+ 1 B.

+1 for B

IMO: B

Gotcha ! B !

(B) is the clear winner,
"citing" is referring to the "new study"

I have doubt that i getting the sentence has a flaw; what I'm seeing is a "new study of the 2000 United States presidential election" means total of 2000 election in united states, not election held in 2000 in US.

Can someone clear this thing?

A) "which" modifies the noun preceding it, which is "the 2000 US presidential election": illogical since the election cannot estimate anything. Moreover, the pronoun "they" is confusing since it has no antecedent
B) Correct
C) "Votes" cannot cite, but the study instead.
D) "had not been counted" is wrong. Here we need simple past tense as the action happened and ended in the past; it has no effect to the present.
E) Same as D

Choose B

Faulty voting equipment, confusing ballots, voter error, and problems at polling places have been cited by a new study of the 2000 United States presidential election, which estimated that they did not count 4 million to 6 million of the 100 million votes cast.

(A) faulty voting equipment, confusing ballots, voter error, and problems at polling places have been cited by a new study of the 2000 United States presidential election, which estimated that they did not count 4 million to 6 million of the 100 million votes cast. (antecedent to they?)
(B) Citing faulty voting equipment, confusing ballots, voter error, and problems at polling places, a new study of the 2000 United States presidential election has estimated that 4 million to 6 million of the 100 million votes cast were not counted.(Correct - very clear and precise)
(C) Citing faulty voting equipment, confusing ballots, voter error, and problems at polling places, 4 million to 6 million of the 100 million votes cast were not counted in the 2000 United States presidential election, a new study estimates.(Passive-voice and a new study estimates)
(D) A new study has cited faulty voting equipment, confusing ballots, voter error, and problems at polling places in estimating that 4 million to 6 million of the 100 million votes that were cast had not been counted in the 2000 United States presidential election.(sequence of time)
(E) A new study of the 2000 United States presidential election, citing faulty voting equipment, confusing ballots, voter error, and problems at polling places, has estimated 4 million to 6 million votes had not been counted of the 100 million votes cast.(simple past tense could be used)

SO, B.

Earlier I chose D but B is best answer.

If D should not have "had" then is a strong answer.