poly + open overlap, neither is a subset
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Theory question really, but is open a variant on poly or a completely different class of relationship?
Poly can be a different class of relationship, for those who do not start from being a couple.
Open relationships tend to mean that a couple decide to allow extra partners beyond the traditional idea of exclusivity.
The things that define polyamory, for me, are
1. Honesty: every partner knows who else you are being sexual/romantic with
2. Integrity: if you make committments to your partners, you keep them. (This could include, for example, the quite common committent about safe sex: I will have safe sex except when I am with certain named people -- google 'fluid boundary' about this)
3. All sexual relationships contain an element of love. For me, relationships where partners are free to have non-loving partners are swinging. Relationships where partners are free to do either are poly/swinging.
I currently consider 1 and 2 above to be the aspects of poly that make it ethical, whereas 3 is more a personal preference. So I have moral issues with 'cheating', but not with 'swinging', even though I would not personally do either.
The things that define 'open' for me are that a partner is free to have sex with other people, outside the defined relationship.
So a triad, where all three people have loving sex with the other two, but have no sex or romantic attachments outside the triad, would be poly but not open. So I disagree with M, who says above [not quoted] that poly is a subset of open.
A relationship where two people had a long term loving relationship and they also had casual sex outside the couple, would be open but not poly.
It often looks like poly is a subset of open, as in our culture it tends to start from opening up a couple: in practice M is often right. But in theory, as per your question, there is no need to start from there.
My preference is for poly relationships, as per the above definitions. I would like to make it clear I am not putting a moral case here; I am stating my own preference, and no more than that.