Most religious bodies choose their leader. The Latter-day Saint movement does not, and the mechanism by which it avoids doing so is one of the more consequential pieces of institutional design in modern religion.
When a president dies, the First Presidency ceases to exist at that moment. Its counsellors return to their seats in the Quorum of the Twelve Apostles at their original seniority, and the quorum becomes the presiding body of the church. Its senior member, determined by the date on which he was ordained an apostle and not by age, is then ordained president, usually within a fortnight. There is no election, no conclave, no campaign and no shortlist, and because ordination dates are public the identity of the next president is known years in advance to anyone who cares to look.
The rule emerged from the crisis it now prevents. Joseph Smith's death in June 1844 left several claimants: Sidney Rigdon as surviving counsellor, James Strang with a letter of appointment, and the Quorum of the Twelve under Brigham Young, who prevailed at Nauvoo in August 1844 and was ordained president only in December 1847 after more than three years in which the Twelve governed directly. Comparable gaps followed the deaths of Young in 1877 and John Taylor in 1887. Since 1898 the reorganisation has been immediate.
Seventeen men have held the office. Not one succession in the main body has been contested since the rule settled, which for a movement that fragmented spectacularly at its first transition is a considerable result.