This is a very difficult case to make because it relies solely on conjecture. We cannot provide any evidence to actually prove that a feminist perspective (if indeed there is such a thing) would solve the world’s problems. This school of thought relies on the idea that there is a perspective that is uniquely female and that it would ease tensions in international relations. The only way to “prove” this is to point at specific situations in the world and argue that women would treat them differently.
For example, let us look at the situation with Japan and China and the Senkaku/Diaoyu Islands. In this dispute, both countries are stridently claiming sovereignty over the islands and their surroundings. We can argue that this is based on the masculine idea that the world can be divided into things that are “mine” and things that are not “mine.” We can also argue that this dispute is based masculine tendencies to be aggressive and to abhor the idea of backing off when challenged.
We could make the same argument about the 2003 war in Iraq. We can argue that President Bush pursued the war largely out of his masculine ego. We can say that a woman would have been more willing to back down from her original pro-war stance when she saw that the evidence was lacking.
The problem with all of this is that is based on conjecture and there is no way ever to prove that our arguments are correct.