What exactly does the Judge presiding over impeachment hearings do? As of now it is clear that John Roberts will not be sitting in for the second impeachment, and Rand Paul and many Republicans have raised points that it is a conflict of interest to have democrat Senator Leahy presiding over the trial.
On its face, I would tend to agree with that...since as a Senator, Leahy would be required to vote himself so he would quite literally be the "judge and jury".
Is there something I am missing about this conflict of intrest? And what power will the Judge have over the trial regardless of who it is?