By Ronald L. Conte Jr. based on the Apostolic Constitution Universi Dominici Gregis, published on the Vatican web site.
The rules governing the election of the next Pope are determined by the Apostolic Constitution Universi Dominici Gregis (UDG), written by John Paul II and promulgated on February 22 of 1996. After the death of Pope John Paul II, the next Pope will be chosen by the Cardinals of the Roman Catholic Church. "Confirming therefore the norm of the current Code of Canon Law (cf. Canon 349), which reflects the millennial practice of the Church, I once more affirm that the College of electors of the Supreme Pontiff is composed solely of the Cardinals of Holy Roman Church." (UDG).
However, the Cardinals of the Church who are 80 years of age or older cannot vote for the next Pope: "those Cardinals who celebrate their eightieth birthday before the day when the Apostolic See becomes vacant do not take part in the election." (UDG). If a Cardinal reaches his 80th birthday prior to the day the Pope dies, he cannot vote for the next Pope. These older Cardinals can "take part in the preparatory meetings of the Conclave," but they cannot vote.
An interesting question arises concerning the maximum number of Cardinal electors (voting Cardinals). Pope John Paul II, in UDG, established a maximum number of 120 voting Cardinals: "In the present historical circumstances, the universality of the Church is sufficiently expressed by the College of one hundred and twenty electors, made up of Cardinals coming from all parts of the world and from very different cultures. I therefore confirm that this is to be the maximum number of Cardinal electors...." (UDG) By some counts, the Pope has now chosen more Cardinals under the age of 80 than the maximum 120. Some Cardinals might reach the age of 80 prior to the Pope's death and some might be unable to attend the Conclave due to illness or political circumstances. But if more than 120 Cardinal electors are present for the Conclave, they will most likely all be able to vote, despite the above rule. Only the Pope can change the rules for electing His successor, and, by choosing more than 120 "young" Cardinals, the Pope did in fact change that rule, by his actions if not by his written words.
During the Conclave, the Cardinals must stay in Vatican City State: "for the whole duration of the election the living-quarters of the Cardinal electors and of those called to assist in the orderly process of the election itself are to be located in suitable places within Vatican City State." (UDG) And the election itself must take place within the Sistine Chapel: "I decree that the election will continue to take place in the Sistine Chapel, where everything is conducive to an awareness of the presence of God...." (UDG)
Strict secrecy governs the Cardinals concerning the election of the next Pope: "I further confirm, by my apostolic authority, the duty of maintaining the strictest secrecy with regard to everything that directly or indirectly concerns the election process itself." The actual voting cannot take place by a voice vote, nor is it permitted for the Cardinals to choose a Pope by means of a compromise agreement made by the representatives of differing groups of Cardinals. The election can only occur by a secret ballot: "the only form by which the electors can manifest their vote in the election of the Roman Pontiff is by secret ballot...." (UDG)
The election process should begin more than 15 full days, and no later than 20 days, after the death of the Pope. "I furthermore decree that, from the moment when the Apostolic See is lawfully vacant, the Cardinal electors who are present must wait fifteen full days for those who are absent; the College of Cardinals is also granted the faculty to defer, for serious reasons, the beginning of the election for a few days more. But when a maximum of twenty days have elapsed from the beginning of the vacancy of the See, all the Cardinal electors present are obliged to proceed to the election." (UDG 37) The 15 full days is to be counted from the moment of the Pope's death. This could be interpreted to mean 24 hours times 15, or the 15 calendar day after the day of the Pope's death. A subsequent comment within UDG favors the latter interpretation: "and thus on the fifteenth day after the death of the Pope or, in conformity with the provisions of No. 37 of the present Constitution, not later than the twentieth – the Cardinal electors shall meet...." (UDG, 49)
In order to maintain secrecy, the Cardinal electors are not permitted to have outside communication during the Conclave. Any devices which can record or transmit audio or video are forbidden. "It is specifically prohibited to the Cardinal electors, for the entire duration of the election, to receive newspapers or periodicals of any sort, to listen to the radio or to watch television." (UDG, 57.)
The number of votes required for the election of the Pope is often misunderstood. A two-thirds majority is sufficient to elect the next Pope. "I therefore decree that for the valid election of the Roman Pontiff two thirds of the votes are required, calculated on the basis of the total number of electors present." (UDG, 62) Therefore, if 120 Cardinal electors are present, then 80 votes or more are needed to elect the next Pope.
The often-quoted "2/3rds plus one" rule only applies if 2/3rds is not a whole number. For example if 119 Cardinal electors are present, then 2/3rds is 79-1/3. Since one cannot have 1/3rd of a vote, one additional vote is required, that is, 80 votes. "Should it be impossible to divide the number of Cardinals present into three equal parts, for the validity of the election of the Supreme Pontiff one additional vote is required." (UDG, 62)
If the Cardinals are unable to elect a Pope by a two-thirds majority, after a period of time and a series of unsuccessful votes, the rules for electing the Pope change. The Cardinals can decide, by a simple majority vote, the manner of proceeding with the election. They specifically are permitted to decide to elect a Pope by an absolute majority of votes (1/2 the Cardinal electors present plus one). They are also permitted to elect the Pope by taking an initial vote to determine the two men with the most votes, then to elect the Pope in a subsequent vote choosing only one of those two men. "Nevertheless, there can be no waiving of the requirement that a valid election takes place only by an absolute majority of the votes or else by voting only on the two names which in the ballot immediately preceding have received the greatest number of votes; also in this second case only an absolute majority is required." (UDG, 75)
When is the Pope elected? "The Scrutineers add up all the votes that each individual has received . . . if however it turns out that someone has obtained two thirds of the votes, the canonically valid election of the Roman Pontiff has taken place." (UDG) As soon as someone receives 2/3rds or more votes, (or a simple majority of votes in the special case mentioned above,) that man has been validly elected. However, he is not yet the Pope of the Roman Catholic Church.
The man who is elected Pope does not become Pope until three conditions are satisfied. (1) canonically valid election, (2) he accepts his election as Roman Pontiff, (3) he must be an ordained Bishop of the Church.
A woman can never validly have the role of Roman Pontiff, because a woman cannot be validly ordained as Bishop. Usually the man chosen to be Pope is a Cardinal, or at least a prominent Bishop, although the Cardinal electors can choose any adult male Catholic. On rare occasions a non-Bishop has been chosen, and the UDG allows for this sheer possibility: "After his acceptance, the person elected, if he has already received episcopal ordination, is immediately Bishop of the Church of Rome, true Pope and Head of the College of Bishops. He thus acquires and can exercise full and supreme power over the universal Church. If the person elected is not already a Bishop, he shall immediately be ordained Bishop." (UDG, 88)
"Should the election take place in a way other than that prescribed in the present Constitution, or should the conditions laid down here not be observed, the election is for this very reason null and void, without any need for a declaration on the matter; consequently, it confers no right on the one elected." (UDG, 76)
"Wherefore, after mature reflection and following the example of my Predecessors, I lay down and prescribe these norms and I order that no one shall presume to contest the present Constitution and anything contained herein for any reason whatsoever...."
"As determined above, I hereby declare abrogated all Constitutions and Orders issued in this regard by the Roman Pontiffs, and at the same time I declare completely null and void anything done by any person, whatever his authority, knowingly or unknowingly, in any way contrary to this Constitution." (UDG, promulgation)