"x and y are what drive them" vs "x and y are what driveS them"

Which of the following is correct?

It seems evident that self-confidence and a desire for power are what drive them to enter this competition.

It seems evident that self-confidence and a desire for power are what drives them to enter this competition.

Solution 1:

The actual usage stats from the Corpus of Contemporary American English and the British National Corpus look as follows:

                  COCA    BNC

are what drive      10      0
are what drives      3      1
are what have       11      2
are what has         6      0
are what make       97      6
are what makes      25      3
are what tell        2      0
are what tells       0      0

So as you can see, American English rather clearly leans the plural way, while British English is either undecided, or the corpus size is simply too small to say anything definitely.

Personally, I do have to point out that the COCA results are actually at odds with the dialect I speak, where the variant with "what drive" strikes me as ungrammatical. (The antedecent of what might be plural, but the what itself is singular. All you need to do is to look at the what clause, an embedded question. And "*what drive them to do Z" is not a grammatical question in my dialect, or indeed for all I can tell in any variety of English. The question is, "what drives them to do it", and you are providing the answer to that. The "are" is a red herring, because it agrees with "X and Y" and is not part of the what clause at all.)

However, this kind of discrepancy between different dialects is nothing unusual, and there is even a name for this particular phenomenon: notional agreement. (For example, that's also the reason why we say "a lot of people are", even though "a lot" is clearly singular.)

Solution 2:

Well, the deck is a bit stacked in the way you ask the question. You offer

X and Y are what drive them to do Z

X and Y are what drives them to do Z

In both examples, you have treated X and Y as a plural concept, as indicated by the use of are instead of is. In that case, what is logically plural and should take drive, the third person plural form.

However, there may be circumstances in which you want X and Y to be seen as a collective, a single driving force. In that case you could use a single verb form throughout

Fish and chips is what drives them into the restaurant.

But where the forces are independent (either alone might drive the actors), you should preserve the plural throughout

Both dedication and monetary gain are what drive people into the field of medicine.

SUPPLEMENT

The above answer was crafted before the illustrative sentences were added, but the logic is the same. It still is not clear as to whether both characteristics must be present for the result or either one alone might drive the result.

It seems evident that self-confidence and a desire for power are things that can drive them to enter this competition.

but

It seems evident that the concurrence of self-confidence and a desire for power is what drives them to enter this competition.