It's probably hard to answer that accurately. I've read arguments about how commonplace polygamy and harems were and they usually go like this:

I've heard that absolute rulers liked to keep everyone else down, to cement their own position. This often involved limiting the number of wives other men could have, and limiting how closely they could marry (oftentimes the emperor would ban cousin marriage for everyone else, but then marry his own cousins and sisters, to prevent having to lose anything by way of dowry).