I don't know. It depends on how common it would be. The more common, the more single male losers out there. This has an impact on their happiness of course, but also social stability; I'd bet that rape would increase for example.
Polygamy is the topic of the week on the Becker-Posner blog. Here's Becker. Here's Posner.
Posner should be a hero of mine and I take what he says seriously, but I can't help it, I just don't like him.