Relax the condition that prevents person A from marrying person C if A is already married to B. This allows A, B, and C to marry one another, or allows A and B to both marry C but not one another, as they choose.
Most legal practices related to marriage won't be altered by this.
Some will -- the practices that assume that "A's spouse" uniquely identifies a single individual -- and those practices will have to change. For example, if the law says that in cases where A dies intestate then A's spouse inherits, then the law will have to either be modified or a canonical interpretation arrived at to handle the case where "A's spouse" is more than one person.
I agree that this adds some complexity to the law.
For example, one relatively braindead way to do this is to assert that for those laws, "A's spouse" is understood to refer to their spouse with the longest tenure. (aka "senior spouse")
The tenure/seniority rule does seem to be a shaky one. Anyways, I'm not claiming that these are unsolvable, merely that "legalize poly marriage" is insufficiently specified, and there's several tunable parameters that need to be tuned.
You propose for marriage to be non transitive. That's fine, but then that does lead to other things like how tax/insurance/etc should work. (One possibility would be that joint filing benefits be completely separated from marriage and instead work like this: Anyone is allowed to jointly file with ONE other person.)
T...
A thought occurred to me today as I skimmed an article in a rationality forum where the subject of gay marriage cropped up; seeing as the issue has been hotly contested in various public fora and especially the courts, what about poly? After all, many if not all the arguments for gay marriage apply to poly marriage as well.
Questions for LWers who are currently in a such a relationship, or have an opinion to share:
Do polies want to marry each other or do such relationships not lend themselves to permanence above a threshold of partners? Should polies campaign for the right for a civil union anyway? what are the up and down sides of this? etc