Repeated balloting is when a voting method is used multiple times with the same voters. It can be done until a certain stopping condition is reached i.e. a majority are in agreement, and other constraints can be added, such as eliminating some candidates in between ballotings or weakening the stopping condition over time.
One variation of repeated balloting is to require a winner to win two consecutive rounds, rather than only one. An anecdote that explains the reasoning for this is as follows: the cardinals who vote for the Pope once used Approval voting with a 2/3rds majority threshold and repeated balloting. In one election, a cardinal managed to convince several other cardinals to give his friend, a candidate, some "pity approvals" so that he wouldn't feel bad at losing overwhelmingly. That friend ended up nearly winning because so many cardinals were about to approve him.
- "RangeVoting.org - Catholic Popes elected via Approval Voting - election stories". www.rangevoting.org. Retrieved 2020-05-14.
One strategem which almost worked was the following. Cardinal B. Cueva and his assistant went around privately meeting a large number of cardinals asking them to vote for Cueva just so the poor fellow could know he had at least one friend, or as a "personal message of honor and respect." Thirty-two "kind polite" pseudo-votes were thus solicited, enough to assure his election, but the effort was discovered just before the ballot. It was laughed off as a joke when it didn't quite work.