Do you like the toilet seat UP or DOWN?
In my household, it is every person for themselves. Women expecting men to leave it down is hypocrisy. It takes every bit as much "cognizance" for a man to lift the seat in the first place, as it does for a woman to put it down. The hypocrisy lies in the "splashdown syndrome", where women, every bit as sleepy as men (at night), FAIL to LOOK and... splash!
If men can manage to lift the seat (and aim), so should women put it down. Or, would they rather we just leave it down? (it can be arranged).