Sexism in Reincarnation

There seems to be the idea in reincarnation that one can become human or animal in their next life. This allows for many options of existence. A curious instance is that the Dalai Lama has never reincarnated into a woman. The question is whether the Dalai Lama chooses to be reborn as a man or whether society plays a role in the decision of the new Dalai Lama. I don't think it really matters if the Dalai Lama is male or female but it is curious to think that they have always been male. I believe that people would have a hard time believing that the powerful ruler had reformed as a woman, women not being very respected until recent. I think that this would lead people to believe that when you are reincarnated your sex remains as part of your soul. I disagree. For the Dalai Lama to continuously reincarnate into a man there must be some pretty slim odds otherwise there's another force coming into play.