What is the typical pattern of votes during the papal conclave, before reaching the two-thirds supermajority? A recent statistical study shows that during each ballot there is a bandwagon effect, i.e. votes do converge on those cardinals that have received more votes during the previous ballot, and especially on those whose voting tally has been increasing. Moreover, a rather peculiar effect of "nocturnal conversations" can be identified, i.e. the vote tally of the leading cardinal drops sizeably the morning after.
The papal conclave that is to choose Benedict XVI's successor will likely start before March 15th, since Benedict himself is considering the option of speeding it up with a specific law (motu proprio). The question is: what is the typical pattern of votes the various candidates-cardinals receive, before one of them does reach the required two-thirds supermajority? A recent statistical study gives some hints about it.
In 1179, Pope Alexander III had ruled that a candidate should receive at least two-thirds of the cardinals' votes, and that no candidate could give himself a vote. Paul VI, resuming an amendment introduced by Pius XII and abolished by John XXIII, introduced then the "two-thirds plus one" majority rule, so that there is no need to check whether the winner has voted for himself. John Paul II heavily modified the electoral rules with the decree (Apostolic Constitution) "Universi Domini Gregis", reducing the required majority into a simple majority, in case of lack of a winner after the 34th ballot. However, Benedict XVI, who was elected according to those rules, reversed them again in 2007. Hence, we are currently back to a "two-thirds plus one" majority for all ballots.
The evolution of votes
During the past conclaves, which was the typical time pattern of votes the cardinals obtained? As far as we know, there is only one statistical study on the subject. Exploiting several memorials written by attending cardinals, Jayne Toman (Sydney University) has gathered data on vote dynamics during seven conclaves, starting with the election of Benedict XV in 1914 (Cardinal Della Chiesa) to John Paul II in 1978. The conclave that elected Pius XII (Cardinal Pacelli) happens to be the shortest, with three ballots, while the election of Pius XI (Cardinal Ratti) required 14 ballots. The dependent variable studied by Toman is the number of votes obtained by each cardinal who received at least one vote, and whose name was mentioned by note-taking cardinals.
There are three variables that have a statistically significant correlation with (maybe influence on) the vote tally:
(i) The number of votes obtained during the ballot before is strongly and positively correlated with the votes obtained during the ongoing ballot. In other terms, votes do converge on candidates that obtained more votes during the previous ballot. This effect is statistically significant for all conclaves under study with the exception of the one electing John XXIII (Cardinal Roncalli). The lowest estimate of this effect concerns the conclave electing Pius XI: each additional vote in the ballot before is correlated with 0.44 additional votes during the ongoing ballot.
(ii) There is a momentum effect, that is, a growth in votes a cardinal obtains between the last ballot (at time t-1) and the one before the last (at time t-2) is positively correlated with votes obtained during the ongoing ballot (time t). So, on top of the effect discussed above, candidates tend to give more votes to a cardinal whose votes are seen as growing. For example, during the Pius XI conclave, cardinal Gasparri obtained 8 votes during the first ballot, a figure which grew up to 24 at the sixth ballot, and stood still at that level for two more ballots. The loss of momentum helps when explaining the shift of Gasparri's supporters to other cardinals, especially to Ratti. During the last ballot (the 14th) Gasparri got no vote. The momentum effect is statistically significant but comparatively small in size: for example, during the Benedict XV and Pius XI conclaves, an additional vote between the t-1 and t-2 ballots is correlated with 0.02 additional votes during the current ballot.
(iii) In 1904, a decree issued by Pius X doubled the daily number of ballots from two to four. Excluding the lunch break, cardinals have more time to discuss and make deals in the evening, when private conversations are in principle feasible. According to Toman estimates, the main effect of those "nocturnal conversations" is to sizeably reduce the number of votes obtained by the leading cardinal. A reasonable explanation for this finding is that nocturnal conversations allow cardinals to coordinate and hinder the election of the leading cardinal. The only exception to such pattern is the John Paul II conclave.
The short life of the simple majority rule
The Universi Domini Gregis decree issued by John Paul II in 1996 introduced the possibility of simple majority rule after the 34th ballot, or a run-off between the two most voted cardinals during the previous ballot. According to the rules adopted so far, only a unanimous vote could have changed the two-thirds plus one majority requirement. After the introduction of this new rule, a simple majority of cardinals was considered enough to introduce a simple majority quorum or a runoff, starting from the 35th ballot. Those rules were applied only during the 2005 conclave, which elected Benedict XVI: their likely effect was to give more bargaining power to a simple -and cohesive- majority of cardinals during the first ballots, because of the credible threat of choosing a simple majority quorum after the 34th ballot. Since Benedict XVI brought back a permanent two-thirds plus one majority in 2007, we expect the upcoming conclave to converge at a cardinal with a wide consensus. We are not in the business of reading the retiring Pope's mind, but his decision in 2007 might have been driven exactly by this purpose, that is, to elect a non-divisive successor.
@ricpuglisi (with Gianluigi Vernasca)
This is the updated version of a piece that was published by lavoce.info in April 2005.
Toman, J. T. . "The Papal Conclave: How do Cardinals Divine the Will of God?". Mimeo, University of Sydney. Available here.
Federico Fellini, "Roma", 1972. Defilé di moda ecclesiastica