Although I'm a Venetian, I'm not very knowledgeable on the topic, though I can tell you that there were three distinct phases in the history of the Venetian government:

-the first phase went from the election of the first Doge, Paulus Lucius Anafaestus in 697 AD to 1141, with the creation of the "Consilium Sapientum". During this period the government called itself "Ducatus Venetiae" (Duchy of Venice) and Doge was nominated, not elected, by the "Concio", which a was a popular assembly to which all citizens (that is male, Venetian-born, property owners) had access to. At the same time however, the Doge's power was basically unlimited, like a king's, and this created an unstable situation where there were these two very powerful organs, and often the Doge would overrule the "Concio" or the "Concio" would depose him.

-The second phase began in 1141 and ended in 1297, with the "Serrata del Maggior Consiglio". During this phase the Venetian government started calling itself "Commune Veneciarum" (Commune of Venice) and more developed Venetian institutions were created through various reforms, like the Senate, which handled foreign policy, and the Major Council (Maggior Consiglio) which handled the legislative part of the government. These organs were elected through complex systems of direct voting and drawing by lot, in order to ensure more stability and less corruption, and the "Concio" was made practically powerless. The Doge also saw a great decrease in his authority, though not as much. Any Venetian citizen could however still run for office until 1297, when the richest noble families decided that the institutions had become too big and voted for the "closure of the Major Council" (Serrata del Maggior Consiglio),which began the

-third phase, from 1297 to the Republic's fall in 1797 when seats on the Major Council were hereditary and new institutions to keep the reigning families in power and stop dissidents, such as the Council of Ten in 1310, were created. The Doge lost all of his powers in this phase, becoming only a symbolic figurehead, and the "Concio" was abolished altogether. This phase is the Oligarchic Republic phase of Venetian history, and this when the government finally started calling itself "Res Publica Veneta" (Venetian Republic) like we know today. During this period, if your family name was not written in the "Golden Book" (Libro d'Oro), a list of all Venetian noble families to which a family could access only with the payment of an exorbitant sum of money, you didn't have any decisional power at all and were only slightly more privileged than someon living in a feudal monarchy. One of the reasons for the Republic's fall in 1796-97 was also this unwillingness to adapt and reform, even though there was a quite large illuminist progressive faction even within the Major Council from the 1750s onwards, though it never quite managed to get through with the majority, its greatest success having been the approval of a large-scale army reform in 1788, which finally established a standing Venetian army, like all other developed European states had. Alas, the Republic's end came but sadly the freedom and decisional power that many Venetians longed for did not, and instead the city was under foreign French and Austrian for sixty-nine years, until it became part of Italy in 1866.