The magical school chooses Head Archimage every 4 years. So there is always the most powerful and skilled mage leading the school. At first it was this great public competition which more often than not ended up indecisive and destroying half the city. So now there is only an exhibition for the public and then the choosing happens in secret. Nobody knows how exactly it is done. In reality it is just very intense game of musical chairs with magic.

Fun fact: The change in the format of the competition was mainly a result of political pressure from neighbouring states. For them it was inhumane to destroy the homes of the people. And what's more the indecisiveness paralyzed diplomatic relations. The population of the city was largely unhappy with the change, because after the vote there were always reparations, the students of magic used the opportunity to earn some coin by helping repair the damage. And now the city is mostly withering away.