As we all know, in the Catholic Church, the College of Cardinals, made up of those appointed to their office by previous popes, come together and elect a new pope by at least a two-thirds vote. While this method has the benefit of at least of millennia of use, it is not a divinely-mandated method, and in the past, Popes were chosen in different ways (before the office of cardinal even existed).
I recently learned the Copts have a very different way of selecting their "pope." Candidates are nominated by being endorsed by at least 6 bishops. A committee of 9 bishops then narrows the list of all nominees down to five or seven. The Coptic Synod then votes to narrows the list further down to three. The three names are then written on slips of paper and put in a chalice. A blindfolded five-year-old then pulls one of the three slips out of the chalice during a Divine Liturgy, and that person becomes the next Coptic "pope."
The initial stages of the process seem far too much like politics to me, but the final stage certainly leaves the matter up to God. I wonder if they get better results.