Ballot or $B$
The choice of naming the concept of the protocol container logic is a true mistake on Lamport's part. It confuses the concepts he's trying to explain with no additional clarity. It's easy to consider this a round of voting but that's not quite either.
In truth, it's not object; it's a mathematical concept and logical organization for the protocol. For ease of use I will refer to it as both as a round or as a ballot when such terms will make it more clear what I am referring to. IE: I will try to use ballot when referring to the actual protocol proof and round when referring to the process.
A round is successful if the number of nodes that have voted for a decree meets or exceeds the quorum threshold.