I would bet good money that both door handles are equally filthy, by nature of it being a school. Kids are walking talking germ incubators. We all are, but kids especially. And that's before we even get to the kids who are intentionally malicious little bastards -- I guarantee you, in some school districts, with some kids, signs like these would just be asking for an aspiring Poo-casso to smear their shit on the door handles.
Here's an idea:
The sinks should be outside the bathroom.
That way, you can wash your hands after touching the dirty door, and everyone in the hallway can see if you don't wash your hands.
I recall there was a story from Predictably Irrational where the experimenters were trying to figure out how to get participants to avoid double-dipping tortilla chips.
Along with a control condition, they tried setting up a sign that said "NO DOUBLE DIPPING", and I think they also tried paying people or getting them to promise not to double dip, stuff like that.
The thing they found most successful was to set up two bowls of dip: One labeled "For double-dipping", and one "Not for double-dipping".
They supposed that once they had to do a physical action where they sorted themselves according to "what kind of person they are", they wanted all of their visible actions to be consistent with that.
This problem is solved by having paper towels (air dryers suck) and placing the paper towel trash bin next to the door so that you can use your hand-full of towels as a barrier between the handle and throw the towels away as you leave.
first off, the clean handle should be on top. the nasty handle shouldn't drip onto the clean handle.
second, as you are leaving a public bathroom, reach under your shirt/jacket (hopefully something untucked. ) use the fabric as a barrier for your hand and grab the handle with the front of the shirt/jacket.
Based on the differences in color for each handle it makes me wonder if the one for not washing your hands is a different material. Maybe an antimicrobial metal like a copper alloy.
I’m too lazy too lazy to wash my hands or don’t feel it’s necessary. Upon encountering this door I see both handles and decide to follow their instructions and open the door for unwashed hands. My hands are now unspeakably filthy as filthy people following the signs have accumulated a ton of germs on this handle. I get sick.
I was my hands, follow the signs and use the washed handle. Unbeknownst to me some unwashed game theorists decided that obviously the handle for washed hands would be cleaner so they used it without actually washing their hands first. It’s now also filthy.
I didn’t wash my hands, I don’t give a fuck about signs, use the one most convenient for me.
This could easily be because the top handle is in a more convenient spot so everyone uses it and nobody uses the bottom one, I can’t think of a reason someone would be so inconsiderate as to not wash there hands but so altruistic that they go out of there way to use the inferior objectively worse handle. And human nature would say nobody is going to care about the slightly inconvenient option after it gets boring, don’t believe me? Then why do so many people choose the convenient less boring option of not washing their hands?