An expansionist empire may choose to assimilate the conquered peoples in its culture and society, or it may choose to keep them separate. The Romans, the Chinese, the Arabs, and the Russians chose to assimilate newly conquered peoples into the dominant culture, with the result was that after a while, all inhabitants of the empire were proud to be Romans, or Arab, or Chinese, or Russians. The Americans, the British and the French chose to keep their subjects separate from the high and pure dominant culture, with the result that violence never stopped unless, in the case of the Americans, the conquered peoples were all killed, or, in the case of the British and the French, the empire fell to pieces.
One may then consider that the best choice is to incorporate the conquered peoples into the dominant culture and society, so that with each conquest the empire’s strength grows and grows, instead of being sapped by constant guerilla warfare, and unstoppable insurgence, and general strife and ill-will. But if the choice is not to assimilate them into the superior culture and society, then it is best to go the American way and just kill them all. True, this is inhumane, and difficult, and will use up a lot of resources; but on the long term it avoids the never ending problems which have plagued the humane British and French empires; dead people don’t start insurgencies and independence movements, and they don’t resort to terrorism. The major disadvantage of this radical method is that it is not sustainable: for it is inhumane, and most people, most of the time, are not inhumane, and won’t stand for it. The Americans killed off all the Indians, or at least almost all the Indians, but when they expanded into the former territories of the French and Spanish empires they just could not do it any longer; and yet killing was all they knew, and when they could be killers no more they fell back on the definitely bad choice of letting the conquered peoples unassimilated, with the result that today many American web sites offer both English and Spanish, and the empire has a large section of the population that still primarily speak Spanish, many of whom live in ghettoized conditions.
It appears then that the best and sustainable choice is to assimilate the newly conquered peoples. This choice is not without its downsides, but those are mostly aesthetic; for example, assimilation is never really unidirectional, and some of the words and habits and cuisine of the conquered peoples will indeed percolate and modify the conquering society and culture. But then again, maybe this is not such a bad thing after all.
Before considering specific examples, it must be said that the one thing an assimilating empire absolutely must do is to encourage mixed marriages. Ties of blood are stronger than ties of tribe or city or nation. An empire where mixed marriages are rare, or are not socially acceptable, is not going to last long, because in the absence of mixed marriages the division between us and them persists with dire consequences. Colonists are to be encouraged to marry local women, and soldiers and merchants of the conquered peoples are to be encouraged to take wives from other parts of the empire. Ties of blood.
So how did the Romans do it? How did the Arabs do it? The Chinese? The Russians?
In the case of the Romans, it helped that the Romans themselves were not a pure people. From the very beginning their city was the result of a merger between the original Romans of Romulus, and the Sabines of the nearby Caere; the Romans even had a splendidly beautiful and multilayered myth about the abduction of the Sabine women, explaining how this came to be. (The traditional English translation of the name of the myth is “the rape of the Sabines”, and under this title you will find it illustrated by countless painters in countless paintings; but alas languages change and today the traditional translation would be severely misunderstood, to the point of conveying the exact opposite meaning; for the Romans most definitely did not offer sexual violence to the abducted girls, but were rather keen on honorable matrimony.)
The Making of an Assimilating People, picture by 17th century painter Pietro da Cortona, available on Wikimedia. Public domain.
So when the Romans conquered the Celtiberes of Iberia, or the Afri or Africa, or the Greeks or Greece, or the Gauls of Gaul, they made them Romans, in the same way that they had made Romans the Sabines, and the Sabelli, and the Samnites of Italy.
In the case of peoples which were on a much lower level of development, Romanization proceeded by showing them a better way of life. The Romans had rule of law, a protection of private property, and rights for women. What Gaulish peasant would not want to be a Roman when he finds out that he does not have to leave in fear that his more powerful neighbor can seize his land? What Gaulish woman would not instantly become Roman when she finds out that under Roman law she is a real person, who can own property and engage in trade, and that her daughters cannot be married off against their will?
Future Romans: soldiers of Gaul, as imagined by a late 19th-century illustrator for the Larousse dictionary. Picture available of Wikimedia. Public domain.
In the case of civilized peoples, such as the Greeks, the Romans came with a different proposition. They got to keep all their local laws and customs, and any Roman who wanted to live in a Greek city had to obey and follow them; and in addition, now the enterprising Greeks had the liberty to trade all over the immense empire. The empire got a large economic boost, for the Greeks were traders and navigators and engineers, and the Greeks became loyal citizens, and begun calling themselves Romans, a name which they kept until the middle of the 19th century.
The Arabs came at it from a different angle. To the conquered peoples of the Syria, and Egypt and Northern Africa, they promised a community of equals, predicated on the holy principles of their Mohammedan religion, which prohibits any kind of discrimination among Muslims. They combined this with a constant stream of religious propaganda, and with tolerance for those who did not wish to convert, while at the same time providing clear social and economic advantages to those who did. And lo and behold, one thousand years later most of the people of Egypt and Syria and Mesopotamia and Northern Africa consider themselves Arabs.
Their descendants are now Arabs. Portraits of Egyptians from the Roman times. Fayum mummy portraits, 3rd to 7th century AD.
The Russians had the advantage that the core of their empire was established in the Middle Ages, or what passed for Middle Ages in Eastern Europe, a time when nations were in flux and national allegiance was unknown. They also had the advantage that, medieval as they were, the Russian feudal lords were nevertheless on a much higher stage of development than the Uralic or Turkic-speaking peoples whom they encountered in what is now European Russia, not to speak of the poor hunter-gatherers of Siberia.
The Chinese had the dual advantages of having a superior culture and infinite patience. That China is a large and stable empire is proof that waiting for a long enough time works very well; for the Chinese did not do anything special to assimilate the numerous and various peoples inhabiting their immense empire, they just waited centuries and millennia, until the very memory of a time when the emperor of China did not rule was lost in the mist of time and all inhabitants could not even imagine themselves as anything but Chinese.
Future conqueror should note that no method of assimilation is perfect, and all of them will fail occasionally. The Romans could not assimilate the fanatic Hebrews, who considered themselves to be chosen by the gods for a special mission, and who took active measures to resist assimilation; the Russians could not assimilate the Caucasians of the Caucasus; the Arabs could not assimilate the Persians (and the Hebrews, them again).
(Note to readers: This is an impressionist essay. It is not intended to be completely historically accurate, and indeed it isn't. There are many aspects which have been artfully avoided. And there are no links; use your favorite search engine, for the journey is at least as important as the destination.)