Even if your conditions are granted, different LLMs can easily consistently hold divergent "worldviews". LLM A might consistently state that fact P is true (i.e. it will never hallucinate a string that states or implies ¬P), while LLM B consistently states that fact ¬P is true. You don't have a way out of this with these two, and adding a third LLM is an additional confounding factor, not a solution. You can't settle questions of fact by survey, you need to test or use reliable sources.
This is really a theoretical problem and not a practical one though. Practically, for everything I use these tools for today (complex low-level systems programming), hallucinations don’t even exist anymore.
When they don’t know something, they figure it out empirically. For things they already know, they are consistently correct.
