The Generals should always have an arbiter, try asking anyone else in their household if they are interested in arbiting the game (who knows, they might be interested in actually playing some day). The arbiter could just have the rulebook in-hand for easy reference of what piece beats what, and could be doing something else when pieces aren't clashing, albeit with some difficulty, as pieces clash fairly regularly.
Failing that, I've come up with a protocol whenever pieces clash, the players should run through these things to determine who wins:
- Both players check if their own battling piece could be removed by a Private. If it can, the player/s removes the piece. (this removes spies, tied spies, tied privates, and flags)
- Check if their piece can be removed by a Sergeant.
- Check if their piece can be removed by a 2nd Lieutenant...
- Continue up the ranks until one or both pieces are eliminated.
It takes fairly long to resolve one clash, and it slows the game to a crawl but I think it's the only way to play without an arbiter. So always try to get one.