I have the idea to propose a world and some initial stories and offer other authors online to add their stories to this world. Could that work and yield interesting stuff? How should it organized to keep quality high?
A supplement to this answer:
All the shared-world anthologies I've read had "framing" stories written by the primary author, the one who came up with most of the setting and is driving the process. For example, Eric Flint wrote or co-wrote several of the 1632 novels, including the first one, and Robert Asprin was heavily involved in the Thieves' World books.
Coming up with an interesting setting is useful, and if well-done is a lot of work. But it's still "just ideas" until somebody creates something from it. That should be you, both to demonstrate investment and to show people what you had in mind. There are lots of ideas out there; most authors have many that will never come to fruition. So your idea is "just another idea" until you give it real shape by writing something based on it that invites others in. You need a story that's engaging enough to capture people's imagination and that has "holes" that can be filled in -- opportunities to develop interesting plots and major characters that fit into the world.
Also, do make sure you do the necessarily legal/licensing stuff so that people know they can safely write in your world -- you're not going to come back and sue them later for creating derivative works, etc. Since most authors have ideas of their own already, they're unlikely to see the benefit of taking such risks to write in yours. So make it clear that there's not a risk there.
Partly it depends on whose idea of quality you want to enforce. If you want to enforce your own personal idea of quality, you will have to involve yourself personally in selecting writers and stories, or in editing the stories:
- Invite only writers that you trust to write high quality stories.
- Select and publish only the high quality stories. If you pay professional rates for the stories, that will attract professional writers.
- Edit the stories yourself. If you're a skilled editor, you can improve some pretty good stories to be even better, though it's unlikely that anyone can edit a bad story into a good one.
- Frame it as a contest, where you select the top few stories each week or month or quarter or whatever.
If you want to use your readers' ideas of quality:
- Allow readers to rate the stories. Though this doesn't ensure the quality of any given story, it does give readers a general indication of each story's quality (or at least popularity).