If you're actively attacking you shouldn't have many ties.
I don't think it's ever happened to me once outside of when neither of us attacks. That happens fairly often lately since I'm not that into GAC. I still play it when the mood strikes. i don't hate it. But I don''t try, and especially when I have other things going on (like TB, or real life) that's the part of the game I don't bother with.
I'm often paired with higher total GP folks, and that means that my top 80 matches up fairly well with the top80 of more developed players, so more than half the time (and I don't keep track, but I think it's way more than half the time) they get the win.
Is that fair?
Well, two things.
First, I can't really complain that someone else got the tiebreaker if neither of us even cared enough to attack once. Obviously if either of us cared to win, that person would have won. If no one cares about winning, why should anyone care what happens in a tie?
Second, and this applies in your situation, if your top 80 stands up against the top 80 of a player who has been in the game longer, with more chances to develop more characters and those extra resources still didn't help them beat you who had less time/resources, then obviously they're the worse player and the need the help more than you do.
So in the very rare case that you get a tie when both of you actually attacked, when the computer gives your opponent the win just take it as a sign the computer thinks you're the better player & need less help. It's a compliment.