I fought the toilet seat battle with the wife when we first started living together. After many bloody and destructive engagements I finally figured out a compromise that both of us can live with.
See the whole issue here is one of sloth. Us men don't want to think about putting the seat back down after peeing and women don't want to think about checking the status of the seat before squatting to pee.
My solution was to satisfy the wife's demand by remembering to put the seat back down afterwards but I also put down the seat cover so she is equally inconvenienced. The American way.