This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the voters have made their choices, each vote can be inspected to determine which candidate received that vote. The time (or cost) to inspect each of the votes is known in advance. The task is to (possibly adaptively) determine the order in which to inspect the votes, so as to minimize the expected time to determine which candidate has won the election. We design polynomial-time constant-factor approximation algorithms for both the absolute-majority and the relative-majority version. Both algorithms are based on a two-phase approach. In the first phase, the algorithms reduce the number of relevant candidates to $O(1)$, and in the second phase they utilize techniques from the literature on stochastic function evaluation to handle the remaining candidates. In the case of absolute majority, we show that the same can be achieved with only two rounds of adaptivity.

翻译：本文考虑选民根据已知概率分布独立选择一名候选人的选举场景。获得绝对多数（取决于版本，指绝对或相对多数）的候选人胜出。选民投票完成后，每张选票可被查验以确定所投候选人。每张选票的查验时间（或成本）事先已知。任务在于（可能自适应地）确定查验选票的顺序，以最小化确定胜选者所需期望时间。针对绝对多数和相对多数两种版本，我们设计了多项式时间常数近似比算法。两种算法均基于两阶段方法：第一阶段将相关候选人数减少至常数 $O(1)$，第二阶段利用随机函数评估领域的现有技术处理剩余候选人。在绝对多数情形下，我们证明仅需两轮自适应即可实现相同目标。