Imagine, that you have a 3 sided dice. This way the population is stable.
Yet, your parents have probably more children than you will have. You will have 1, 2 or 3 (p=1/3 for each case) − 2 on average.
But since you are alive, it is only 1⁄6 that your parents have 1 child, 1⁄3 that they have 2 and 1⁄2 that they have 3. It looks like you will have smaller number of children than your parents. Most probably.
A small modification of the initial post and there is no population growth or decline.
Imagine, that you have a 3 sided dice. This way the population is stable.
Yet, your parents have probably more children than you will have. You will have 1, 2 or 3 (p=1/3 for each case) − 2 on average.
But since you are alive, it is only 1⁄6 that your parents have 1 child, 1⁄3 that they have 2 and 1⁄2 that they have 3. It looks like you will have smaller number of children than your parents. Most probably.
A small modification of the initial post and there is no population growth or decline.
Yes, this was an example I considered, too, but it does not seem to highlight the problem with under-sampling of the low-sibling families as much.
A side note. In the real world, on average, one HAS less children than his parents. Parents can’t have zero children, a child can.
Both are true, but the former doesn’t follow from the latter. In particular, I suspect the former was false a few decades ago.
Indeed, this self-selection is the reason that the SIA Doomsday is a bad prediction.