In a conclave, if no one receives the required two-thirds of the votes on the first day, the cardinals celebrate Mass at 8:15 a.m. in the Pauline Chapel then meet again in the Sistine Chapel at 9:30 a.m. on the second day. After reciting the Divine Office, they again vote. If they are again unsuccessful, they immediately vote again. From then on, there can be two votes in the morning (beginning at 9:30 a.m. Rome time) and two in the afternoon (beginning at 4:50 p.m. Rome time). Each morning and afternoon, new scrutineers, infirmarii and revisers are chosen by lot.
If a second vote takes place, the materials from two votes are burned at the same time. Thus twice a day, there will be black smoke around noon and 7 p.m. Rome time from the stove until a pope is elected. White smoke could appear at these times or earlier, around 10:30 a.m. or 5:30 p.m. Rome time if a pope is elected on the first ballot of the morning or afternoon.
If after three days the cardinals have still not elected anyone, the voting sessions can be suspended for a maximum of one day for prayer and discussion among the electors. During this intermission, a brief spiritual exhortation is given by the senior cardinal deacon (in this case, French Cardinal Jean-Louis Pierre Tauran). Then another seven votes take place, followed by a suspension and an exhortation by the senior cardinal priest (Belgian Cardinal Godfried Danneels). Then another seven votes take place, followed by a suspension and an exhortation by the senior cardinal bishop (Italian Cardinal Giovanni Battista Re). Voting is then resumed for another seven ballots.
If no candidate received a two-thirds vote after this balloting, Universi Dominici Gregis  of John Paul II allowed an absolute majority (more than half) of the electors to waive the requirement of a two-thirds majority vote. Thus, an absolute majority of the electors could decide to elect the pope.
Some criticized this innovation, including me, as contrary to centuries of tradition. We pointed out that if an absolute majority of the electors favored a candidate in the first ballot of the first day of the conclave, the election could in practice be over because they could hold firm for about 10 to 12 days until they could change the rules and elect their candidate.
In the past, the two-thirds requirement was an incentive for the electors to compromise or move to another candidate. Under John Paul's rules, a majority did not have to compromise. It could hold tight while the minority is pressed to give in since everyone knows eventually the majority will prevail. In such a case, the minority would undoubtedly give in rather than scandalize the faithful and upset the man who inevitably would become pope.
Cardinals who attended the 2005 conclave told John L. Allen Jr. of the National Catholic Reporter they were very conscious of the fact that anyone who came close to a majority would be difficult to stop.
John Paul II did not explain in Universi Dominici Gregis why he made this change. Perhaps he feared a long conclave. By giving the cardinals more comfortable quarters, he reduced the discomfort factor that discouraged long conclaves. Allowing the cardinals to elect a pope with an absolute majority reduces the likelihood of a conclave going on for months.
In 2007, Pope Benedict overturned John Paul's innovation and returned to the absolute requirement of a two-thirds majority. Instead, the pope instructed that if the cardinals are deadlocked after 33 or 34 votes (depending on whether there was a vote the first day), which would take 13 days, runoff ballots between the two leading candidates will be held. This procedure is problematic because if neither candidate is able to get a two-thirds vote, the conclave will be deadlocked with no possibility of choosing a third candidate as a compromise. The two leading cardinals cannot vote in the runoff ballots, though they remain in the Sistine Chapel while the voting takes place. Nor do Benedict's new rules say what to do if two candidates are tied for second place.