Traditionally the following stages are counted for the political order of the Ancient Rome:
- Empire (subdivided into Principate and Dominate)
The "kingdom" is usually regarded as monarchy, the "republic" as the republic in modern meaning and "principate" and "dominate" as either monarchy or military dictatorship (with dominate more often regarded as monarchy).
I would question the claim that political order had changed sufficiently in ancient Rome from the era of Romulus until at least the reign of Heraclius.
Just some facts.
The Roman state was always called "res publica" both in the times of the kingdom and later until Latin language ceased to be used. Even the Catholic Church, centuries later, used this term to refer the Christian world. The terms "regnum" and "imperium" were also widely used under the Republic, later and before.
The Roman rex was an elected public magistrate. He was suggested by the senate and elected by the people of Rome via the Curiate Assembly for a fixed term of 6 years (they extended the term with legal tricks via formal adoption). Then a special law should be passed to grant him imperium. His power was not hereditary and was restricted by the senate and the assemblies. On one occasion when Romulus freed some prisoners on his own will the senators became very discontent.
Thus it is quite difficult to see how the Roman kingdom was not somewhat like a modern presidential republic.
- The event known as expelling the kings was in fact redistribution of powers between the magistrates. The very office of the king (a ceremonial one from then on) remained for the duration of the Republic until the rule of Theodosius, who abolished it.
Thus it is inevident how the Roman republic was not a "constitutional monarchy" with a ceremonial king alike medieval Japan.
Under the republic, some new offices were raised that were not less powerful than that of rex. Those were of military tribunes and dictators. Arguably the Roman dictator was even more powerful than a rex (he even had twice the number of lictors than a rex).
Under the republic (and possible under the kingdom as well) the title "Imperator" was quite frequently used to refer to military leaders. For example Sulla was proclaimed Imperator in 86 B.C. Multiple imperators at the same time were all under the republic, under principate and under dominate.
The power of the state leader under principate was due to the office of popular tribune which had veto power. Those now called "emperors" actually had different sets of public offices. Tiberius, for example, never was proclaimed Imperator.
The title of consul continued well into the Empire period although the title fell in prestige because it had no veto power unlike that of tribune. Still the rule of Heraclius started from being proclaimed consul (along with his father).
Under dominate order it was theorized that there should be four emperors at a time, a practice unusual for a monarchy. The practice of several emperors at a time (although usually relatives) was continued till the end of the Byzantine empire. This followed the previous tradition of two consuls or two military tribunes at a time. The term of office of an emperor under dominate was theoretically set at 8 years.
Thus it is difficult to see how the Dominate as was envisaged by Diocletian was more autocratic than principate as often asserted
- The senate always retained theoretical power for electing new emperors and disposing the ruling ones. For example Phocas was disposed by the senate and Heraclius was elected instead.
Summing the above up, it can be said that through the whole period from Romulus to at least Heraclius
- The positions of supreme magistrates were not hereditary, although often occupied by relatives or people of the same clan
- The supreme ruler could be elected and disposed by the senate
- The source of power theoretically belonged to the people and the senate
- The supreme office had a fixed term in theory with some exceptional cases
- There were always possibilities to acquire dictatorial powers even without changing the state political system, and this was in fact often done throughout the whole of Roman history.
- The real power of a leader mostly depended on his personal qualities rather than on the title of his office and epoch.
So what are the reasons to ascribe certain periods in Roman history to monarchy and certain to republic? Was not the political regime always the same with only names of the offices changing?