# Papal conclave in the Vatican: too quick?

1. Mar 13, 2013

### Lucas Ayres

I was wondering yesterday how much time it would take to elect a new Pope for the Catholic Church... Well, I reached a quite bizarre conclusion and it seems very strange to me that the whole election was settled in only two days.

Since I am not an expert in probability, I would like to know if I made any mistakes in my calculations!

There are 115 cardinals and each cardinal writes down the name of another cardinal (in secrecy). Then, after the voting process is finished, someone counts the votes. A new Pope is elected if he receives more than 2/3 of the votes (i.e., 77 votes)

Therefore, the probability of a new pope being elected in any given day is:

p=115×(38)^114/(115)^114≈10^-53

(There are 115^114 different voting results - each cardinal can vote for any of the cardinals other than himself. A Pope is elected if he gets 77 votes (there are 115 possible winners). The are other (38)^114 possible voting results for each winner.)

According to the geometric distribution, the expected number of days it would take for a new pope to be elected is 1/p≈10^53. That's about 10^44 billion days, or more than 10^41 billion years... I can only conclude the elections were rigged! What do you think?

2. Mar 13, 2013

### micromass

Staff Emeritus
The votes are not random, of course. And the probability distribution is certainly not random: some people have more chance of winning than others (although a outsider seem to have won this time).

3. Mar 13, 2013

### Staff: Mentor

Sure they were. By the Holy Spirit.

4. Mar 14, 2013

### ImaLooser

Demand a recount!

Oops, they burned the ballots. Typical.