Good point
Also, wouldn't a "Support" action be nice? Publicly support an action of a council member, even if it is impopular? (such as Judge rulings)
But then that may cause some degree of complication. If you remember, protests can at the moment be vocal (so your name is attached) or more covert. Would the Support action have the same idea behind it? If so, then overtly supporting an action that is unpopular can cause trouble for the character in question. But then, I suppose they know what they would be getting into, so it might well be a moot point (intrigue, yay!).
The second point though is how "Support" and "Protest" would react, if at all. An example - it takes 5 protest "votes" to remove the Judge from office. Those protests are made, but someone also hits the "Support" action and means that without an extra protest, the Judge cannot be removed. On the one hand, I can see this being abused to some degree. On the other, if the protests are so overwhelming that it would drown out any support, then there is no issue.
In short, it would be a nice idea. But I'm firstly waiting for a certain someone to come along with his trademark "Requested, discussed, and rejected" line, and proceed to make people feel stupid for even suggesting the idea in the first place. The second would that as I mentioned right at the start, it could be complicated. But a whole lot of fun if it devolves into some kind of rebellion or civil war, I suppose..