Meaning: Within a certain period of time, presidential elections were frequently won narrowly.
Something has or
some entities have a bargaining power that few of them have ever enjoyed before. We can also deduce from the tone of the sentence that the presidential elections seem to be two-horse races. From the meaning, I expect the
something or
the entities to be either
participants in the presidential elections or
key stakeholders in such elections. With this in mind, let's look at the options.
Option A: At a time when narrowly won presidential elections seem more the rule than the exception,
the proliferation of small third parties would have a bargaining power that few of them have ever enjoyed before.
It does not make sense to say that
the proliferation of small third parties would have a bargaining power. We are expecting a concrete noun. An entity or stakeholder in the presidential elections. The
Small third parties themselves seem more logical to have a bargaining power. We can eliminate option A.
Option B: At a time when narrowly won presidential elections seem more the rule than the exception,
the number of small third parties have a bargaining power that few of them have ever enjoyed before.
First of all, there is a subject-verb agreement error in this option. The singular subject
the number has a plural verb
have. This is not correct. A singular verb
has is required. But of more importance to me is the fact it is illogical for
the number of small third parties to have a bargaining power. This is hogwash. Eliminate option B as well.
Option C: At a time when narrowly won presidential elections seem more the rule than the exception,
the existence of small third parties has a bargaining power that few of them have ever enjoyed before.
The existence of small parties cannot have a bargaining power. This is balderdash. Eliminate option C.
Option D: At a time when narrowly won presidential elections seem more the rule than the exception,
the proliferation of small third parties has a bargaining power that few of them have ever enjoyed before.
Just as in option A, option D says
the proliferation of small third parties has a bargaining power. This is fiddle-faddle. Eliminate option D.
Option E: At a time when narrowly won presidential elections seem more the rule than the exception,
small third parties have a bargaining power that few of them have ever enjoyed before.
Small third parties have a bargaining power. Correct. Finally, we've got something that we anticipate based on the meaning of the sentence.
PS: This is my attempt to be a bit funny

I hope I have not used any of the above words out of context. In case I did, please take it on a lighter note.