Conclavism is the practice that has existed since the second half of the 20th century which consists in the convening of a conclave — a human institution — to elect rival popes ('antipopes') to the current pope of Rome. This method is used by some Catholics, often sedevacantists, who do not accept the legitimacy of their present papacy. Those who hold the position that a conclave can be convened to elect a pope to rival the current pope of Rome are called Conclavists.
This claim is usually associated with the claim, known as sedevacantism, that the present holder of the title of pope is not pope, which implies they consider they have the right to elect a pope. However, not all Sedevacantists are Conclavists.
Conclavism is different from what George Chryssides calls the "Mysticalists" phenomenon, i.e. people declaring themselves popes after receiving a personal mystical revelation. This is because in the Mysticalists' cases no human institution is used to have a pope appointed; an example of those cases is the Apostles of Infinite Love.
The term "Conclavism" comes from the word "conclave", the term for a meeting of the College of Cardinals convened to elect a bishop of Rome, when that see is vacant.
The description and explanation of Conclavism of Chryssides is:
Since most Sedevacantists (although not all) object to Pope John XXIII's modernization of the Roman Catholic Church, they argue that he nullified his appointment to the papacy in 1958. It is therefore inferred that the conclave of cardinals who elected him was also invalid. Conclavists, however, hold that the method of electing a pope by a conclave remains the valid process and hence that it is necessary for a conclave to be reconstituted and convened. Since none of the members of that Pope John XXIII conclave remain alive, one must resort to the principle of epikeia ('reasonableness'), and that membership of a conclave should be drawn from the faithful community who are invited.
The idea of "reconvening a conclave arose in the late 1960s and early 1970s". One of the first proponents of the idea is Joaquín Sáenz y Arriaga, a Mexican priest.
In the late 1980s, David Bawden promoted the idea of a papal election and ultimately sent out over 200 copies of a book of his to the editors of all the sedevacantist publications he could find, and to all the priests listed in a directory of traditionalists as being sedevacantists. He was then elected in 1990 by a group of six people who included himself and his parents, and took the name "Pope Michael".