The state's interest in marriage is stability. Generally speaking polygamy does not work for stability. Inherent in the whole polygamous movement is a deep and abiding misogyny and denigration of women. So polygamy is objectionable on lots of grounds.
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Instead I think over the years we have cut the strength of marriage and relationships by the law and weakened the institution. We have tried to deal with relationships with no-fault divorce with child custody with so many other avenues and it has not helped.