During the republic, Roman government
was a well balanced consitution
Polybius describes in his Histories (6.15) the Roman government as:
Regal, aristocratic and democratic.
When the consuls, invested with the power that has been mentioned, lead the armies into the field, though they seem, indeed, to hold such absolute authority as is sufficient for all purposes, yet are they in truth so dependent both on the senate and the people, that without their assistance they are by no means able to accomplish any design.
To the senate belongs, in the first place, the sole care and management of the public money. For all returns that are brought into the treasury, as well as all the payments that are issued from it, are directed by their orders.
Since the members of the senate were not elected, but in principle appointed for life, the senate guaranteed the stability of the government of Rome. The censor though had the power to exclude someone from the senate for misconduct.
To the people belongs the power of approving or rejecting laws and, which is still of greater importance, peace and war are likewise fixed by their deliberations. When any alliance is concluded, any war ended, or treaty made; to them the conditions are referred, and by them either annulled or ratified.
Indeed after the first Punic war, the people rejected the peace treaty because the terms weren't favorable enough for Rome.
Model of the Campus Martius in Augustan time
Centuriata assembled at the Campus Martius to vote.
The voting system was not one man one vote. The population was divided into classes by the taxing system based upon property, that was said to have been introduced by Servius Tullius. These classes had been divided into centuries.
In the third century this system had evolved to: 193 centuries.
The first class held 80 centuries + 18 for the knights and 2 for the engeniers
The second, third and fourth class each had 20 centuries
The fifth class 30 + 2 for the hornblowers
The proletariens were all squeezed into a single century
Every century had one vote. So only if there was disagreement in the first class, the second class could come to to vote, and so on. Not too democratic though!! See also Dionysius of HalicarnassusDion(7.59)
Apart from the consuls the government consisted of other elected Roman magistrates. Most of them also for the term of one year. The militairy character of the Roman society is emphasized by the rule that one could only opt for a public function after having served at least ten campains in the Roman army.
In the imperial period nothing changed much, theoretically. The same structure remained, but of course the emperor ruled.