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Alexander Hamilton and the Vice President's Tiebreaker
Andrew Hyman

Following up on co-blogger Mike Ramsey’s recent post about Federalist 69, the sentence in question by Alexander Hamilton is as follows: 
In the national government, if the Senate should be divided, no appointment could be made; in the government of New York, if the council should be divided, the governor can turn the scale, and confirm his own nomination.
Mike concludes that, “Most likely, Hamilton simply forgot about the Vice President's tiebreaker in writing Federalist 69.”  But take a look at the last paragraph of Federalist 68, published by Hamilton the very same day:
The appointment of an extraordinary person, as Vice-President, has been objected to as superfluous, if not mischievous. It has been alleged, that it would have been preferable to have authorized the Senate to elect out of their own body an officer answering that description. But two considerations seem to justify the ideas of the convention in this respect. One is, that to secure at all times the possibility of a definite resolution of the body, it is necessary that the President should have only a casting vote. And to take the senator of any State from his seat as senator, to place him in that of President of the Senate, would be to exchange, in regard to the State from which he came, a constant for a contingent vote.
So Hamilton was aware when he wrote Federalist 69 that the Vice-President of the U.S. would have a "casting vote" (i.e. a tie-breaking vote) as president of the Senate.  But I do agree with Mike that the Vice-President of the U.S. can certainly break ties on nominations, as has been happening for centuries, and the quote above from Federalist 68 shows that Hamilton thought so too, or else he would not have written that the President of the Senate would “secure at all times the possibility of a definite resolution of the body.”
That leaves the question of what the heck Hamilton meant in Federalist 69 when he wrote that, “In the national government, if the Senate should be divided, no appointment could be made….”  Evidently, Hamilton was simply referring to a situation where the Senate (including its president) had finished voting, leaving a tie vote.  After all, the Constitution explicitly contemplates that the Senate shall have a “President pro tempore, in the absence of the Vice President.” Hamilton’s point was that, if the Vice-President does not break a tie, the President of the United States cannot break that tie like the Governor of New York could.  Recall that back in those days, the President and Vice-President of the U.S. were not elected on the same ticket and were often political enemies (e.g. President Jefferson and Vice-President Burr), so people like Hamilton did not presume (as people do nowadays) that the Vice-President would support presidential nominees.
John Langford recently argued at the Balkinization Blog that Hamilton meant in Federalist 69 that the Vice-President has no casting vote on nominations, but looking at both Federalist 68 and 69 together gives quite a different impression, and Langford does not mention the former.  More importantly, the language of the Constitution does not limit the matters to which the casting vote applies: “The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.”  It's true that that provision is in Article I rather than Article II, but no one disputes that other aspects of Article I apply to nominations (e.g. "Each House may determine the Rules of its Proceedings....").  Had the vote on Justice Kavanaugh been tied, Vice-President Pence could have broken the tie, just like Vice-Presidents have been doing for hundreds of years.