Why can a Chief Justice break ties in the Senate during an impeachment trial?

Question

I came across a Politico article that suggests that Chief Justice John Roberts can vote to break ties in the US Senate during an impeachment trial.

Unless Chief Justice John Roberts shocked Washington by wading in with a tie-break, Democrats need one more Republican to break ranks and upend GOP plans for a swift Trump acquittal.

However, it is stated in Article I, Section 3 of the US Constitution that the Vice President breaks all ties in the Senate.

The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided

So, why does the Chief Justice break ties during a impeachment trial and not the Vice President, which is the usual case? Also, what authorizes the Chief Justice to cast tie-breaking votes?

Answer 1

So, why does the Chief Justice break ties during a impeachment trial and not the Vice President, which is the usual case?

See Does the Vice-President retain their tiebreaking vote during an impeachment trial of the President?.

Also, what authorizes the Chief Justice to cast tie-breaking votes?

Precedent. In the impeachment trial of President Andrew Johnson, the Senate rejected attempts to prevent the Chief Justice from voting.

Procedure and Guidelines for Impeachment Trials in the United States Senate, pp. 40-42.

Chief Justice as Presiding Officer

Vote by:

The Chief Justice has voted in the case of a tie in an impeachment trial on two occasions. On March 31, 1868, a motion was made that the Senate retire for consultation. The yeas were 25 and the nays were 25, and the Chief Justice voted in the affirmative. At this point the Senate retired to its conference chamber.

Various amendments to the impeachment rules were discussed in this conference. As a result of the vote by the Chief Justice, Senator Charles Sumner of Massachusetts moved "That the Chief Justice of the United States, presiding in the Senate on the trial of the President of the United States, is not a member of the Senate, and has no authority, under the Constitution, to vote on any question during the trial, and he can pronounce decision only as the organ of the Senate, with its assent." This was defeated by a vote of 22 yeas to 26 nays. [...]

At the end of the conference Senator Sumner raised the issue of the right of the Chief Justice to vote on any question during the trial, but objection was raised to the fact that this was not germane to the matter on which the Senate had retired to confer and a motion that the Senate return to the Chamber without acting on Senator Sumner’s proposal was agreed to.

During the next day’s proceedings, Senator Sumner again raised the issue of the right of the Chief Justice to vote. During the reading of the Journal, he proposed an amendment to the Journal as follows: "It appearing from the reading of the Journal of yesterday that on a question where the Senate were equally divided the Chief Justice, presiding on the trial of the President, gave a casting vote, it is hereby declared that, in the judgment of the Senate, such vote was without authority under the Constitution of the United States." This was rejected by a vote of 21 yeas, 27 nays. Thus the Senate turned down each attempt to prevent the Chief Justice from voting, and in a subsequent action concerning a motion for adjournment, the vote being yeas 22, nays 22, the Chief Justice voted in the affirmative, deciding the issue. This vote was not challenged. [Emboldening added.]

At the end of the trial of President Johnson, however, another occasion arose on a motion to adjourn to a date certain when the vote was tied 27 to 27 and the Chief Justice refrained from voting.

Answer 2

Let's go back to the 18th century (when the process was set up) and consider why that is.

In modern US politics, the Vice President is the running mate of the President, meaning they are from the same party. In the first few US elections, however, the VP was the runner-up

The original system for electing presidents provided that the candidate receiving a majority of Electoral College votes would become president, while the runner-up would become vice president.

That wasn't a good idea, so they went with Plan B: elect a VP directly

The states soon ratified a twelfth amendment to the Constitution, requiring separate contests for the offices of president and vice president.

Now, let's go back to impeachment trials. With a VP looking to benefit from the impeachment, and a potential conflict of interest, it makes more sense to have a non-political person step into that role instead. Thus, they tap the Chief Justice to do it. Since they can't vote in the final removal process, the Chief Justice is mostly there for procedural votes. The power to break ties is part of the Senate rules from 1868

In 1868, Chief Justice Salmon Chase cast two tie-breaking votes in President Andrew Johnson's impeachment trial. Indeed, the current Senate rules for impeachment trials include a history section noting, "The chief justice has voted in the case of a tie." (The same section says that in the Johnson trial, the senators also voted to support the chief justice's conclusion that he could cast tie-breaking votes, noting "the Senate turned down each attempt to prevent the chief justice from voting.")

The Vice President presides over all other impeachments (including, potentially, their own).