The government should stay out of the private lives of citizens. There is nothing inherently anti-social about polygamy and so leave it alone!
The lawsuit is not demanding that states recognize polygamous marriage. Instead, the lawsuit builds on a 2003 United States Supreme Court decision, Lawrence v. Texas, which struck down state sodomy laws as unconstitutional intrusions on the “intimate conduct” of consenting adults. It will ask the federal courts to tell states that they cannot punish polygamists for their own “intimate conduct” so long as they are not breaking other laws, like those regarding child abuse, incest or seeking multiple marriage licenses.
LINK: http://www.slate.com/blogs/xx_factor/2011/07/12/kody_brown_of_sister_wives_is_challenging_utah_polygamy_law.html?wpisrc=obinsite