Technological weirdtopia: (This is slightly similar to Eliezer's description of scientific weirdtopia but not quite.)
Each piece of technological equipment is only allowed to those people who've displayed sufficient mastery of the corresponding technology of the previous level. Nobody's allowed a car or motorbike, unless they've mastered driving a horsecart or riding a horse (or atleast a mule). Pens are only allowed if someone can write sufficiently well with quill-and-ink, matches and lighters are only permitted to those who've mastered usage of the flint-and-tinder. Pocket calculators are restricted to those mathematical operations that their user could (given sufficient time) work out with pen-and-paper.
The idea behind this is to increase appreciation of technology, and to also maintain an adequate level of knowledge in the population about former technical levels if there's a catastrophic collapse/decline in civilization that destroys more modern technology.
Some things actually work like that. Pilots have to learn old-fashioned navigation before they are show how to switch on the autopilot.
Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."
So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.
I'll start off with a worked example for public understanding of science:
Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.
Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.
If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.
If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.
If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)
Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.
Economic...
Sexual...
Governmental...
Technological...
Cognitive...