This seems like something that should be true, but I think I remember seeing a Mythbusters episode where they decided it didn’t make a difference. That show was more about entertainment than science, so I wondered if there was a more rigorous study done? I’ve definitely seen splashes of water(?) come out from flushes so that alone seems to argue for closing lids.
In France they have public toilets that basically do number 4. The toilet gets completely cleaned automatically with hot water and detergent after you used it. It works by locking up after you unlocked the door after using it. If you hold the door for someone, they get the cleaning treatment.
Unfortunately, I’ve never been to France, but nothing beats a spotless clean public toilet. And, thanks for the tip: if someone holds the door for you, kindly step back. That alone should be highlighted in all tourist guides.
It’s written quite clearly on the door, but last time I used one I saved a tourist who would have had an unfortunate shower. She grabbed the door when I went out and was going in, I had to warn her and tell her to first let the door close so that the wash cycle would do its job.
