This is an interesting one!
Yes what is an empire?
The USA are in the list and they certainly never have had an empire in the traditional sense but are certainly guilty of neo-imperialism pursuing economic and cultural conquest.
What is meant by greatest?
In terms of physical extent it is a toss up between the British and the Mongols. But it is questionable if the Mongol Empire was ever under central control. They did not have the means of communication to control an empire of that size. (I believe the first of Asimov’s Foundation series has reasons why an empire’s size is determined by comunication). The British Empire was definitely exploititive and only of benefit of a certain class, even at home.
The Celts did not have an Empire but their culture certainly spread from the Black Sea to the Atlantic. There is no mention of Alexander the Great’s empire but as he died before it was consolidated I think it can be ruled out as the greatest.
The more I learn about the Moslem empire and it’s spirit of tolerance the more I would rate it as the greatest. Without it there would have been no continuation of the intelectual progress from the Greeks and therefore probably no renaissance. But we don't have the choice of that one.

I don't beleieve in empires so I think non were great.

I didn't vote because there isn't an other. I don't think that there is a "greatest" empire because all have made contributions to the uplifting of the human species and contributions to the downfall of humanity. I think that deciding on the "greatest" leaves us open to fall for the all or nothing mindset that tends to get us into trouble.

I didn't vote anyone,because I don't know these empires very much,but I
know China very well.I think if there is a choce,I will vote China.
Because China was the cradle of Eastern civilization.

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