A lot of the knee-jerk reactions against polygyny are from people who can't add up. In a society with equal numbers of men and women, each man with four wives gives women the additional pick of three men—the poor saps whose potential wives decided they'd prefer one-quarter of a billionaire instead. In the Sahel region of Africa, half of all women live in polygynous households. The other half have a good choice of men and a lot more bargaining power.
Hmm, but doesn't history say that women in polygamous societies get a raw deal? Has there ever been a polygamous society where men treated women like equals? Jane Galt opines that "polygamy is only a stable social institution as long as one gender is pretty radically oppressed," and I don't have any good counter-examples.
So is the economic argument wrong? I doubt it, and there is a simple way to resolve the paradox. Consider this:
1. Widespread automobile ownership drives up the price of gas.
2. Automobile ownership is most widespread in places with cheap gas.
It's not much of a paradox. Yes, automobile ownership makes gas more expensive than it would otherwise be - it shifts demand up. But automobile ownership rises when gas is cheaper - when supply is high.
The same goes for polygamy. All else equal, polygamy raises the demand for women. But you're most likely to see polygamy arise in places where the supply of women is high relative to demand. To take an extreme example, if half the male population dies in a war, the price of women is going to be low. This encourages polygamy, which partially mitigates the damage for women.
The upshot, of course, is that legalizing polygamy in modern Western societies would probably have very little effect, because women here are too expensive to make it affordable.