Originally Posted by ThePhanastasio

This is true, however, here's the way I look at it:

The toilet is used for pee, poop, and less frequently (in my experience) vomit. Vomiting isn't really dependent on the seat being up or down; if someone has the foresight to realize they're about to vomit, they may try to get the seat up, but it's really a matter of convenience and the time that can be expended prior to vomit. Therefore, I'm only going to count the use of the toilet for peeing and pooping.

Women:
Peeing: Seat down.
Pooping: Seat down.

Men:
Peeing: Seat up.
Pooping: Seat down.

So, out of the four most common toilet related scenarios, the seat is required down 75% of the time. As such, and for convenience, the seat should, by all logic, be left down.