GM-less systems

Thoughts on eliminating a dedicated GM and splitting the narrative responsibilities across the members of the table? Are there any systems that do this somewhat successfully?

Hypothetically:

1. A player initiates an encounter.
2. They roll on a table based on their current setting (in a cave, town, forest, etc) and are given a narrative prompt. That player narrates based on the prompt.
3. The players work together and interact with the encounter
4. Disputes on rules interpretations and what is or is not possible is settled by player vote
5. The encounter resolves and the players document their results
6. The player sitting to the left of the last narrator initiates the next encounter. The process repeats for the duration of the session.