Given the chance, the voters choose women. Really?

Politicalbetting.com has a novel reason for predicting a Royal victory in the French Presidential elections. He says that her gender may be critical:

Just looking at the countries of the world that have had women leaders, the UK, Germany, Ireland, New Zealand, Iceland, Sri Lanka - to name but a few, the female contenders have won the first time their electorates have had the chance of voting for a woman.

What about Kim Campbell?