What were politics like in medieval merchant republics such as Venice? Were officials elected?

The majority of the merchant republics from the Italian Peninsula had a pretty specific system of government. For example, The Republic of Venice was lead by what was called a "Dogi"(or dodge in English.) A few other Italian Republics had them. The doge was elected into office by a committee of wealthy and educated nobles. The political system of the Venetian Republic is often described as a "communal aristocracy" since the group of people that got to vote was around 40. Now you are probably asking "who got to be part of that group?how did they get elected?" The citizens of Venice that were allowed to vote were picked by the "Maggior Consiglio"(The Great Council.) The Great Council was even more exclusive and in order to qualify to be part of it you needed to be able to find your name in the "Libro d'Oro" (The Golden Book) which listed the families with noble titles in the history of Venice. Overtime, regulations were introduced into the Venetian Republic to avoid a few families to gather too much power over the other families.

The election of the dodge was lengthy,a visiting pilgrim to the Republic wrote an account in 1462: "The Venetians met to elect a new doge by the appointed councilors. Called to the election were all the eminent nobles, who oath, were to choose from among the more noble of those lords firm in their Catholic faith. They themselves had to swear, on pain of losing all their worldy goods, to choose the man who was the wisest, the best provided by circumstances, the staunchest in defense of the faith and the most experienced in the affairs of the world, to serve the city and its dominions. Those 100 with some notaries, were confined to a house from which they were not to emerge until they had elected forty of the more noble for this honorable task."

The Doge would typically rule for life but some were killed or removed from office, such as Marino Faliero. He tried to establish a system that would grant him absolute power over the Republic, something which obviously pissed off the communal aristocracy. The ceremony of the doge being given power in Venice was very very ritualistic. It involved giving out an annual ceremony which reminded Venetians of their control of the seas, the ceremony was basically the reaffirmation vows between Venice and the sea.

Overall, the merchant republics, in this case Venice, were ruled by a set of distinguished noble and merchant families that would pick among themselves the wisest candidate.