Now I want to know what's the probability of any two women in that world having the same sperm donor. I hope someone smarter than me comes along and figures it out.
We have the ratio, but it's still depend of the number of sperm donor in a city and their semen's quality, because some donors may have a better sperm count than the others men. Also, we need to consider the average age of the inhabitants and the total fertility rate.
For the males population, we need to substract the boys under 16 and men with a low sperm count or infertile (see chapter 19), and elders if they hit andropause or the sperm quality drop drastically. So arbitrarly, we can assume only half of them are in capacity to be a donor.
In the end, the less donor there are, the higher the chances for children from different mother to share the same father.
Besides, in this world, men gave their sperm once a month (chapter 19), so 12 times a year minimum but they can do it once week at most (chapter 28) for a maximum of 52 times a year which increase the chances further if the difference in sperm quality or the number of sperm donation between donors differ greatly.
Dunno, if I'm clear because I've spent too much time to write this and it gave me a headache
Edit : I've forgotten to say, if the number of donors stays the same then the more children different women have, the more chances they have to share the same father. Example, if two women have 1 child each, the probability is low but if they have 3 each, then the probability increase a little. Now imagine 10 donors with the same sperm quality for 390 mothers who end with 3 children each
