Papal conclave, 1513

The papal conclave, 1513 elected Giovanni de'Medici as Pope Leo X to succeed Pope Julius II.
==Balloting==
Twenty-five of the living thirty-two cardinals entered the conclave on March 3Roscoe, 1888, p. 295. or March 4.Trollope, 1876, p. 180. The first several days were spent on the drafting of a conclave capitulation, regulating the procedures of the conclave and agreeing on the benefices that would be granted to the various cardinals, including a payment of 1,500 ducats by whomever was elected, upon the completion of the election. Among the conclavists was Giacomo di Brescia, the private physician required by Cardinal Medici; Giacomo, despite his plea, was not permitted to leave early once his services were no longer required.Trollope, 1876, p. 181.
The first scrutiny took place on March 10 after a ceremonial reading of Julius II's bull against simony. The voting itself took place in the no longer extant chapel of S. Niccolo da Bari.Setton, 1984, p. 143. As the ranking cardinal-deacon, Medici himself was charged with the counting of the ballots.Roscoe, 1888, p. 297. Cardinal Serra i Cau (called Alborense) received thirteen votes on the first ballot. Although Pirie subscribes this outcome to chance (see below), Roscoe argues that Alborense had the support of the older cardinals, while the younger, and particularly the royal and noble cardinals supported Medici.
That night at dinner, Cardinal Medici and Cardinal Raffaele Riario (the two leading papabile) were seen in closer conversation although no other observer was able to make out the subject.Trollope, 1876, pp. 181-182. Even before the vote took place the next morning, a rumor spread among the cardinals as to the outcome of the conversation, and every other cardinal flocked to Medici's cell to congratulate him.Trollope, 1876, p. 183. Trollope claims that every cardinal did such because "it is ill voting against a man to-day who is to be the despotic master of your fate and fortunes on the morrow". 
Medici was unanimously elected on the first scrutiny in the morning. A window which had been boarded closed for the conclave was smashed open and Cardinal Alessandro Farnese (future Pope Paul III) announced Medici by his chosen papal name, Leo X.
Florentine banker Filippo Strozzi the Younger accompanied Medici to Rome for the conclave; Strozzi's brother (a disciple of Savonarola) claimed that: "inasmuch as the latter aspired not without good reason to the Papacy, it was likely enough that he might have to vail himself of Filippo's credit".Trollope, 1876, pp. 183-184.
==Pirie's account==
According to Valerie Pirie's The Triple Crown (1936):
:"Twenty-five cardinals entered the conclave. The absence of the French element left practically only two contending parties-the young and the old. The former had secretly settled on Giovanni de' Medici; the second openly supported S. Giorgio, England's candidate. The Sacred College had been assembled almost a week before the first serious scrutiny took place. Many of the cardinals, wishing to temporise and conceal their real intentions, had voted for the man they considered least likely to have any supporters. As luck would have it, thirteen prelates had selected the same outsider, with the result that they all but elected Arborense, the most worthless nonentity present. This narrow shave gave the Sacred College such a shock that its members determined to come to some agreement which would put matters on a more satisfactory basis for both parties."Pirie, 1936, p. 49.
===Mathematical evaluation===
Prof. Anthony Lo Bello of Allegheny College tested the ex ante probability of Pirie's account, assuming that the cardinals assumed that all but a handful of the assembled twenty-five cardinals were not among the papabile, and thus were not perceived as being able to receive the requisite seventeen votes, and that only a smaller number of these, m, had absolutely no supporters.Lo Bello, 1982, p. 231. Lo Bello further assumes that r cardinals participated in the strategy that Pirie outlines and calculates the probabilities for 17 ≤ r ≤ 25, using factorials. The probability of Pirie's account occurring in terms of r and m was:
\frac{m(m+r-14)!r!}{(r-13)!(m+r-1)!}
and the probability of a candidate receiving seventeen votes was:
\frac{m(m+r-18)!r!}{(r-17)!(m+r-1)!}
Lo Bello concludes that the probability of Pirie's account is <1% for reasonable values of r and m, and that, were Pirie's account to be correct, the "shock" of the cardinals was misjudged because the probability of actually electing a pope with this method was far less, <0.1%.Lo Belo, 1982, p. 233.
==Electors==
Twenty-five cardinals participated in the election:
*Raffaele Riario
*Domenico Grimani
*Jaime Serra I Cau
*Marco Vigerio della Rovere
*Francesco Soderini
*Giovanni de' Medici (elected Pope Leo X)
*Alessandro Farnese (future Pope Paul III)
*Luigi d'Aragona
*Tamás Bakócz
*Marco Cornaro
*Francisco de Remolins
*Niccolò Fieschi
*Adriano di Castello
*Robert Guibé 
*Leonardo Grosso della Rovere
*Carlo Domenico del Carretto
*Sigismondo Gonzaga
*Sisto Gara della Rovere
*Christopher Bainbridge
*Antonio Maria Ciocchi del Monte
*Pietro Accolti
*Achille Grassi 
*Matthäus Schiner
*Bandinello Sauli
*Alfonso Petrucci
Six more cardinals chose not to participate in the conclave:
*Ippolito d'Este
*Philippe de Luxembourg
*Amanieu d'Albret
*François Guillaume de Castelnau-Clermont-Ludève
*Francisco Jiménez de Cisneros
*Matthäus Lang von Wellenberg
Four more had been excommunicated by Julius II, and thus could not participate (all were reinstated by Leo X):
*Federico di Sanseverino
*Bernardino López de Carvajal
*Guillaume Briçonnet 
*René de Prie
==Notes==
==References==
*Lo Bello, Anthony. 1982. "A Papal Conclave: Testing the Plausibility of a Historical Account". Mathematics Magazine, 55(4): 230-233. 
*Pirie, V. 1936. The Triple Crown. New York: G. P. Putnam's Sons.
*Roscoe, William. 1888. The Life and Pontificate of Leo the Tenth.
*Setton, Kenneth M. 1983. The Papacy and the Levant (1204-1571). 
*Trollope, Thomas Adolphus. 1876. The papal conclaves, as they were and as they are.
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Category:1513
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