As far as the second definition goes, I don't see a problem with it, as long as the electorate wants it. There would need to be a proper framework put into place governing the various rights -- it's not quite so simple as with two people. When the husband dies, for example, in a monogamous relationship, there's no danger of squabbling among the wives.
Yes, there are genuine problems here unforeseen by the drafters of laws mentioning marriage. For instance, I could marry everyone named in my will and evade inheritance tax. On the other hand, if everyone is financially dependent on the one breadwinner, it seems moral to ensure they're all provided for. Tricky stuff.
Now, personally, do I have a problem with polygamy? I'm not sure.
I guess i've got a nagging feeling that polygamy is more likely to be coercive and unconsenting than monogamy, but that might just stem from unfamiliarity -- I'm sure people who knew no gay couples (back in the day when gays were very much an underground culture) would have said the same about gay partnerships.
I think there's a cost/benefit thing going on here: it seems implausible that we'll ever have a definitive list of
all types of consensual human sexuality, but even in the face of that unattainability it makes sense to design our mechanisms of state to encompass the most common cases. Monogamous gays were obviously missing from earlier mechanisms of state; but the way I've never heard of a polygamy rights movement (outside Utah) says to me that there's not as much inequality there to be rectified.
It'd be interesting to get some viewpoints from countries where polygamous marriage is more widespread or traditional: India? South Africa? At least some polygynous traditions have a notion of "the primary wife", which could tidy up some of the legal rights issues.
Peter