That (a)-(d) are descriptive of a living sandbox didn't mean they are prescriptive of one. I only claimed that those 4 criteria are true of living sandboxes - not that they were only true of living sandboxes.
So I agree, I wouldn't describe those games as living sandboxes - although they do appear to share those 4 criteria in common.
Ok, so multiple posters - including you - have hauled me over the coals because "backstory first" has more than one instantiation, depending on the principles used to move from backstory to (i) situation and (ii) consequence of declared actions.
But now you seem completely relaxed about having described "living sandbox" using criteria that are also satisfied by Burning Wheel and Prince Valiant played in the standard way.
I'm not suggesting hypocrisy - that's not really apposite in this sort of discussion - more just saying that I'm a bit uncertain as to what your standards of adequacy are for an analysis of RPG play.
In an infinite world (or one that approaches an infinite one) 'everything' is in the world. So what becomes most important isn't how the world is generated, but what the players focus on in the world.
I don't really say how it can't be important
how the fiction of a RPG is created, especially in a thread about
authority in respect of the fiction.
And in play it's likely to be pretty significant. What is a player allowed to stipulate about his/her PC's personal history? Relationship? Shed content? And what principles does a GM use to decide things like
who the factions target or even
where the factions are active? I've used Pholtus vs St Cuthbert a couple of times now in my examples. But that will play out very differently if one of the players is playing a cleric of one or the other of those gods.
It's not a sufficient description of my 4e game to mention that opponents included Orcus cultists, without also mentioning that 3 PCs were Raven Queen devotees.
The general point is that RPG fiction isn't significant just on its own terms, but in terms of its relationship to the PCs (as central components of the fiction). An "infinite" world can be incredibly varied in this respect, which has pretty profound ramifications for the experience of play. I mean, in your example of the faction and the brother, what if - in a world that's not infinite but only as big as our earth, the PC lives in Kuala Lumpur and the only people who know what happened to the brother live on the tip of Tierra del Fuego?
Now maybe that's bad design for a living sandbox - but I can't work that out from descriptions of an "infinite" world in which players are free to set their own priorities for their PCs and choose what actions to declare. At a minimum we need a principle like
once the players set their priorities, the GM should ensure that there are reasonably feasible actions the players can declare for their PCs which will meaningfully engage those priorities. But if you apply that principle frequently and with rigour, I believe - based on my own experience - that you will drift towards "situation first" play because the utility of pre-authored backstory will start to fade away.
Conversely, sticking to pre-authored backstory speaks against trying to implement a principle like the one I just described. But in that case, the idea that players are free to set their own priorities for their PCs starts to lose its purchase - as
@Ovinomancer posted way upthread, that part of the GM's backstory which is feasibly available to the players given where their PCs are in the "sandbox" generates something like a list of options/setting elements for the players to engage with.
@Campbell upthread sketched a way of trying to split the difference -
story now in the streets, right to dream in the sheets - which is to say, apply the relevance principle in prep between sessions, but stick rigorously to prep during actual run-time and adjudication. But I'm not sure that still counts as a "living" sandbox, because the "life" isn't based on naturalistic extrapolation from prep plus the events of play.