Polygyny?

Tony H asks:

Your procreation argument for heterosexual marriage is consistent with polygyny, so if it is sound, it may rule out homosexual marriages, but be of great use to defending polygynists since it maximizes procreation and the perpetuation of the state quantitatively. What is the state's interest in monogamy?

I was afraid my argument could be misinterpreted as promoting increased procreation.  But I took no stand on that.  My argument does not "maximize procreation." It says nothing about whether there should be more procreation or less.  Here is what I wrote: "The state has a legitimate interest in its own perpetuation  and maintenance via the production of children, their socializing, their protection, and their transformation into productive citizens who will contribute to the common good."  Let me break that down paratactically.

We collectively need some offspring; they need to be socialized and instructed in the rudiments of our culture; they need to be protected; they need to be educated to the point where they can function as productive citizens.  No one of those coordinate clauses, or their logical conjunction, entails that levels of procreation should be increased, let alone that the state should have a hand in such an increase.

Is my argument logically consistent with countenancing polygyny?  I suppose it is as it stands; but that is only because my argument was restricted to only one aspect of this multi-faceted issue.  I was just assuming that marriage is dyadic in order to focus on the question of why the state shouuld recognize opposite-sexed dyadic unions but not same-sexed dyadic unions.   The issue of the 'adicity' of marital and quasi-marital unions was not on the table.  One cannot talk about everything at once.

Why should the state have an interest in monogamy over polygamy (whether polyandry or polygyny)?  I have no answer to that at the moment.  I have only started thinking hard about these questions recently and I have an open mind on them.

As a conservative, I of course subscribe to the quite general principle that there is a defeasible presumption in favor of traditional ways of doing things.  But I am open to the possibility that the presumption in favor of traditional marriage (dyadic, between humans only, permanent, exclusive, opposite-sexed, open to procreation) can be defeated.  For while I am a conservative, I am also a philosopher, and you can't be a philosopher (in the strict sense!) if you simply assume dogmatically this or that.

I should also add that I play for a draw, not for a win.  It sufficies to 'neutralize' the liberal-left arguments.  All I have to do is show that they are not compelling.  I don't have to refute them.  There are precious few refutations in philosophy, and none of them pertain to 'hairy' issues like same-sex 'marriage.'