Nothing in the premises establishes that politicians should avoid conflicts of interest. So (A) doesn’t trigger and doesn’t strengthen the argument.

(B) is directed toward what special interests should not do. But the argument concerns whether judges’ positions should become elected; what special interests should or should not do is irrelevant.

(C) establishes a necessary condition (”only if”) for judges to be appointed to their positions. This allows us to argue that judges should NOT be appointed to their positions, if the necessary condition is not met. But it doesn’t help us argue that we should keep judges’ positions appointed rather than elected.

We’re trying to prove that judges should remain appointed. (D) tells us what happens IF judges should be appointed. But that doesn’t help us prove that judges should be appointed.

(E), restated, asserts that if a public office is one for which election campaigning would be likely to produce conflicts of interest, then it should NOT be changed from appointed to elected. We know based on the premises that if judges ran for election, their campaigning would likely result in conflicts of interest. (E), then, allows us to conclude that judges should NOT change from being appointed to being elected.