The default should be for the toilet seat to be down because the only time it 'needs' to be up is when men are peeing standing [with the exception of puking, but that isn't as common and can be done in a waste basket]. And even then, it's not as though the hole shrunk down to the size of a freaking peanut or something. A man, I would HOPE, can still manage to get the pee stream in the bowl even if he didn't put the seat up. Then? Just wipe it down if there's backsplash.
Then, on the other side of things, both men and women poop with the seat down, women pee with it down, men can (and sometimes do) pee sitting down. And if someone sits with it up, they fall in.
The only way the seat should be kept up as the default is if there are no women in the house, and it happens to be the guy's preference. Women are your guests? Keep the seat down as the default.