Carissa wants to back off and forget this whole line of discussion very badly but she keeps her face relaxed. She is foolish and eager to learn and too valuable to murder and you can't actually pass a loyalty test you don't understand.
It does seem like there is not much difference between Freedom telling everyone who to vote for and everyone not voting at all, but obviously she's not supposed to think so as Alfirin is saying that like it's a bad thing.
"...well the important difference is obviously that if you make everyone 'vote' then you can tell who's loyal and who isn't? Cheliax does that with Detect Thoughts but Andoran doesn't have enough wizards, so it's clever, really. It's not as good as Detect Thoughts because you can lie but I think making people lie is still useful, usually."