Some dithering algorithms are deterministic, not all of them. The simplest & most basic dithering you can do is random, and that works quite well when targeting 8 bits per channel.
The reason I bought it up is because deterministic dithering can definitely be gamed by gerrymandering, so if you want to avoid that you might need to introduce randomness, but then you will have an even harder time getting people to buy in than with a deterministic algorithm.
You don't need randomness. Dithering looks random, but is fully deterministic.
It does suffer from the 'butterfly effect' - a few extra votes in one place can change the assignment of a lot of nearby seats.