We really have quite a long way to go on this front.
I'm sure your vagueness is really slowing down the investigative arm of law enforcement that normally goes around searching the internet for evidence of dastardly polys.
Bigamy requires being officially married whilst already being officially married. The state already has records, by definition.
Let's not bring up the argument of legislating for maximal gene propagation, unless you're willing to ban all forms of marriage that don't serve maximal gene propagation. Fertility tests before marriage! No marriage among the elderly, because what's the point! Let's set up a new 3-letter agency for matchmaking!
Marriage is not a government mechanism to encourage mating. Stop trying to put government in the business of animal husbandry. We're not animals.
And this doesn't already happen? M/Dating does not require marriage.
I think we have yet to see all the consequences of this cultural change.
I made that argument to a couple of friends - that they were not fighting for equality (which will be fairly easy to set up) but for inclusion in the privileged club. They responded with "Well marriage is between couples, but defining the sex of the participants is discriminatory".
One of the problems with polygamy/andry is that we could hollow out the lower social classes of mating opportunities (it happens in india and china right now due to girl infanticide and it is not pretty).
Anyway - congratulations to the winners.