Thank you for the explanation. I wonder what Cboldt thinks?
Vote pairing - I would read Riddick for the explanation ;-)
A Senator announcing a pair is not excused from the rule as to assigning reasons for not voting, but the fact of being paired excuses from voting when the question is raised. Pairing can be done for votes of 2/3rds, where the pairing is tw in the affirmative to one in the negative (e.g., for treaties).
Pairing has no play in a cloture vote, as cloture requires a certain number of votes to pass; not a "majority" or "2/3rds" of votes cast, but (today), 60 votes must be cast in favor - and in order to cast a vote, a Senator must be at his desk.
More on vote pairing ...
Pairing is announced (which means the paired Senators are "there"), and where there are sufficient Senators present who have announced their pairs and, therefore, withheld their votes, the Presiding Officer has held that a quorum was present for the transaction of business.
So, "pairing" is a way to reduce the number of votes cast and permits Senators to hide which of the pair is on which side of an issue. That's about all it's good for, by my first reckoning on the subject.