The women can bring whoever they want to the event, provided they are responsible for how their guests behave. They only give three to four parties a year, however. Everybody invited must RSVP, so I can track total size and gender balance. Single men are encouraged to RSVP early. The gender balance matter is very rigidly enforced in the Swingers world.
Parties are usually open only to couples and single women.
Men must arrive with or after their female companions, and depart with or before she leaves. They were not having much fun, and I haven't done that again. Some allow post-ops. In general, I'm quite satisfied with how I handle the gender balance issue. Furthermore, because the women on my list know they won't be overwhelmed by men if they attend, they generally feel very comfortable coming to a party or social.