Global hegemony could, first of all, be about leadership in the world economy: doing the right thing at home, coordinating the actions of your friends, restoring growth to the Transatlantic economies.
Or, alternatively, it could be about representing the world’s peoples, one person one vote as in any electoral democracy — to elevate the sum total of good for humanity:
(Graphic is from Kenneth Myers. The Valeriepieris Circle. May 2013.)
Sometimes these two do not coincide.
Draw a circle 4,000km in radius around Hainan Island in the South China Sea. The land area carved out is only 25 mn sq km, or one-sixth of the world’s total land area. More people, however, live within that circle than outside. The world’s median voter? Here’s where she lives.