What I am going to talk about is not actually a new concept for role playing games. In fact the idea of arbitrated storytelling is, more or less, the traditional mode of role playing. One way some players express a more modern look at it would be cooperative storytelling. The players and the games master work together to tell a story that is mutually enjoyable. People use the term cooperative storytelling in a broad way, maybe even applying it to games and sessions that perhaps do not really apply to that term. I also want to be clear that I do not think that arbitrated and cooperative storytelling are mutually exclusive and I am not going to compare and contrast the two. Please, play your games the way you want to play them; you do not need nomenclature to do that.
Arbitrated Storytelling I just want to talk about my thoughts and how I think role playing games work, in general. Traditionally, we tend to see the games master as a sort of "god" who arbitrates the rules, creates the world, and generally curates the experience. Curate, a term I heard Matt Colville use (don't know if Matt C used it first or not, but that is where I heard it), I think establishes the job of the games master pretty well. And depending on the GM, they may curate less or more.
But I think that the games master is an interpreter of the rules and the world; a living program that takes the code and makes it available to the players and their characters. The true 'god' or arbitrator is... The Dice. Man proposes but God disposes. God in this case are the dice used to decide if the proposed action, attacking or seducing or investigating those alien ruins, succeeds or fails. In terms of character it represents both random chance and skill on the part of the character. But in terms of the game and the universe, it is the die that arbitrates the action and decides who lives or dies. In simple terms, a player proposes an action. The games master decides if it is indeed possible and the impact on the world. Something easy does not require arbitration, but something more difficult requires the intervention of a die or many dice (depending) to determine success and the effects of that success. We often see dice as an impediment to storytelling and narrative in a game, but don't think that is the case. An impartial arbitrator, and the dice are (in theory) impartial arbitrators, makes accepting the results easier. It was not a games master making a decision or even the rules allowing or denying an action, but the proposed action ad a certain chance of success and the dice made the final arbitration on that success.
As always, these are just my thoughts. Feel free to disagree and we will let the dice decide who is right. ~SMH