This paper answers a long-standing open question concerning the $1∕e$-strategy for the problem of best choice. $N$ candidates for a job arrive at times independently uniformly distributed in $[0,1]$. The interviewer knows how each candidate ranks relative to all others seen so far, and must immediately appoint or reject each candidate as they arrive. The aim is to choose the best overall. The $1∕e$ strategy is to follow the rule: ‘Do nothing until time $1∕e$, then appoint the first candidate thereafter who is best so far (if any).’

The question, first discussed with Larry Shepp in 1983, was to know whether the $1∕e$-strategy is optimal if one has ‘no information about the total number of options’. Quite what this might mean is open to various interpretations, but we shall take the proportional-increment process formulation of Bruss and Yor (2012). Such processes are shown to have a very rigid structure, being time-changed pure birth processes, and this allows some precise distributional calculations, from which we deduce that the $1∕e$-strategy is in fact not optimal.

本文回答了一个长期存在的关于 $\mathrm{1个}∕Ë$最佳选择问题的战略。 $ñ$ 求职者有时会独立均匀地分布在 $[0，\mathrm{1个}]$。面试官知道每个候选人相对于​​到目前为止看到的所有其他候选人的排名，并且必须在每个候选人到达时立即任命或拒绝。目的是选择最佳的整体。这$\mathrm{1个}∕Ë$ 策略是遵循以下规则：“直到时间不做任何事情 $\mathrm{1个}∕Ë$，然后任命迄今最佳的第一位候选人（如果有）。”

这个问题最初是在1983年与拉里·谢普（Larry Shepp）讨论的，目的是要知道 $\mathrm{1个}∕Ë$如果没有“关于期权总数的信息”，则-strategy是最佳选择。这可能意味着各种解释，但我们将采用Bruss和Yor（2012）的比例增量过程公式。这些过程显示出具有非常严格的结构，是随时间变化的纯出生过程，因此可以进行一些精确的分布计算，从中可以推断出$\mathrm{1个}∕Ë$策略实际上不是最佳的。