The General Congregation begins with a prayer to the Holy Spirit said by all the delegates. The first order of business is the election of the new Superior General.
The election itself is preceded by four days of “information gathering,” called “murmuratio.” Each member of the congregation is allowed to ask any other member of the congregation about any member of the Society who might be an apt Superior General. There can be no lobbying, and no Jesuit may seek the position for himself or for anyone else. All a delegate may do is seek information about another Jesuit.
Any Jesuit who has taken the vows of poverty, chastity, obedience (and special obedience to the pope for mission) is eligible to be elected Superior General. Not every Jesuit takes the fourth vow. The successor need not be a delegate in attendance, but always has been.
At the end of the four days of conversation, a secret ballot in writing is taken, collected and counted. Paper ballots are used for as many rounds of voting as necessary until someone receives a majority vote and is elected the new Superior General.
The election process could take only days, and as soon as the pope has been informed of the Superior General-elect (by messenger or phone), his name will be announced. The rules don’t require the pope’s approval, but he always has given his blessing.
Once a new Superior General has been elected, delegates will tackle matters of mission, governance and the state of the Society. Topics could range from the Society’s changing demographics to challenges in worldwide ministries, to the Jesuit (and Pope Francis-inspired) response to a rapidly changing world, environmental concerns, poverty and violence.
Sources: GC36.org, Central and Southern Province, Fr. John Padberg, SJ, Midwest Jesuits, Wikipedia