I think polygamy has sometimes followed wars, when males became scarce. In any event, sex has an obvious biological purpose, which can be served in polygamy, but not in homosexuality. Just because two people have an unnatural urge to imitate intercourse with a person lacking the wrong plumbing, it does not mean that society has to allow them to imitate marriage.
But polygamous behavior also precedes wars...as when it is prescribed by the values of the prevailing norms such as those allowed by the religion such as with Mormonism and Mohamadenism.