If the world already contains more than 7 billion people. If supporting resources are contracting at 3-6% a year, then, by the end of this century, not more than 50 million people can live at European lifestyles (sans cars and planes) (a, b, c).

There are other populations and lifestyles that could result from this reduction in supporting resources. If we let nature have her way, through conflict and starvation, earth's population could be a billion people living like 17th century peasants. Civilization's death throes could degrade the environment so these peasants would be trapped and unable to rebuild a high-tech civilization.

However if we, in a stroke of human ingenuity, find another way to rapidly reduce population to 50 million by the end of this century, so the human footprint stays under the declining supporting resources we could retain a civilization with present technology, current potential for advancement, and move to less conflict and more equity.

Some might suggest just killing most of the population justifies the difference in outcome. However, I suggest that there is a number of annual births that: accomplishes this population reduction, balances consumption with supporting resources, and then holds the population constant at a sustainable level. That number is half a million. I have proposed a birth lottery to distribute these birth permits among the present population.

Leaving to another discussion how we conflate the current global civilization into three engineered cities totaling 50 million this century, and the why and how we put the lottery in place, this discussion describes who pays the price caused by the lottery’s limits on births. Who is injured because the lottery did not allow him or her to have all the children he or she desired.

What follows shows who is injured, calculates their numbers, and describes the time table of their injuries.

There are two time periods when the lottery causes no injuries.
      1) before the lottery is implemented, and
      2) after the total global population is so low (50 million) that
            the available lottery tickets don't limit most of the world's individual's
                  from attaining their birth choices.
Let me describe how the second time period is possible.

Half a million birth permits is enough to replace the oldest cohort (~half million in size) in the 50 million population. While this is known as replacement fertility, this does not mean that each women must have two children - one to replace herself and one to replace her mate. It means all the children that all women have this year must add up to the lost cohort — half a million. It means, for every women that has less than 2 children during her lifetime, some woman must have more than 2 children. Any imbalance would cause population change.

Let me give one example of a distribution of these births in a high tech, high education, high wellbeing civilization:
            1/3 of the women choose no children
            1/3 choose one child.
            1/3 choose 2 or more.
In this example, the average number of births in the "2 or more" group (to achieve replacement) would be 5 -- two of their own, plus -- two from the "no child group," plus -- one from the "one child" group.

Again this does not mean that every woman in the third group has five. It means for every woman that has less than 5 some woman must have more than 5. Now assume in the natural world a woman will want some number of children between 0 and 8. So it is possible that:
      If: ==> there are women in the third group that want only 2 children
      then: ==> there can be women in the third group that have eight.
If the distribution of the half million lottery tickets allows every woman to birth their choice of children then the lottery produces no injury.

Actually the lottery produces "no injury" long before the total population drops to 50 million circa ~2100. The injury stops when the fertile portion of the world's population matches the fertile portion of an equally distributed 50 million person population. This happens in the 35th year of the lottery. Let me explain:  
      Today, there are 7 billion people.
      3.5 billion of them are women.
      Half are over the age of fertility and cannot be injured by the lottery
      1.7 billion are fertile or will be fertile during the next 35 years.
      After 35 years they will all be infertile.
      The fertile women in the population in 2050 will be 35 cohorts
            (one quarter of million each) that were allowed by the lottery.
      This number and distribution of fertile woman is the same as that in
             the above 50 million person population.
Thus the injuries resulting from the lottery stop accruing in the 35th year.

Now let's add up the injuries that accrue in those 35 years. The half a million lottery permits annually will allow 1 woman in ~140 women to have a desired baby in the first year.  This means if this percentage held for 35 years more than 99% will be injured by a lottery. This injury percentage does decline over 35 years but never gets below 99%. So we can conclude that almost all of the 1.7 billion will be injured.

Thus the total injury caused by the lottery (all happening in a 35 year period) is 1.7 billion women, (or 1.7 million families) who will not have children.

1.7 billion childless couples is the injury number we have to compare with the injury number produced by humankind's current course. These injuries come in two forms.
      1) 5-8 billion people starving to death and dying in conflict during this century.
      2) beginning in the 22nd century a global population of a billion, lives low tech
            lives with little medicine, education, metal tools, using mostly animal power,
                  instead of electricity, … forever.

Can your tell if our present course or the lottery produces more injury?