Abstract: The long-term global goal for emission reductions under negotiation stirs up the dispute between countries on how this increasingly scarce atmospheric resource should be equitably shared in the world. Developing countries advocate for the philosophy of equal or converging per-capita cumulative emission rights over time. Four operational definitions of per-capita cumulative emissions dealing with the changing populations were presented and interpreted by means of mathematical expressions, which thereby derived four possible emission rights allocating options. Simulation results and comparative analysis demonstrate that the Option 1# always deviates from the assumed global emission path, the “population freezing” Option 4# does not hold water to freeze the actually changing populations, while the Option 2# and 3# both make sense.