I thought I'd start a discussion on this forum asking what problems they have, or why they're in favour of any of the above relationship boundaries (or there, a lack of).

I'm going to take them to mean:
Monogamy-1-1 based relationship because of not wanting your partner to be with anyone else either romance wise or sexual wise.
Polygamy-giving your partner more sexual freedom but not wanting them to have love based relationships with others.
Polyamory-only allowing sexual relationships with others to occur when there's a romance there.
Open-fully sexually liberal in the sense of letting your partner getting on with it (excluding if it goes against others wishes in cases such as rape, and some bestiality) as well as allowing for other emotional bonds to being formed.

Personally I enjoy the idea of an open relationship the most. I view monogamy as something incredibly limited and I hate the possessive sides I've seen of it whilst in monogamous based relationships.

However if you're in favour of monogamy because you don't feel you have the time, or your partner has the time, to make new loved based relationships, I would label that, as time is the only factor prohibiting anything more than that, as in stead polyamory/polygamoy/open (depending on the implications of having more time to play with).

Furthermore as a pre-warning. Do not refer to polyamory or polygamoy, or an open relationship as cheating without explaining why it is cheating. Cheating implies a broken contract, and appears to only be applicable in very certain situations in polygamy and polyamory, and many more in monogamy.

If there's already a thread about this feel free to redirect me (I searched but couldn't find one).
If you have any corrections to what I've put please feel free to make them (I've categorised things in a certain way to help differentiate between different concepts).