I got this one wrong, but here's how I figured it out in blind review.
Stimulus breakdown:
(1) most people favor the bill
(2) doesn't violate anyone's human rights
(3) those adversely affected are influential
(4) (sub-conclusion) Therefore, the bill won't pass
(5) (main conclusion) This county isn't a well functioning democracy
Gap: We need a principle that tells us that if a country is a well-functioning democracy, then 1-4 occur OR if 1-4 do not occur, then said country is not a well-functioning democracy
Answer Choice (E) gives us the former. The trick is that they carefully hid the conditional relationship in the language, so I re-wrote (E):
Well functioning democracy --> (bill doesn't violate anyone's basic human rights + favored by most --> passes)
If the relationship does not hold, then we've effectively failed the necessary condition. We know from the stimulus that the relationship doesn't hold. Therefore, the necessary condition fails and we can conclude that we Country X isn't a well-functioning Democracy.