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Although Rome was a republic it was not how we think of today they had 2 consuls who held the most power (not absolute power) and the senate would limit a bit their influence. The laws were made by the senate but only some ordinary wealthy and influencial citizens could vote. Rome was quite similar to Sparta's oligarchy but instead having 2 kings they had 2 consuls.

Athens was the only democrat republic how we think of now and all through her history it was marked by quarrels and demagogy of the members of the state. Most statist just cared about their personal interests instead of the wellbeing of the state. It quickly fell in her influence first with the loss of the Peloponnesian war against Sparta and then was conquered by the Macedonians.  

The Italian city states were also oligarchies modeling mostly the Roman Republic. They were ruled typicaly by a faction or family and they had one or two persons (some city states called them consuls others Doge but it was same idea) who held the actual power.

Democracy was only present in Athens which in my opinion was a failure. Republics modelled acording to Rome can work and do work but it has to have a union of purpose which is the serving of the state but us humans are sick with original sin so it is inevitable that some use it for personal purposes.

I am only sceptic of democracies, the Roman Republic was a success until the soldiers started to pledge more loyalty to their commanders instead of Rome because of the Marian reforms but it was because of their sense of loyalty and service of the state that they succeded.