[quote=@Dervish]
Having the involved players talk among themselves and determine the outcome is usually the best solution. It keeps a fight scene from dragging out from a lot of repetitive back and forth and it can lead to an honest assessment of the character skills and their advantages and disadvantages. By walking through the scene and what would likely happen via PM or IM, you can streamline the process and make it into a collab that reads excellently and the outcome is unknown by the rest of the RP.[/quote]
This is (when used in combination with some real time simulation tests to gauge unpredictable elements in the characters' IC tendencies), in my opinion, the most ideal way to write combat when it's not strictly Arena; in fact, it's how I usually go about dealing with battle scenes in my story-driven role-plays (especially since I've done a lot of role-playing over IM in my 'career'), and I plan on doing exactly the same thing in the role-play I'm currently running on this site now (with an additionally little gimmick that should make things quite intense for the players and readers).

Ideally, people simply being good sports should be the priority in Arena -- it's what determines a good Arena player. That said, I can understand why rolling dice might be needed to people who can't be mature about this sort of thing. I can acknowledge that, since for some people the desire to win overrides the desire to win [i]logically[/i]. Tossing in RPG mechanics just isn't something I like to do, because I feel like it takes from the realism/depth/immersion. As [@ArenaSnow] said, picking your opponent is the key to having an enjoyable battle role-play. Honestly, it's the same as not playing against people in fighting games who've got a reputation for rage quitting or lag abusing.

The idea you gave about doing it as a collaboration is, in my eyes, the best method. It doesn't feel as 'pointlessly long', but it's still run in 'real time' and therefore feels realistic and doesn't suffer from the OOC problems created by predetermining the outcome. I find myself pretty good at running battle simulations without even needing to write the battle, so that sometimes helps the outcome move forward smoother.