I assure you it works and has never, ever sown disfunction in any game I've run. In fact it is extraordinary in how well it works toward producing "Paladin-ey play." So I would ask folks (even if you haven't played it...merely by extrapolating from what I have written above), why does this work without a negative feedback system and/or a strong central role of the GM in adjudication of matters of faith, sin, and fallout?
Let me start at the end first and work back to the top.
I started to write a (different) long response to this thread and realized it would be pointless, because the fundamental problem is we have no way of not talking past each other. Without common experience, we don't have the words or the frame or reference to actually communicate. We are all talking at each other, but no one has the actual means to understand the other (and be assured in their understanding).
I'm glad you brought up DitV though. When I first heard about DitV I immediately wanted to play and/or run it because it sounded like it was aiming to create exactly the sort of play experience I enjoy the most.
In answer to your question about how it 'works' (for you), I would suggest that one of the reasons it 'works' is that it is hugely self-selective in its audience. The only people who end up playing it or who can play it are people who fundamentally agree with its precepts. When I actually sat down and started studying the game, I realized that I couldn't actually play it. It was trying to create the game that I enjoy, and in many ways it was designed correctly for doing so but I personally wouldn't be able to play it.
One of the reasons is that as a Christian, I find that there isn't enough distance between the world it creates and the world I actually inhabit. It blurs the line between fantasy and reality in ways that I'm hugely uncomfortable with. Moreover, I realized immediately that even if I tried to play it, I'd likely make everyone I played with hugely uncomfortable. I spent some time thinking about the players I could actually play with, and realized that it was an empty set. In order to play the game, I'd have to completely rewrite the setting so that it wasn't a trope off of Mormonism (and hense Christianity). I couldn't play the game with pious Mormon friends, lapsed Mormon friends, Christian friends, non-Christian friends, or anyone else I could think of. Each would present a separate but real discomfort.
So the question is, does the game actually 'work'? And the answer is, "Not for me it doesn't. It works so badly it's broken right out of the box." The distance polytheism and the two-axis alignment system has from the real world is a feature for me, not a bug. The system manages to stay close enough to reality to comment on reality, while being remote enough from reality that it is clearly not an allegory for reality. No one has to insist on one to one and on to relationships between the system and reality, and there is no pressing reason to be uncomfortable with feeling like this particular departure is, for lack of better words - heretical, sacrilegious, dangerous and well evil.
I have the strong impression that the setting self-filters so that the only people playing are ones with a particular real world moral, ethical, and cosmological outlook. You have to be the sort of person that fundamentally accepts the precept that each person is their own best judge, that what is right and wrong is different for different people, and that no one can question anyone else if they are following the dictates of their own consciousness. You must believe deep down that each individually is the source of moral authority.
Ironically, DitV postulates a setting where the only persons in the setting for which this is true are the Dogs. I would argue that if you enjoy DitV and think it's approach highly reasonable and not at all niave, you would find it impossible to enjoy the game from the perspective of any character other than a Dog. After all, at that point absolute moral authority would then lie in the hands of an NPC (and not perforce the player), and you are then subject to all the things that you say you hate about alignment (and then some)!
In other words, it requires players the preeminently don't represent the ethos described in the setting and which (IMO) would consistently make a real hash of it. You're asking people to pretend to be Mormon/Christian inspired leaders while rejecting the fundamental tenants of those belief systems. That is never going to 'work' as I see it, though I'm sure there are groups for which it 'works' in the sense that it produces the play the author desired.
Here is what Vincent Baker has to say about:
Does this [the extreme boundaries of authority outlined in "A Dog's Authority"] mean that your character can't sin?
No. But it does mean that no one's in a position to judge your character's actions but you yourself. Your character might be a remorseless monster or a destroying angel- I the author of the game can't tell the difference, your GM and your fellow players can't tell the difference, only you can.
This is quite frankly unmitigated nonsense to me. I suppose there are people that read that and actually believe it, but I find it impossible to imagine that in practice this actually happens unless on the really big questions about life all the players (including the GM) are on board the same train. Does the author really believe that no one is going to be able to discern the difference between good and evil (or think that they can) and there are things that another character ought or ought not to have done under the circumstances?
Fundamentally what is going on her is a deeply embedded moral belief - "no one can judge another person's actions but themselves". In my D&D homebrew, this would be a 'chaotic' belief system. As a real world belief system we could apply a number of different labels. Existentialism would be one, for example. Baker's quote almost immediately brings me back to studying Camus's 'The Stranger' in philosophy class.
One of the fundamental assumptions Baker is making is essentially that no one is going to be acting in a way that the other players consider monstrous, and before that is true the players are going to have to be in pretty close agreement to begin with.
But even to the extent that is true, there seems to be an almost willful blindness going on here. I've read DitV scenarios. It isn't not true that sin is defined ambiguously and that winning and losing are defined ambiguously and that the setting (and therefore the GM) applies and passes no judgment on the PC's actions. Actions are supposed to have consequences and those consequences are supposed to follow a certain framework defined by The Faith. The only way that can not be true is willfully ignoring the setting.
As play progresses, you'll have the opportunity to consider your character's actions and change your character's Stats, Traits, and Relationships to reflect them. That might mean that you give your character Relationships with sins and demons, problematize his or her Traits, and burn out his or her Relationships with the Faithful - or it might mean no such thing. Sin, arrogance, hate, bloodlust; remorse, guilt, contrition; inspiration, redemption, grace: they're in how you have your character act, not (just, or necessarily) in what's on your character's sheet. Those moments, in play, are what matters.
This is I think incredibly naïve and relies on the implicit trust that players are going to behave in a way that other players are going to deem to be rational, coherent, and sympathetic. In other words, it assumes that there will be a natural consensus agreement on what it all meant, that I think that in practice isn't going to happen if you have a real wide audience playing the game. You are GMing the game and the Dog does one thing and annotates his character sheet completely at odds with how you saw the game play out and which seems designed to mitigate the consequences of his actions, and this isn't going to bother you? As a player, you're doing your best to adhere to what you see as the Faiths strictures and annotate your character sheet with your characters failings (or otherwise play as you think the game was intended to play), and this other player is in your opinion completely ignoring them and annotating his character sheet not only in a way that suggests he's meta-gaming to enlarge his character's prowess during play but that he's judging himself righteous for doing so, and you don't think he's missing the point of the game and ruining it for everyone?
I find that simply impossible to believe. And to the extent that it is possible to believe, it must be equally possible to believe that no one every argues about alignment.
tl;dr - DitV works without creating table arguments??? We are barely going to be able to discuss it without shutting down the thread, much less play it together.