In what you say, there is a postulate that a common intuition will be found that will grow and lead to convergence. In one sense it is an observation. You just meet hundreds of people who see the world like this and there are many occasions when people acted in this direction. So putting this together gives you the idea that there is a chance for such a development. On the other hand, it is also a hope that such a movement will bring the social contract in time.
Nobody can prove that.
The outcome could be quite different. We might not be able to come to reasonable world-wide agreements with a result that the world community will have to pay the high price of hundreds of thousands of people starving The market place is increasingly geared to short term gains rather than such considerations as a social contract. Will the intuition of a large number of individuals be suficient to change the course of society against the driving force of the market place. We have the wrong global market structure. We don't have a global market order.