It does not make sense to discuss income disparity without discussing production disparity. Consider the production disparity between Steve Jobs and the average blue-collar worker. Consider the vast difference in contribution to society and markets made by the two of them.

If you wish to reduce income disparity, you will necessarily have to reduce production disparity - for the former is generally the consequence of the latter in a market economy. Competition for productive resources will drive the price paid for those resources ever higher (encouraging production and ensuring that such production falls upon the most efficient utilizer of such production).

So, unless you can get the productiveness of the blue collar workers raised to the level of Steve Jobs, you will instead have to reduce the productiveness of Steve Jobs down toward the blue collar worker.

Income disparity will diminish to the extent society moves toward universal impoverishment.