Minos was the judge of the third and final vote, when the jury was composed of just Rhadamanthys, Minos and Aeacus . After the fourth judge was added, the majority in the judgement was not guaranteed, so I can only see two possibilities here:
- The vote of Minos (owner of the final vote) will decide if the result is 2-2.
- Triptolemus is not allowed to be part of the "old" judges cases, neither could they participate in Triptolemus's ones. Making Triptolemus the only judge over the souls of Initiates of the Mysteries.
After Triptolemus being added to Hades' jury, is Minos the most important judge?
I'm trying to know wether I'm wrong about the meaning of the term "final vote" when a 4th judge appears and creates the possibility of a nonconsensus scenario. From my own point of view, Minos was the most important judge, as it was the one who resolved a nonconsensus scenario. Since this is a totally subjective oppinion, and I also may be wrong, didn't want to title this question "...is Minos STILL the most important judge".
Again, I may also be confused because of the fact that Triptolemus owns his own sphere of action and there's no possibility of such a draw, as Codosaur's answer states.