I kind of agree with this.
I think of the runtimes in a Geth network as competing ideas that don't always agree on an action, but always agree on the decision because that is their doctrine, philosophy, religion, or programming. They can do this because they share all information and trust that each other is making an intellectually honest decision. The more information available to a runtime, the better its decision. Thus when multiple platforms are in the same local area, with more information that they can share, the runtimes have more awareness, they may even participate in local platform decision making of other platforms, and so the units or platforms appear smarter. This explains Tali's Geth "subconscious" from ME1.
Depending on how you define a hivemind, this kind of behavior on the macro level for all Geth may or may not qualify as such. I guess it could appear to be a hivemind, but since the Geth keep referring to themselves as "we" and their collective as "Consensus", I see it more as many individuals that know each other intimately, are just really really REALLY comfortable with their process of thinking (or "government").
When they stick together in one platform, that intimacy of local networked consensus may see itself as a single entity.
The question I have is, do the runtimes "care" about the entity (or have a motive to consistently maintain the entity) they create when networked locally, especially after the Reaper upgrades with peace, or do they just care about the ability for the local platforms to function more intelligently? If the runtimes can transfer into Quarian suits after peace is made, I'm guessing at least some don't.
If I remember correctly, it's not just the availability of more information, Tali further explains that, when in proximity, controlling the physical platforms can be handled by fewer runtimes/programmes, freeing up more processing for higher thinking.
I don't know if either "doctrine, philosophy, religion, or programming", fits into it, from my point of view on it.
It's hard to come up with a human analogy.
Principally, if I had the entire sum of experiences, that makes ie. a murderer a murderer, I would be one too.
Technically, there are "hardware differences" in our brains, that allmost guarantees that I would not react to these experiences in the same way as anyone else. I could become much "worse" or "better" than him/her.
Even identical twins, would have a certain amount of differences in the physical makeup of their brain.
With the geth, I think we can assume that if every basic runtime/program are made to be allmost identical, they would be much more identical than any organics could ever achieve. You can make a perfect copy of the coding, unlike organics where it's dependent on miniscule variations in the physical machine (brain).
Meaning, that if you replaced, the experiences from one geth, with the experiences of our murdering geth example, then the first one would become a perfect copy. Whatever reasons and experiences that drove the original geth to murdering would be equally valid to our copy.
Here we have millions, billions or maybe even trillions of experiences and points of view, that when combined, will form some form of average of everyone.
So it wouldn't be the doctrine, you were talking about, but a point of view, which would be wholly obvious and seem perfectly valid for every geth.
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It seems though, that if every disconnected runtime/program, should have access to every, til the point of disconnection, experience from all other geth, then they have unfeasibly large hardware requirements.
A disconnected runtime would probably be programmed with just a simplified version of the current concensus or an approximation.
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None of this explains why a greater schism occurred. My speculation would be that some runtimes/programs experienced something which, when they reconnected to the greater "concensus", or amalgam of geth, was provocative enough, that it kept some greater portion of geth on various servers, from averaging their experiences/viewpoints as they normally would. Leading to 2 (or more) different concensus's, from that point on.
That, or some of the servers were based on hardware of revision A and others on revision B.
EDIT and PS: I think that the Geth DO "care" about individual runtimes/programmes, probably even more than we humans care about the death of some stranger half a world away (that we didn't even notice had died). Each runtime/programme would, in my scenario, have an effect on every other runtime/programme. But as with humans, the amount of caring we can afford to each "individual", quickly drops off with increasing numbers of individuals.
Ie. there are approximately 1,8 deaths and 4,17 births per second worldwide. Noone is able to give each of those the same amount of "caring" as they would anyone who's directly affected our lives. For the Geth everyone of those would have had a direct and intimate effect on themselves.