Eh, there will be a lot they don't agree on, but they could very easily agree on lots of stuff that's detrimental to the populace, i.e. mainly agree on who gets the spoils of exploiting the government. That's plenty to incentivize them to limit their competition to just each other.

No, they could not agree on who gets the 'spoils of exploiting the government', because (a) the whole concept is mostly fictional narrativizing, and (b) neither one person getting something, nor everyone splitting something equally, is something fifty important people can agree on, and the exact percentage split could be bickered over for a decade.

To be clear, I meant to say "mainly disagree on who gets the spoils" etc, but didn't notice until too late. (that might sound like a lame excuse, but I agree it obviously doesn't make sense as written.) We seem to be in vague agreement on that mechanic. But I think it's pretty plausible that an oligarchy would agree on keeping access to the pie, even as they fight over the size of their slices. Which, in the original context of designing a voting system, is a very relevant concern.