When a sitting senator is nominated for a cabinet position, they usually don't vote for themselves (like Jeff Sessions did). And that's usually no problem, because in most cases nominees also receive votes from the opposition party. But is it legal for a senator to vote for him or herself?
Even more interesting as I was thinking ahead for a possible scenario in my alternative history (
https://uselectionatlas.org/FORUM/index.php?topic=245690.0): Could a sitting senator vote for himself, if the senate has to elect a vice president and there is a 51-seat majority of his party, while the outgoing VP (who would break the tie) is from the other?
Btw: In parlamentary systems, it's not uncommon. Konrad Adenauer, Germany's first chancellor, only got first elected in 1949 by one vote. His own.