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That assumption will only allow you to pick based on a relative standard not an absolute one. Also, a degree being an eligibility criteria makes no sense. If you want to hire well then you should be willing to meet any relevant candidate. So in effect, with a degree being a REQUIREMENT you are actually lowering the pool of people who will apply and hence reducing your probability not increasing it.

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The most desirable companies get so many resumes that they need to filter out most of them. I used to work for a popular search engine before Google came into the picture. As an engineer I had to interview people every week. HR handed me lots of resumes from people with CS degrees from top universities for phone screening. They didn't bother with the rest unless someone was heavily recommended by a trusted source.

Do you think you were doing it the best way possible?

His employer's search business got eaten by Google, at the time I think Google were hiring 50%+ PhDs.

Sure - a smaller search space will not enhance the value of the maximum your are searching for.

But the cost of searching my lower drastically.

And as another poster pointed out it is the total of (quality of candidate - search cost) that you want to maximize.

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