Many times, I've heard it said that Chinese families prefer to have a boy child over a girl child.  Supposedly, this has created a population imbalance in some areas where there are now more boys than girls.  However, the more I think about it, the preference for boys alone cannot create this imbalance.  I will use numbers in thousands for my example, but the numbers could be millions or single digits.  The math is the same.  Let's assume that 16,000 couples have children (ignoring the chance of twins which goes by the same rules of random selection).  Those couples each have one child, 8,000 boys, 8,000 girls.

For the next generation, the families with boys have no more children.  The total at this point is even, 8,000 of each gender.  Now, the 8,000 sets of parents with girls want to have another child.  They have 4,000 boys and 4,000 girls, again an even match.  But how are the overall numbers.  Are they unbalanced?  No!

8,000 families have one boy. 4,000 families have two girls (for a total of 8,000 girls), 4,000 families have one boy and one girl. The totals? 12,000 boys, 12,000 girls.  The next generation?  All families with any boys stop having children.  4,000 families have two girls.  So they have one more child, 2,000 boys and 2,000 girls.  The total now stands at 14,000 boys and 14,000 girls.  The families with three girls at this point want to have a boy.  So, 2,000 families with three girls have a four child, 1,000 boys and 1,000 girls.  No matter how far you run the numbers, they are still balanced, now, 15,000 boys and 15,000 girls.

So, how could any imbalance have occurred?  One likely source of an imbalance is the active de-selection girls.  How could this occur?  If parents are allowed to know the gender of a child before birth, and end a pregnancy based solely on gender, then the numbers could become unbalance.  However, based on the above analysis and numbers, you cannot blame any imbalance on families with even four girls and no boys.  Why?  Those four (or 4,000) girls resulted from 8 (or 8,000) pregnancies that had half boys and half girls.  You can't get an imbalance when every individual birth is the result of a single random boy/girl chance.  The imbalance has to come from a different source.