It's rather simple: the new Pope elected in Pisa wasn't recognized by either of the parties supporting the existing pretenders.

The Hispano-French camp, backing Benedict XIII seated in Avignon, went so far as to stage a counter-council in Perpignan (in the south of France). The Germano-Italian camp, backing Gregory XII seated in Rome, also staged a counter-council in Aquileia (an ancient episcopal seat near Gregory's native Venice).

Although both Benedict and Gregory's respective supporters either participated in or sent representatives to the council in Pisa, neither of the two competing Popes sent representatives. The council itself, although begun with an air of solemnity in the imposing cathedral of Pisa, quickly degenerated into little more than a series of formalized shouting matches. The German representatives, who arrived a month late, were met with hostility both inside and outside the council and eventually had to flee the city. The French representatives, who arrived three months late, were not any more welcome and also left before the council was concluded. Unencumbered by any opposition, the Council of Pisa declared both Benedict and Gregory heretical to the wide acclaim of all remaining participants, and after an eleven-day conclave elected a new pope: Pietro Filargo, a worldly man of Greco-Venetian origin. Bishop of Milan at the time of his election, Filargo had been one of the council's greatest sponsors.

Enthroned as Alexander V, the hope was that both Benedict and Gregory's supporters would abandon their respective camps and rally behind the new pope for the sake of the church's unity. Indeed, much of the council had revolved around the personal qualities of the two pretenders, and the feeling was that if only a less stubborn man were to lead the church the schism might somehow be brought to an end. The choice of Filargo, an ethnic Venetian who had studied in France and spent most of his career in Lombardy, was almost certainly made in the hopes of selecting a candidate who would appease as many camps as possible. Needless to say, he didn't.

It might seem like Alexander's election was a shot in the dark, but the cardinals in Pisa knew that Gregory had already proposed to Benedict that they both resign in order to hold a new conclave. Of course, the necessary condition for that conclave to be successful was that their respective supporters would get together and participate in said conclave, which clearly wasn't the case in Pisa.

Didn't something similar happen with the American constitutional convention where they were told specifically to not replace the articles of confederation?