The only valid argument against it is the tax code. How does a marriage of 3 file taxes? How are the assets divided if the 3 divorce? How are the assets divided if one of the 3 wants to leave the marriage but the other two want to stay together? How is custody handled? In nations that allow income splitting on their income taxes, is it fair to allow income splitting in a polygamous marriage? Gay marriage is easy enough because you aren't changing anything. Polygamous marriage requires a major re-think of the tax code. The logistics are much more complex.