I think that it should be man and woman, ruling in complete equal authority, ensuring balance. I think its this lack of balance that has had the word so completely screwed up over the past 2000-3000 years. Let me explain.
Not seeking to piss anyone off, but the major three religions Christianity, Islam and Judaism are religions which women were relegated to a second-class system, where they were seen as inferior. The christian religion was created by Peter, a reknowned chauvinist, woman-hater and suspected homosexual as something of an 'all-boys club'. To this day, in hardline Catholicism, women are still not allowed to enter the priesthood, and are probably seen as inferior by the priest. The same with Islam, with veils and perda, and with orthodox Judaism. This notion spread to politics, and to every facet of life. Now, as these religions spread, so too did the notion of female inferiority. Before the arrival of Christianity to what is now the United Kingdom, pagan life was such that balance was the key to life; balance with nature, and balance between the sexes. Man and woman were completely equal, and each tribe would be ruled jointly by male and female, and the high druid priest would be countered by a high druid priestess. It is shown in ancient documents and other forms of archaeology that by the time the pagan religion was firmly established, the ancient Celts were relatively peaceful, and that if either sex made a decision unliked by the opposite, the opposite could counter it, and try to bring around the other party to see reason, and thus balance was ensured. This was also reflected in the fact that the old pre-Christian Irish laws allowed women equal status in property rights, rights of leadership etc etc. When Christianity came to Ireland, the Irish lost these rights. Funny that since this, Ireland has been a continual hot-bed of strife, as it is too male dominated - male aggression is not countered by any real female logic or deterrence.
This is also reflected in the state of the world today - most politicians, and most heads of state are male. Even those females who do become heads of state do not rule as women, but try to rule as men. Look at Margaret Thatcher, or Elizabeth I of 'I may have the body of a weak and feeble woman, but I have the mind and heart of a true man and king' (or an approximation of this).
I think what we need is not a patriachal or matriachal system of governance in the world, but a system of joint governance, in which male and female both co-rule a state. That way, we could see that if each balances the other off, whether there is a greater chance of balance and logic in world diplomacy and leadership. But first, the old religiously based notions of male superiority need to be removed.