When the Senate undertakes a trial of impeachment, what standard of proof should apply, and why? If your answer is whatever standard the Senate wants to use, the followup question is this: what would you use, if you had the sole honor of writing a Senate rule prescribing the standard of proof to be used?
And if you believe impeachment of judges should follow a different standard than impeachment of executive officers, what standard do you use for each and why do you differentiate between them?
For your convenience, here are the relevant and potentially irrelevant clauses of the United States Constitution.
U.S. Const. art. I, § 3, cl. 6
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
U.S. Const. art. I, § 3, cl. 7
Judgement in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States; but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgement and Punishment, according to Law.
U.S. Const. art. II, § 4
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
U.S. Const. art. III, § 2, cl. 3
The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury; and such Trial shall be held in the State where the said Crimes shall have been committed; but when not committed within any State, the Trial shall be at such Place or Places as the Congress may by Law have directed.
~Max