One of my ongoing research projects is on the Mongol invasions. Doing some background research, I realized there's an interesting asymmetry between male and female rulers, in terms of available imperial sexual strategies.Say that the Mongol hordes have just finished annexing another city along their ever expanding frontier. Let's call it Elbonia . In this case the local elite had the good sense to surrender peacefully, and accept the Mongols as their rightful overlords. Everybody knew that if they put up a fight, the Mongols would typically exterminate a significant proportion of the local population, and enslave the rest.What did the Mongols want from Elbonia? Well first of all, obviously they didn't want the inhabitants to ever attack their other dominions, regardless of any preexisting local feuds which may have existed. Secondly, they wanted them to send them money or tradable goods regularly. And thirdly, they wanted them to furnish soldiers for use in their next campaigns. And keep in mind, the Mongols' plan wasn't to keep a huge occupation army in Elbonia to keep coercing the inhabitants to their will -after all, this would have offset the benefits of their conquest. No, the city should have kept its part of the "bargain" year after year, and decade after decade, even if no Mongol troops ever passed again within five hundred miles of Elbonia. How could they achieve this?Well, obviously fear of retribution was one way, but a significant part of the strategy went something like this: the Khan would demand that one of the daughters of the most important person in the city (call him Honcho V) be given to him as wife (the Khan had a principal wife whose offspring could potentially inherit the imperial title, but lots of other wives he picked up along the way). Eventually this wife would give birth to a child - say a baby boy named Honcho VI- which would quite naturally be brought up partially with Mongol customs, and partially with the Elbonian ones of his mother. When Honcho VI came of age, he would be in an excellent position to become a leading man of his city origin: after all, he was the son of Genghis Khan, and the grandchild of Honcho V.But while he was still a toddler, what did the political situation in Elbonia look like? Well Honcho V clearly had little interest in stirring trouble. After all, if he could keep the flow of recruits and tribute going, in a few years his grandson would likely have been more powerful in Elbonia than he had ever been. Honcho V's son probably realized that he was now much less likely to inherit his father's position, but Genghis Khan was now his brother in law! That's pretty cool in anyone's book.Further, if Honcho V was so important, he was almost certainly related to other leading families in Elbonia. Perhaps his wife was the daughter of Kahuna IV, the second most important man in Elbonia. So now another important dynasty knew that the future leadership of Elbonia would be in the hands of their cousins. They could also hope that Honcho VI would marry one of the daughters of their family. So if the Khan's choice of wife was wise, by simply fathering children with the right woman, he had aligned the incentives of the Elbonian elite with that of the Horde, and he could expect that gold and recruits would continue to flow with very little extra effort. If he wanted to improve his chances further, all he had to do was find five minutes at the right time of the month every two years or so. Now there's an Imperial model which can be replicated hundreds and thousands of times (for smaller cities, you can marry the hostage-wife to one of your "mainline" sons).Given these incentives, it is a bit easier to understand how it is possible for 8% of all the males in a swath of land from Northern China to Uzbekistan to be descendants of a single ancestor thought to be Genghis Khan.However this model is only possible for a male Emperor. Regardless of any cultural superstructure, this system would clearly not be viable for an Empress. Yes, she could just as easily get a city to surrender to her, and get a leading man to marry off a son to her, but even if polyandry was welcomed, she could only produce a child every 1.5 years or so. Even if we assumed that some of these men might be married off to her daughters, rather than to herself, it looks like this system could ensure the cooperation of perhaps a few dozen or so cities, rather than the enormous empire that the Mongols controlled.Obviously, in cultural contexts in which polygamy was not tolerated for either sex, this particular asymmetry was not directly relevant. Given the social norms prevalent in Europe, Elizabeth I couldn't have copied the Mongol system even if she had been a man. But it should be noted that the illegitimate sons of kings played an important part in the politics of many European kingdoms. For example, Charles V enjoyed a brief liaison with a maid, which resulted in Margaret of Parma , who eventually became capable governess of the Spanish Netherlands. Another short tryst with a German singer resulted in John of Austria , the admiral that won the Battle of Lepanto. Across the Pyrenees, Louis XIV was of course a huge fan of this practice, and he had at least a dozen illegitimate children, several of which achieved high rank in his army. Quite apart from the repressive cultural context, it would have been dynastically unwise for a Queen to devote one of her scarce reproductive opportunities to such targets of opportunity.At the same time, we can see the Western cultural norm towards (official) monogamy as a fundamentally anti-imperialist institution. Might Napoleon have succeeded in conquering Europe, had he been able to take a few dozen wives?