That's a rather odd ideology. In the books it's quite funny. Egwene, his childhood sweetheart talks to her best friend Elayne, saying she doesn't want to marry him anymore, Elayne say she loves him and they engineer a 'transfer' of him. Elayne and Rand continue to have a normal relationship after that. Elayne is close friends with Aviendha at this point, and they later have an Aiel ceremony to become adopted sisters. Min really likes him, and confides in Elayne and Eqwene. Rand walks in on Aviendha taking a bath, she freaks out and makes a portal (being an Aiel wise one who wields the one power) to Tremalking and he follows her and finds her nearly freezing to death. They end up sleeping together. Later, when all four are in Andor, he confesses that he loves them all, and he thinks badly of himself for it. They sort it out and have him bonded as all of their warders. He later sleeps with Elayne who becomes pregnant with twins.