This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen options is selected. This process generates a power-law-like distribution: the $i^{th}$-smallest value scales with $i^{d-1}$, where $d$ is the number of randomly-chosen options, with high probability. We give a formula for the expectation and show the distribution is concentrated around the expectation

翻译：本文分析了一种著名的“双选择能力”分配算法的变体。经典算法中，从$d$个随机选择的选项中选出最小值。我们探讨了当选择$d$个随机选项中最大值时的情况。该过程会产生类幂律分布：第$i$小的值以高概率与$i^{d-1}$成比例，其中$d$是随机选择选项的数量。我们给出了期望的公式，并证明该分布集中在期望附近。