He [Roberts] ignores the fact that polygamy imposes real costs, by reducing the number of marriageable women. Suppose a society contains 100 men and 100 women, but the five wealthiest men have a total of 50 wives. That leaves 95 men to compete for only 50 marriageable women….
Sterile people are not forbidden to marry, though by definition they do not procreate.
Posner's latter argument seems to be an appeal to exceptions. Some opposite-sex couples are sterile, so an ability to procreate can't be a requirement for marriage. (I address that objection, as well as some of Posner's other arguments, here.)
But there are exceptions to his polygamy argument. A bisexual polygamist (and, remember, there is a B in LGBTQ) could marry one member of the same sex and two of the opposite sex, thereby keeping a balance among the sexes. Since Posner's argument isn't applicable to all polygamous marriages, does that mean we should reject it? Shouldn't Posner at least allow polygamous marriages that maintain a balance among the sexes, thus meaning that he's only arguing against some forms of polygamy rather than polygamy itself? And what about a potential imbalance among the sexes created by same-sex marriage?
Similarly, shouldn't we reject the argument some advocates of same-sex marriage use against incestuous marriage, to the effect that incestuous marriage can produce genetic defects in children? Some incestuous couples are sterile, after all.
There doesn't seem to be much concern for consistency on these matters among advocates of same-sex marriage. Their concern for consistency is also lacking in other contexts (e.g., their acceptance of practices like opening government sessions with prayer while raising the "theocracy" objection to religious arguments against same-sex marriage, as Posner speciously does).