Biases impair the effectiveness of algorithms. For example, the age bias of the widely-used PageRank algorithm impairs its ability to effectively rank nodes in growing networks. PageRank’s temporal bias cannot be fully explained by existing analytic results that predict a linear relation between the expected PageRank score and the indegree of a given node. We show that in evolving networks, under a mean-field approximation, the expected PageRank score of a node can be expressed as the product of the node’s indegree and a previously-neglected age factor which can “amplify” the indegree’s age bias. We use two well-known empirical networks to show that our analytic results explain the observed PageRank’s age bias and, when there is an age bias amplification, they enable estimates of the node PageRank score that are more accurate than estimates based solely on local structural information. Accuracy gains are larger in degree–degree correlated networks, as revealed by a growing directed network model with tunable assortativity. Our approach can be used to analytically study other kinds of ranking bias.

偏见会损害算法的有效性。例如，广泛使用的 PageRank 算法的年龄偏见削弱了它在不断增长的网络中有效排列节点的能力。PageRank 的时间偏差不能完全用现有的分析结果来解释，这些分析结果预测了预期的 PageRank 分数和给定节点的入度之间的线性关系。我们表明，在不断发展的网络中，在平均场近似下，节点的预期 PageRank 分数可以表示为节点的入度和先前忽略的年龄因素的乘积，该因素可以“放大”入度的年龄偏差。我们使用两个众所周知的经验网络来表明我们的分析结果解释了观察到的 PageRank 的年龄偏差，并且当存在年龄偏差放大时，它们使节点 PageRank 得分的估计比仅基于局部结构信息的估计更准确。正如不断增长的具有可调分类性的有向网络模型所揭示的那样，度-度相关网络的准确度增益更大。我们的方法可用于分析研究其他类型的排名偏差。