That mathematical problem (the secretary problem) is often cited, but it's not how real hiring works. The problem defines the only success criterion as hiring the single top candidate, and everything else fails. That's not at all what you're looking for in the real world - there are a spectrum of results, where any one in the top decile will be great and the next decile only slightly lesser and so on.
One-dimensional ranking is one aspect of how it breaks in real-world hiring, but I think almost the bigger might be that the secretary problem assumes you need to decide immediately and can't just wait around until you've seen the whole batch of applicants.
The main difference is that you're trying to solve the problem of turning an interview into a way to choose between candidates, while the secretary problem assumes you already figured that out and is trying to solve something different entirely!
