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Kevin Trudeau has made a fortune with his idea. He wrote that the New York Times ran a article stating that super low calories can lead to a longer lifespan. Only the Times was reporting on the belief that some people think a diet of 1200 calories a day can increase your lifespan, and Trudeau was talking about 500 calories a day.
If eating 500 calories a day doesn’t thin out the herd, nothing will.
Put every man, woman, and child (OK, maybe not child) in a paper bag. Make a combination lock the only means of egress.
I don’t think sterilization would be completely off the table. Just start adding contraceptives to the water supply along with the fluoride.
The small percentage that are off the reservation and not drinking the adulterated water should be adequate for breeding stock to kick start a brighter new generation.
Have celebrities be seen drinking pennyroyal tea.
I’ll see your quack and raise you full insanity: Breatharianism
Nah, combination locks are dead-easy to spring. Make it a Rubrik’s Cube. 
Better: Add contraceptive drugs to all junk foods. Don’t screw up the water supply.
You know the Nazi’s also assumed they were inherently superior to everyone else.
Not if they’re drawn on with a crayon.
I’d start *two *religions, and let the problem solve itself.
No No No…
I remember a story like the OP and the sent people off in rockets to their death. Not viable.
However…say that a new continent or dimension with a new earth was discovered and it is GREAT! Get people to go there (an island or an area faked as a new Earth). Treat them well and have them write home. After some time, kill em.
People hear all the rumors about how it is great and they will clamor to come. Since they as a population are getting dumber (say average IQ of 75 instead of 100) they won’t think too deeply about it. After it takes off one could possbily kill new immigrants right away and come up with a story that life is so great there that they forget about the old Earth.
One could get rid of a good chunk of unskeptical people like that.
At least they had a grasp of what the apostrophe was for, so they had that going for them.