Hm...
Does support matter when there is no opposition though? Or are you looking to make it more rewarding to hold government positions by allowing support to give honor/prestige?
It'd not be hard to make it so that protests and supports are tracked by position on a table, then after a public protest is declared, only make it have penalties if not enough people declare support in a day or two or three or something.
I'm kind of leery of anything that can become "set and forget", even if you have to reset it every few months--then you just have people complaining about the timeline and when they set it and how it didn't count when they thought it should of.
If it's going to be directly countering protests, you may want to consider also how many people are in a realm that can support or protest. If 3 people protest and 3 people support, the situation is different in realms of 6, 15, 25, and so on.
