My experience is this: that someone (eg you, or
@Micah Sweet) posts that you don't want any constraints on the GM.
I reply taking that literally, and - as per this post of yours I'm replying to - you tell me you don't mean it literally.
Then I try and talk to you about constraints, perhaps drawing comparisons to my own experience or conjecturing principles and heuristics that seem like they might be applicable to a trad-ish sandbox-sort of game. And you (or Micah Sweet or whomever) tell me that I'm wrong, and that no such principles or heuristics apply.
Hence pushing me back to the literal reading of the claim. Only to be told it's wrong. Etc.
So I guess I'll ask up front: what constraints do you think govern the GM playing in a trad-ish sandbox-sort of game?
The primary and most important constraint is the same one that applies in every game -- the agreement of the group as a whole to distribute power and authority in a particular way. People have mentioned constraints "with teeth" but this is the only constraint that actually has any teeth at all, and any other constraint can only exist inasmuch as it derives it's "toothiness" from from this one.
Any specific, more precise constraints on the GM, then, are ones that the group as a whole agrees should be there and is willing to enforce. I understand that Burning Wheel has a set of very clear and unambiguous rules about what the GM can and can't (or should and should not) do. If the group agrees to work within that framework, then they do. If the group doesn't agree to abide by these official, default Burning Wheel constraints, or they do agree but then the GM ignores them and the group just lets it happen, then the fact the constraints are written on the page means nothing. Now, I can certainly understand that having the constraints written on the page might help some people feel more comfortable in speaking up. But that's a completely separate issue. It's irrelevant to those who are comfortable speaking up anyway, and there are other ways of helping people feel comfortable in speaking up (such as, simply being straightforward, letting people know their opinion is important, and asking them for it).
If the group decides that the GM is relatively unconstrained and can make judgement calls with an eye towards a world that feels naturalistic and plausible, then the ways in which the GM is prevented from running rampant come down to, first, the GM's own honesty and willingness to do what they have agreed to do and, secondly, the ability of the rest of the group to call out the GM if they don't feel they are doing what the promised. Specific expectations of restraint might include things like the GM being expected to make rulings in a consistent manner, to honour the agreed tone and style of play, to ensure that the players have sufficient information to make informed decisions with the same degree of reliability as their characters etc... I'm not going to try and state a set of specific, universal constraints, because they will vary from group to group (and, within the same group, potentially from game to game).
In any case, no special rules or mechanics are required to enforce these constraints; they are enforced by the players speaking up if they feel they are not being met. This is the exact same way (and the
only way) I would expect any constraints to be enforced if a Burning Wheel GM is not adhering to the agreed constraints of that game.
There is no need for some outside force or framework that is able to measure the GMs adherence, all that is required is the players' own understanding of their satisfaction with the GM in meeting the agreed expectations. If the players feel they "have sufficient information to make informed decisions with the same degree of reliability as their characters" then the GM is meeting their obligations in that area for all practical purposes. Quibbling over "what if the GM is secretly conning the players" and other similar arguments I've heard are meaningless to me. Such a situation most likely indicates GM operating in bad faith and, in any case, if the output is indistinguishable to the players, I really can't see that it matters. We're talking about an obscure edge case that has barely any (or possibly absolutely no) impact on play, so don't understand why some people seem so focused on it.
So, in summary, what constrains a GM who is given vague and wide-ranging powers by the group? Their own self respect and the absolute ability of the rest of the group to withdraw the granted powers at any time, for any reason.