How many votes does it take to elect a pope?
Pope
Traditionally, the vote was conducted by Acclamation, by selection (by committee), or by plenary vote. Acclamation was the simplest procedure, consisting entirely of a voice vote.
The election of the pope almost always takes place in the Sistine Chapel, in a sequestered meeting called a "conclave" (so called because the cardinal electors are theoretically locked in, "cum clave", i.e., with key, until they elect a new pope). Three cardinals are chosen by lot to collect the votes of absent cardinal electors (by reason of illness), three are chosen by lot to count the votes, and three are chosen by lot to review the count of the votes. The ballots are distributed and each cardinal elector writes the name of his choice on it and pledges aloud that he is voting for "one whom under God I think ought to be elected" before folding and depositing his vote on a plate atop a large chalice placed on the altar. For the Papal conclave, 2005, a special urn was used for this purpose instead of a chalice and plate. The plate is then used to drop the ballot into the chalice, making it difficult for electors to insert multiple ballots. Before being read, the ballots are counted while still folded; if the number of ballots does not match the number of electors, the ballots are burned unopened and a new vote is held. Otherwise, each ballot is read aloud by the presiding Cardinal, who pierces the ballot with a needle and thread, stringing all the ballots together and tying the ends of the thread to ensure accuracy and honesty. Balloting continues until someone is elected by a two-thirds majority. 
One of the most prominent aspects of the papal election process is the means by which the results of a ballot are announced to the world. Once the ballots are counted and bound together, they are burned in a special stove erected in the Sistine Chapel, with the smoke escaping through a small chimney visible from Saint Peter's Square. The ballots from an unsuccessful vote are burned along with a chemical compound to create black smoke, or "fumata nera". (Traditionally, wet straw was used to produce the black smoke, but this was not completely reliable. The chemical compound is more reliable than the straw.) When a vote is successful, the ballots are burned alone, sending white smoke ("fumata bianca") through the chimney and announcing to the world the election of a new pope. Starting with the Papal conclave, 2005, church bells are also rung as a signal that a new pope has been chosen.
Pope Paul II
He was elected to succeed Pope Pius II by the accessus in the first ballot of the papal conclave of 1464 with a majority of fourteen of the nineteen cardinals present. Beforehand, to secure to the cardinals a greater share of power than they had enjoyed under Pius II, a capitulation was subscribed by all except Ludovico Trevisan. It bound the future Pope to continue the Turkish war, but he was not to journey outside Rome without the consent of a majority of the cardinals, nor to leave Italy without the consent of all. The maximum number of cardinals was limited to twenty-four, and any new Pope was to be limited to only one cardinal-nephew. All creations of new cardinals and advancements to certain important benefices were to be made only with the consent of the College of Cardinals. Upon taking office, Paul II was to convene an ecumenical council within three years. But these terms of subscription were modified by Paul II at his own discretion, and this action lost him the confidence of the College of Cardinals. The justification for setting aside the capitulations, seen to be under way by the Duke of Milan's ambassador as early as 21 September, lay in connecting any abridgement of the Pope's absolute monarchy in the Papal States with a consequent abridgement of his sole authority in spiritual matters. Almost from his coronation, Paul withdrew and became inaccessible: audiences were only granted at night and even good friends waited a fortnight to see him. His suspiciousness was widely attested.