Low-Tech Democracy.

[combatmedic]

I wouldn't call it "centralized" or very large in population (only about 300 K people) but is the familiar with the Yeomanry League of the World of Greyhawk?



http://www.canonfire.com/wiki/index.php?title=Yeomanry

I always found it a plausible sort of medieval fantasy democratic state.

Warriors form local groups which elect representatives, who form groups which elect representatives who form the council that forms the highest level along with the elected heads of state and governments.
It's bottom up and concrete/organic in development, not top down and abstract/theoretical.
Over time craftsmen got the franchise.

By the late period that the article I've linked to represent, gainfully employed folks who have not borne arms also get the vote. That's not a retcon. It's a historical development, near as I can tell.



The Yeomanry may be rather too small for the OP's purposes. AN d of course it is a fantasy country, not a real world historical example.