I don't usually use numbers outside of Bleach(keeps things easier there), so I resolve conflicts by listening to both sides and going with the better option. You are the GM, so ultimately, you can decide th best course for the RP. 

Mostly, you won't make everyone happy, but from what or seen, unless the resolution is completely out there or unfair, most will go along with it. 

You can decide when to lose when it's bear for the story. Or, prior to it taking place deciding whether losing or winnin is better for the continuation. For Allaria, I have set points where losing is the option, but I let them get there how they like. For instance, there was a war at the beginning that wasn't meant to be won and wasn't. 

Just know they can and will die. If you don't want them too, then they won't. You can have them survive if they are pertinent to the story later. But if their ultimate purpose has been served, then killing them off can be a good point and morale booster for the players. Make them think they are doing well in the story. 

Tell them their characters have a chance to die. People usually accept that line. But don't kill them just because Lols, that'll turn people off. 

In other words, you can definitely have conflict resolution without numbers. It's mostly based on what you think will be the best course of action. People have been doing it on Guild for a while now.