Kaplan official explanation:
There do not appear to be any errors in this sentence. The subject, "assembly," is singular, and the possessive pronoun at the beginning of the underlined portion, "its," is also singular. Remember that on the GMAT, collective nouns such as "assembly" are almost always considered singular entities. Additionally, "would be" is properly used to express a possibility. (A) is likely correct, but check the other choices to see if any improve stylistically upon the original.
A vertical scan shows that (A), (B), and (C) keep the correct pronoun, while (D) and (E) change it to the plural "their." (D) and (E) can thus be eliminated.
Since the sentence's time frame is governed by the verb "voted," a past tense verb, choice (B) with its future tense "will be" can be eliminated. Also, because the invasion has not taken place yet, the completed implication of "would have been" is incorrect here; eliminate (C). The sentence is fine as written; (A) is correct.
TAKEAWAY: Don't be tempted to overcorrect; the sentence is often correct as written.