"How would the points be calculated? It's currently loser's score/winner's score... would it now be an average of the tie-rs' (for lack of a better word) score? or would it be similar to the team game system?"
One way would be to make it the same as if the folks agreeing to the tie were on the same team. No matter who has more men or territories, no matter who has a higher rank, it ends like they were a 3 or 4 way team all along, and points are taken from those eliminated based on the combined rankings of the "tie-ers", and divided equally among them.
"The other issue with a tie button is that keeping anonymity would be exceedingly difficult... if it's a three-player standstill, two want to tie, and one doesn't - a simple question in the game chat could point out the deviant - and from there, its a small step to unintentional secret diplomacies."
Good point. This would align the interests of the lesser 2 players against the main player unless he agreed to a tie. It could be used as blackmail. Imagine the 3-way gunfight standoff where instead of firing, one guy says "let's put down our weapons", the 2nd guy agrees and the 3rd guy doesn't. In that case it's not hard to imagine what happens next.
But even then, if it was an option that folks could select going in - as sort of an insurance policy against endless games, then there shouldn't be complaints from the lead player ... who likely wouldn't be able to cash in for the better part of a year. And of course, gamers could ignore the option.
However, if there's a solution to these, I'd totally be up for this (I'm currently stuck in a three-way tie game, except none of us want to give in... it's been two and a half years, 666 sequential rounds, shows no signs of stopping any time soon.)