Here is the math on several scenarios:
The present average world TFR is 2.75 and decreasing, albeit far too slowly. Blame it on male machismo, or female feminista, religion, stupidity, culture, habit, or just that a third of births are accidental. It is understanding the math and a wide variety of depletion/pollution data to come to future probabilities.
(If)The population must go down fast enough to prevent a mass die-off event. The maximum food and water for humans that the planet can produce in 2050 will be at least a third less than today and possibly even less than half. The cumulative effects of AGW, soil losses, water losses, and oil loss/huge expense, will take a heavy toll on yields, along with oceanic fisheries collapse. If people start to compost more and grow and buy locally more, it will be on the low end. Business as usual until then will be the high end of crop and water loss. The population will be close to 9 billion living on enough food for only 3.5-4.7 billion.
(1) If there was some great leader who could say, and people obey, that we need a moratorium an having kids for 20 years, then the natural death rate would reduce the population by at least 50 million per year. Let's say 60 million per year reduction with almost no births. In 10 years it would reduce .6 billion, in 20 it would reduce 1.2 billion. Then one child families would keep the reduction rate at 20 million per year, so by 2050 there would be roughly 5.4 billion in a world that can only support 4.7 billion in the best case. So 700 million would starve or die of thirst, rather than 8 billion over a period of 20 years or so.
That is if there was such an edict and new morality and it started immediately. That is about the best mitigation we can hope for.
(2) Let us say it was an instant going to one child families with education and free forms of birth control and changes to social systems to provide for the disabled and elderly. Then 38 years of 20 million per year net drop would be 6.3 billion in a world that can support a max of 4.7 billion. There would be more deaths from starvation, 1.6 billion in a short period, and a greater chance of warfare over resources.
(3)Still, it would be better than the crash of 8 billion or more in around 20 years, in similar fashion to Easter Island 1150 AD. Warfare, theft, cannibalism, diseases, starvation, all too fast to even bury the remains. Even if the crash were "gentler" and the reduction took 50 years, it would include most of the births in that period, maybe 2 billion more humans, total. The bottom will be at most a billion left, and probably less than half that. These will survive increasingly grimly until thermal maximum.
(4, 5, 6, or 7?)There are other things that could happen to increase death rate. People could "push the buttons" for nuclear war, or manufacture an airborne very deadly disease and spread it. Possibility, maybe remote. Another is a natural event, like a super volcano eruption. Yellowstone could save the planet if it blew soon enough, but it still looks at least 2,000 years from now or so, too late. Earth isn't due for a giant meteor strike for 13 million years(if you go for the Nemesis theory), but it is possible a very large one could hit and also save the biosphere.
Before every action and decision think of the consequences 7 generations into the future....Ute Rule of Life