If it turns out the only solution to climate change is depopulation as research is starting to point to, would a volunteer service or a random lottery be more humane?
Depopulation will come naturally, as the global population ages. The best solution is to have global governments fund low-income countries, most importantly in good education so that people will have children at an older age and the birth rate will naturally decline. Give a generation or two, and the population will decline, as we have seen in China.