Makes no sense! If you're holding out for one that's better than any in the first group, and there is none, you are stuck with the last one you interview, with expected rank of (N-1)/2, but which could be the worst one.
I suppose this 1/e stratagem maximizes the expected rank of your choice. But after all, you're only going to do it once!
Well, I quickly ( cough, cough ) wrote up a simulation for the suggested stratagem assuming 100 candidate interviews, ranked 1 through 100, and taken in random order. I used 36 for the cutoff of the “automatic refuse” sample, and then followed the strategy of taking the first one better than any of the sample of 36, or settling for the last interviewee.
1000 trials are well within trivial response time, and here are the results for several runs of 1000 trials:
358 142 81 28 21 12 7 7 6 11 7 7 4 3 4 2 4 3 2 5 3 3 3 6 5 2 3 3 4 5 6 4 4 2 2 1 4 6 3 6 4 1 6 0 4 3 4 3 5 4 2 5 4 1 6 7 3 3 2 2 2 5 4 3 7 1 5 5 4 2 4 0 2 4 3 5 3 1 1 3 4 5 5 5 4 4 4 3 2 4 2 7 1 7 8 4 0 4 4 1
405 153 62 30 28 15 10 3 7 4 5 1 6 2 0 5 3 4 5 5 1 4 2 5 4 4 4 6 5 2 4 8 8 4 2 2 4 3 5 2 3 0 2 0 5 4 1 3 4 4 3 2 0 3 3 0 3 1 5 3 2 6 3 1 3 3 0 2 0 2 7 4 2 5 5 2 6 3 4 1 4 2 4 2 2 1 1 0 2 4 5 8 4 6 4 1 0 2 3 3
371 157 67 23 16 12 5 5 8 6 2 3 3 1 5 2 2 4 3 2 1 1 5 9 6 2 6 4 2 6 2 4 5 5 5 6 2 4 0 2 3 4 3 1 1 4 3 3 3 4 0 1 1 3 6 5 4 8 6 1 2 7 1 3 4 1 4 3 2 5 3 4 6 6 3 6 3 2 4 1 1 6 6 4 4 4 4 7 4 1 6 5 2 4 3 5 4 6 10 6
... so it looks like a good strategy, in that it seems to optimize my chance of selecting a high ranking candidate. It gave me a top 10 candidate in 673, 717, and 670 out of 1000 trials in the three runs shown.