Ask and you shall receive:

The idea is that if women think that most or all of their kids will probably survive ('because of vaccines' or whatever), they will be less inclined to have as many kids as possible.  They will (and do) point to the 'developed world' as an example of this phenomenon.

The idea has enough merit to study.  For my part I'm not going to reject it as absurd, but nor am I going to latch onto it as obvious.  It's an idea worth studying in observation and in theory.

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For my part, I believe strongly that vaccines are causing vastly more harm than good and the very reason for having kids in the first place is that they grow up to be capable people.  If they are vaccine damaged in high numbers then you get right back to needing a shit-load of kids in the hopes that one of them has a functional enough brain to raise a family and has some left-over resources to help you in your old age.

I also believe fairly strongly that the 'simple' interpretation of what Gates said (through his disgusting smirk) is the accurate one.  Vaccines will kill a ton of people, and make the rest into a kind of Idiocracy which is easy to control and which poses zero threat to the rich and powerful.