It's just another variable to influence the decisionmaking process that they start with, nothing more. By that logic, people don't always breathe at the same rate - exercise, sex, various emotive states (e.g. anger) cause them to breathe faster and therefore exhausts more air. But in the context of the film, Zimit's insistence is just to frame the reason for cutting off half the class in a slightly believable way, it doesn't have a basis in reality.
Also to add, just sort of put it out there, the "experiment" is rigged. Zimit's intent, as Petra sees right through, is not to have a classical philosophy discussion/roleplay based on an apocalyptic premise. It is two-fold: first, to punish John and, by extension, get back at Petra for being with him. Second, he also wants to show her that her emotional decisions are (to him) simply wrong, and that (his) intellect will triumph over emotion easily (with the perk of demonstrating that he's smarter than the boy, as well.) Zimit always influences the way things go (like the exit code thing) up until Petra, by popular vote, gains control of the experiment and lets it run its own course.
They only survive in the third iteration, which Zimit again attempts to change by constantly banging on the idea that Petra's decisionmaking was wrong, and it has doomed them all, because her reasoning is different than his, and his is the only kind of reasoning worth going with.
One more for the road: think of the second iteration. Zimit leaps to the point of attacking the other inhabitants because they are not complying with his idea of multiple partners for girls. Instead of respecting their reservations about it, he pressures them, at gunpoint when that doesn't work, insisting that his logic is more important than their thoughts and feelings on the subject. When he can't get what he wants, or rather, when the student strikes back, he just straight up kills them all.
The man who went on and on about the survival of the species, the importance of procreation not five minutes ago decides he'd rather exterminate what he implies is one of the last groups of ten humans in existence, because they don't bow to his superior brain and reasoning. Because they, perhaps reflecting Petra, can't discard their feelings on something and accept that his logic is irrefutable (which it actually isn't and is the subject of another debate), and therefore must absolutely be accepted without question.
So really, oxygen? The whole thing is Mr. Zimit being a faux-egotist (with a very fragile ego) with a superiority complex. It's meant to flex his brainmeats and somehow sway Petra into abandoning her plans for going to college, because Mr. Zimit. So I don't think there should be any actually sound logic in Mr. Zimit's bunker.
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