# How do cardinals vote? A statistical analysis of papal conclaves

**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.

**Electoral rules**

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)

**Note:**

This is the updated version of a piece that was published by lavoce.info in April 2005.

**Reference:**

Toman, J. T. [2004]. "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