Most of those Republics like Venice, Poland-Lithuania and others worked whilst still being very aristocratic. Some of them wouldn't call themselves "republic" though, since the elected Kingship of Poland-Lithuania is very close to the elected Kingship of the Holy Roman Empire which in itself comes from the Germanic tribal law of Kingship. England was certainly not a republic or democracy of any real sort except during the period immediately after English Civil war of the 17th Century, which places it far out of the scope of Battlemaster (and even then they were really apprehensive about making themselves a republic).
The closest thing we have to democracy in battlemaster is Iceland. All the other entities in the list provided by JPierreD were either specifically aristocratically governed with a non-hereditary position such as Prince or were elected by a council of aristocrats/extremely wealthy merchants.
Also the election of Rurik to the Rus' is a very contentious topic, mainly due to the scrutiny placed upon the Primary Chronicle by the Russians who abhorred the idea that they would invite a foreigner, a Scandinavian no less, to rule them. From what I've read they only did this because they couldn't stop fighting amongst themselves. Considering that after Rurik the rulers of most Russian states are usually called "Rurikovich", I really doubt it became any kind of republic. Merovingian inheritence and tribal law and all that snazz.
