I remember reading about a concept a while back where the opposing players would make a small list of arguments why a particular encounter would be resolved to their advantage, the referee would then evaluate the reasonings and make a decision or a suitable random roll. Always wanted to try it out.
That’s exactly what matrix-games are all about. It can work very well, given all players have the right mindset.
Tiny Tin Men Blog: http://snv-ttm.blogspot.com/
Wargaming Mechanics Blog: http://wargaming-mechanics.blogspot.com/