How many first born children are there?

This video from Harvard philosopher Professor Michael Sandel talks about Justice. What is a fair start in life? How should you think about fairness?

He asks his students about their start at Harvard. How did they get there? Was it privilege or hard work? After most of them agree they had some privilege, but maintain it was their hard work, he asks them to raise their hand if they were the first born child in their family (23:16). It’s hard to see exactly, but well more than half of the class raised their hands. I’m guessing 75%.

Interestingly, though, the proportion of children who are first born is probably more than you expect. You’re thinking that the average family has two children. So 50% of children should be first born, right?

But in fact if there is any variety in family size beyond that, the proportion of first born children goes up. So if the average family has two children, but that is made up of 40% single child families, 40% two child families, and 20% three children or more, the proportion of first borns in the population goes up to 65%.

I can play with the numbers to get that proportion of first borns up to nearly 70%, without changing the average family size. Another of the many examples of counterintuitive statistics can be.