He/She doesn’t need more than 50% of the Senate, right? So if there was a stronger 3rd party in the senate, and the vote was still split 34/33/33, it would be the party that has 34 votes to get majority leader.
As a follow-up, what powers does the senate majority leader have?
Art.I Sec.3: “The Senate shall chuse their other Officers…” [other than the Veep as President of the Senate]. If Senate rules allow a plurality, whoever gets the most votes, likely on a party-line basis, is it. If the rules require a majority, then expect much dealing and wheeling, many promises and bribes made, whatever it takes to gain 51%.
AFAIK they have whatever powers they can persuade or force a majority of senators to grant them.
I can’t recall if the Leaders of the Senate are appointee by an organizing resolution… I’ll look that up later.
But the Majority Leader doesn’t really have any powers beyond a few rules which aren’t really written in Senate rules. The Majority Leader is first to be recognized by the Presiding Officer. This means he gets to determine what measures or motions come before the Senate.
Also, per the rules of each party in the Senate, the Leader has lots of say in committee assignments.
Finally, the Leaders have lots of persuasive power in steering political support to and from candidates in future elections.