的公平性结果时,我们所理解的公平性判断的价值观是不同的,我们所持的。在游戏中,我们所持的观念中,我们所持的是,我们所持的观念是不同的,我们所持的是,对等定的对等的观念对等的观念是对等的不的。