I posted this on Steam, but I'll post it here as well:
The Union Council votes system seems weird. For one thing, Sarah doesn't seem to get a vote. If you get everyone's support for your position, there's only 3 votes for that position. Now, this could mean one of the members went back on their word, but if you instead get no one's support, there are 0 votes towards your position. Even with no support, Sarah should still cast her vote for what she wants, so there should be 1 vote.
Also, having two votes (a tie) towards your position is considered a loss, regardless of which position you support. For example, two votes towards unifying the armies means they remain separate, while two votes towards keeping them separate means they are unified. It doesn't really make sense that, in a tie, the one that loses is always the one that you happen to support. It would make more sense for the tie to go to whatever is the current status quo (in this case, keeping the armies separate).
These two things together means you have to get everyone's support for your position to win, which means you are forced to have sex with the Duke. If you refuse him you have no chance of succeeding, even if the other two agree with you.
Viewing post in The Survival of Sarah Rose comments
That wouldn't explain why whatever you support gets 0 votes when you get no one's support. It should still be getting Sarah's vote, so there should be 1 vote for it. Also, I did a lot of testing and can confirm that Maeiv does vote.
If you choose to keep the armies separate (something none of the others initially support) and get no support, it gets 0 votes. Get only her support, it gets 1. Get her support and one other, it gets 2. Get everyone's support, it gets 3. This is true for the others as well, so everyone definitely votes the way they say they will.
I have to assume it's a simple coding error/oversight. My guess is when you talk to each person and get them on your side (or they're already on your side), a counter is increased by one. When you get to the vote, the game just checks that counter and uses that number as the vote count, when it should be adding one to that number to account for Sarah's vote.