Collaborative hypertext fiction
What if a bunch of people got together and started writing hypertext fiction, using a wiki? Each person tells the story from the point of view of one character, inserting links to other bits of the story where appropriate. Maybe the writers agree on a structure for the story in advance, or maybe they improvise from scratch. Each character will have a different voice, with their own style of storytelling cast on them by the writer, with more diversity than a single author would typically achieve.
The idea of hypertext as a medium for storytelling is not new; the idea of telling a story through the eyes of several characters is not new; the idea of collaborative writing is not new either. In fact some quick googling reveals several wiki-style collaborative writing projects, and there's a collective novel I'm really looking forward to reading soon. But I think the constraint that each writer gets to tell the story of his own character can be a powerful catalyst, and an idea worth exploring. And if the writing happens on a wiki, the writers can weave a story for their characters, each adapting their text to what the others are writing, in a way that's not possible otherwise.
