It's not going to work. Even in a perfectly open society, people won't have sex with just anyone. They will choose their partners. This means value judgement which implies hierarchies which establishes power structures. Inequality is inherent. There will be highly promiscuous people at the top and involuntary celibates at the bottom.
This is roughly how actual polyamorous dating pools work. If anything, the bottom of the distribution has a more difficult time in polyamorous settings.
