Dirty dishes are piling up all over the world and here is an idea which might just get a lot of them washed. Let me say in advance that this is not a perfect idea but it might just help.
The idea is that everyone in a household has their own place set (dinner plate, bowl, salad plate, cup, and glass). Everyone's place set is identifiable (i.e. college students can bring a place set from home or buy a set at a thrift store). When people eat something, they are to use their own place set, not other people's. If they don't wash their dishes, it become blatantly obvious. A nearby sign reminding people to "Please immediately wash your own dishes" might help. If you have bugs, draw those bugs on the sign too.
In some cases, it might work out to get two place sets, instead of one. This would help when visitors come over, and some abusers might prefer having a backup set. Although this idea doesn't address the dirty pots and pans issue, those items might just get washed, along with someone's dishes. The cost of soap and sponges would need to be shared. Microwaving a damp sponge for a minute will sterilize it. A drop or two of chlorine on a damp sponge will do the same but will leave a chlorine odor. Water is precious, so please try to conserve water. A plastic bowl with soapy water and a sponge might help prevent water from being wasted.