Piratejm I just want to offer a completely different scenario I used in my own Chronicle where the same thing happened but one of the PCs was an Ancillae:

No one wanted to be Prince. The elders of the city gathered around and backed one of the players for Prince while they just claimed Primogen status for each other.

The end game of the Elders is to have a puppet young Prince they can control an manipulate to further their agendas and who'll take the blame when things go south, after all everything bad that happens in a City is the Prince's fault (who can't keep his domain...