2) Investment capital needs to flow to the poor.
3) Transportation infrastructure needs to connect the poor.
4) An international commitment from the richer countries to distribute part of its wealth to the poor countries on a sustained manner.
I will limit my thoughts to new ideas and focus more on the assistance for poor countries, rather than the poor within a given country. There are existing mechanisms which have certain effect already, whether they are based on free market principles, or based on existing charitable incentives. In order to make a substantial reversal on the trend towards increasing wealth disparity, we need new mechanisms.
On the flow of additional investment capital to the poor countries, free market principles automatically discriminate against countries with little natural resources to exploit, and low education levels. So, for those countries which are lacking natural resources or education, what can we do to help them?
One way is to set up a peer to peer capital investment mechanism. Each person who is willing to participate will set up an automatic electronic payment commitment to distribute his/her "investment" into a global pool. Each person or enterprise in a poor country can register with this global pool to automatically receive "investment" into a trust account, from which it can draw money to finance its business plan. The pre-requisite is to post a business plan with the global pool for approval in a peer review process. The NGO which shall operate this global pool will use the peer reviews to give a rating to each business plan, together with a rating for each country as to its degree of poverty, lack of natural resources, and education level. These rankings will be used to distribute the collected global pool of "investment" to the applicants in the poor countries. Variations of this distribution process can be considered, e.g., to actually match investors with the applicants, so that they become holders of shares in the applicant companies. This would empower a personal relationship between investors and entrepreneurs and would in fact enable a network of supporters for the entrepreneurs.
Transportation infrastructure requires large investment, so for poor countries, financial such infrastructures themselves is impossible at the beginning of their economic development. International investment or loans are necessary. A really "crazy" idea is to have a global agreement to allow the developed countries to print new money in proportion to the size of their economies so as to raise the necessary amount of new investment capital to put into the poor countries. This method is akin to diluting the wealth of the developed countries so as to transfer part of their diluted wealth to the poor countries, as investment. The money is not wasted because the developed countries get some of it back as contracts to build the transportation infrastructures.
In fact, carrying this idea of financing to the general case, this dilution of wealth by the developed countries could be a new international commitment by the richer countries to transfer every year a portion of their wealth to the poorer countries in a sustained manner. An equitable formula can be agreed by all the developed countries, based on their GDP, for example, and the recipient countries would be allocated payments based on their level of poverty, lack of natural resources and education level.
No new taxes need to be raised in the richer countries. Money is not coming out of anyone's pockets. Any subsequent devaluation of a rich country's currency will likely be minimum, as every rich country's currency is proportionally affected. The free market will take care of balancing them to account for other differences in the rich countries.
Perhaps this idea is not so crazy after all?