I believe that the reincarnated spirit of Lews Therin's love was somehow split into three different pieces(Min, Aveindha, and Elayne). This would explain why each woman loves Rand and why Rand loves each one equally even though he has only had brief 90210ish contacts with each of them. On a side note I really think Rand has gone crazy for giving up Lanfear. If the sexiest woman in the world was bonkers over me and had a scheme to destroy the Dark One thereby helping my cause, you know I'd take it. Rand was crazier than a drunken Mydraal stumbling through the White Tower when he passed her offer up. :)