If this report is to be believed, Cardinal Bergoglio actually was selected Pope on the 5th Ballot, but due to an irregularity, a 6th Ballot was held, which gave it to Bargoglio.
What happened? After the fifth ballot was cast and the ballot box containing the votes of the 115 cardinal electors opened, the ballots were counted as always before being scrutinised and the resulting number was 116. There was one extra ballot. One of the cardinals had mistakenly placed two ballots in the box without realising it: one contained the name of his preferred candidate and the other was blank.
The mistake meant the whole voting session had to be cancelled, without the ballots even being scrutinised. If they had, Bergoglio would probably have probably come out on top. It was decided that another vote should be cast immediately. The mishap would not have influenced the cardinals in any way as none of them knew what name (in this case none) was on the extra ballot. On the sixth ballot and after the fifth scrutiny, the Archbishop of Buenos Aires won a clear majority: way above the expected quorum of 77 votes. Then the white smoke billowed out of the Sistine Chapel chimney and Pope Francis greeted the crowds for the first time.
So even though there were five puffs of smoke, there were actually six ballots.
I recently attended the Houston Red Mass which offered a keynote by Cardinal DiNardo. He reflected on his experiences in the Conclave, and described the sheer awe of sitting in the Sistine Chapel, listening to each of the 115 names on the ballots read aloud. Based on this account, on the 5th Ballot, because there was one-too-many, the names were never announced, and there was no possibility of influencing. Imagine if all of the names were read aloud without counting the ballots first. That would mess with the elections. Fortunately the ballots were counted first before they were read aloud.
For some reason, this process makes me think of Vice President Jefferson counting the electoral votes in the election of 1800, in his role as President of the Senate. Recall that the ballot from Georgia was defective, though it was clear that the vote was for Jefferson. Nonetheless, Jefferson counted the votes for himself and Burr. There were no objections. The Constitution was silent on this obvious, potential conflict of interest. How should a candidate count his own votes?
If this vote was disputed, none of the five candidates would have reached the majority threshold of 70 votes, and there would have been a runoff in the House among the top five finishers. But by counting the Georgia ballot, Jefferson and Burr each got 73, which resulted in a tie. So the the election was thrown to the House between Jefferson and Burr. Imagine if somehow John Adams could’ve pulled out the victory there? Boston Strong, right?
The procedures in the Vatican seem designed to promote fairness and efficiency. Eventually, Todd, Laura, and I will get back to a paper we are working on about public choice theory and the Conclave (Papal Choice Theory).