Ive been reading a lot of church history. And it seems rather random to me whether or not a given bishop of Rome is considered a pope or anti-pope, given tthat many claims of men now labeled as anti-Popes were widely recognized in the church at the time. So my question is this: what methodology is used to distinguish a true successor of Peter from a false one in the RCC?
Each is determined on a case by case basis. Sometimes there were irregularities of law, other times individuals simply gathered up enough supporters and proclaimed themselves to be Pope, but usually it was a small group of bishops who essentially attempted a coup of the Church through their choice for Pope.
In days before general education, newspapers, or any means of quick communication over long distance it wasn’t all that difficult to confuse people as to what events had actually taken place.
In almost all cases it was determined relatively quickly that someone was not the legitimate Pope. In those cases the individual was either shamed into repentance or split off with his own followers. The most problematic situation was the Western Schism (1378-1417) which was resolved through a Church council.