In many Nordic larps, the rule is “the person targeted says what happens”. I was shocked how well this consistently works. 

Paul: “I swing my sword at you.”
John: “I dodge” or “I take a superficial wound” or “I get decapitated!”

It is also coupled with a culture of play and workshops that encourage players to “play for drama” and “play to lose”.

Although strangely this works much better in physical conflict. People are happier to roleplay out being stabbed than they are being wrong.