[AnotherUnixGeek]

The problem with poligamy is that after 3 generations, you have a 50% chance of marrying a cousin. Poligamy shuts some many men out of the gene pool: they are driven out of the community, and can lead to severe genetic problems in a population. (Hence, the Mormons) This is called "Founder's Syndrome", where a recessive genenetic problem gets spread throughout a community.

This assumes a closed community in which everyone is practicing polygamy or polyandry. I think it's safe to assume that if they were legalized, they would not be practiced by the overwhelming majority of the population, due to the various emotional, legal, and financial issues involved.

And obviously, those closed communities which do currently practice polygamy (radical offshoots of Mormonism, I guess) can not be allowed to exert any coercion on young women, nor can they be allowed to drive off underage boys - whether polygamy is legal or not. Many of the arguments against polygamy seem to involve the coercion and child abuse found in the Mormon offshoot communities - these things are already illegal and would remain so.

[Campion]

nor can they be allowed to drive off underage boys

Any society where most women are in polygamous marriages necessarily ends up with a large surplus of males. Unless they're killed as infants or in utero, or they're killed in warfare as teenagers or young adults, or there's a non-polygamous society available outside to absorb them, they become a socially corrosive force.

For example, they might end up flying airplanes into tall buildings.