I've always left both seat and lid down even when I lived by myself. Reduces the chance of dropping something in there and, if you don't get the cheap thin plastic ones that crack if you sit on them, you have a seat. But I'm starting to rethink this. No one ever thinks of the children in these arguments. I have a son, for him to prepare for operation #1 he has to first open the lid and then grab the seat with both hands from UNDERNEATH! The bottom of the seat is probably more contaminated than the water in the bowl especially after an operation #2 with the consistency of an operation #1. He's also been taught to put the seat and lid down after which he sometimes does before pulling his pants up and I'm starting to fear what damage might occur if he drops the heavy seat and lid.
I don't get why everyone doesn't do this, it's the best and most logical choice. Not to mention what's even the point of having a lid if it's never used.
Seriously, the 'toilet seat problem' is merely a side effect of the toilet lid cultural ignorance problem.
No. Leave the seat up unless you need it. That keeps it clean.